Precise liquid transport on and through thin porous materials

Subscriber access provided by UNIV OF NEW ENGLAND ARMIDALE

Article

Precise liquid transport on and through thin porous materials Souvick Chatterjee, Pallab Sinha Mahapatra, Ali Ibrahim, Ranjan Ganguly, Lisha Yu, Richard Dodge, and Constantine M Megaridis Langmuir, Just Accepted Manuscript • DOI: 10.1021/acs.langmuir.7b04093 • Publication Date (Web): 29 Jan 2018 Downloaded from http://pubs.acs.org on January 31, 2018

Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a free service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are accessible to all readers and citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.

Langmuir is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

Page 1 of 29 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

Precise liquid transport on and through thin porous materials Souvick Chatterjee1, Pallab Sinha Mahapatra1, 2, Ali Ibrahim1, Ranjan Ganguly3, Lisha Yu4, Richard Dodge4 and Constantine Megaridis1* 1

Department of Mechanical and Industrial Engineering, University of Illinois at Chicago, Chicago, IL 60607-7022, USA 2 3

4

Department of Mechanical Engineering, IIT Madras, Chennai 600036, India

Department of Power Engineering, Jadavpur University, Kolkata 700098, India

Corporate Research and Engineering, Kimberly-Clark Corporation, Neenah, WI 54956, USA *e-mail: [email protected]

Abstract Porous substrates have the ability to transport liquids not only laterally on their open surfaces, but also transversally through their thickness. Directionality of the fluid transport can be achieved through spatial wettability patterning of these substrates. Different designs of wettability patterning are implemented herein to attain different schemes (modes) of three-dimensional transport in a high density paper towel, which acts as thin porous matrix directing the fluid. All schemes feature precise transport of metered liquid microvolumes (dispensed as droplets) on the surface and through the substrate. One selected mode features lateral fluid transport along the bottom surface of the substrate with the top surface remaining dry, except at the initial droplet dispension point. This configuration is investigated in further detail, and an analytical model is developed to predict the temporal variation of the penetrating drop shape. The analysis and respective measurements agree within the experimental error limits, thus confirming the model’s ability to account for the main transport mechanisms.

Keywords: Thin fibrous material; Directional liquid transport; Wettability patterning; Capillary-driven flow; Surface and bulk flow; Droplet, Porous substrate

ACS Paragon Plus Environment

Langmuir 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 2 of 29

1. Introduction Liquid transport using wettability-patterned surfaces is an applicative field with immense importance in several engineering domains – ranging from heat pipes

1

to propellant management devices for

spacecraft 2, soil science 3, personal hygiene products 4 and filtration 5. Applications in all these fields rely on the passive transport (i.e., liquid movement without external energy supply) of liquid on the surface as well as through the bulk of the porous medium. Development of facile techniques of fabricating materials with different porosity and surface wettability, combined with advancements in harnessing open-surface flows for microfluidic devices, have led to the possibility of incorporating such flows in lowcost, point-of-care (POC) biomedical diagnostics 6. Tuning material wettability spatially to control liquidsolid interaction towards specific microfluidic tasks is relevant not only to impervious substrates (rigid or flexible), but also porous and fibrous substances. Several studies have been conducted to characterize the roles of surface wettability and bulk properties (e.g., porosity, wicking property, etc.) of the porous structure on fluid transport. Wang et al.

7

demonstrated unidirectional fluid transport using a special

coating technique that created a wettability gradient along the thickness of the fibrous substrate through selectively-different exposure levels of ultraviolet (UV) radiation. The concept was extended for selective permeation of three different fluids (water, soybean oil and hexadecane) by Zhou et al. 8 who further characterized the depth of penetration of the fluid using 3D-micro computed-tomography (CT). The operation of such porous membrane, fabric or paper, featuring wettability gradients is dependent on the penetration resistance through such materials; this resistance arises from the coupling effect of local geometric angle of adjacent fibers and solid–liquid contact angle 9. The critical breakthrough resistance to overcome for ensuring liquid penetration can be increased by reducing the spacing between the fibers or by increasing the wettability gradient along the thickness direction 9. A sheet of porous material, coated on one or both sides, would exhibit unidirectional liquid transport across it, provided the penetration pressure to transport fluid from one side to the other is much greater than the pressure required to force fluid in the reverse direction. Mates et al. showed that the penetration pressure required to transport liquid across such a coated substrate from the hydrophilic to the hydrophobic side significantly exceeds that for a reverse flow [10]. Zhou et al.

8

also observed that,

while such wettability-engineered fabrics displayed unidirectional transport to liquids of higher surface tension (29 – 50 mN/m), they allowed liquids of lower surface tension (< 29 mN/m) to equally permeate both ways. This phenomenon has been harnessed for separating oil/water mixtures 10-11. Diverse use of such “liquid diode” systems, using different material systems and fabrication procedures, has been shown in other studies 12-14. The aforementioned capability of one-way oil transport has been extended 2 ACS Paragon Plus Environment

Page 3 of 29 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

to cotton fabrics by Li et al. 15 who used TiO2 coatings on cotton that exhibited contact angle (CA) larger than 160° and sliding angle below 5°. Porous materials with spatially-varying wettability have been used in fog harvesting 16 and measuring liquid surface tension 17. Control of porosity and wettability allows to create complex structures, which provide directional transport useful in fields such as drug delivery, biosensors, etc. 18-19. Functioning of these paper- or fiber-based devices rely largely on how the porous substrate regulates liquid flow in a preferred direction, while inhibiting the same in the reverse direction. Porous materials that are made of intrinsically-hydrophilic materials have the inherent ability to transport liquid using the wicking principle 20. When such a porous material rendered hydrophobic in a spatially selective manner, leaving narrow regions of hydrophilic patches, guided transport through directional wicking is achieved 21

. Such transport has been shown to have useful applications for fabricating low cost, disposable

diagnostic devices 22-23. The concept has been extended to 3D devices with complex microfluidic paths, devices known as µPADs 24. These works focus on constant-width surface tension confined tracks. These substrates transport liquid both laterally (along the surface) as well as through the surface. Wang et al. 25

demonstrated that paper-based substrates using capillary action can transport liquid at steady flow

rates in the range of 0.3 µl/s to 1.7 µl/s. They also showed transport of common biofluids, like urine, serum and blood in such mode, underscoring their scope for biomedical diagnostic applications. Threads with good wicking property and flexibility in such fibrous systems can also be useful in low-cost microfluidic diagnostics and biological assays

26-27

. These threads can integrate the directional wicking

nature of absorbent substrates with the established textile manufacturing techniques, such as automatic weaving, knotting and stitching. Hence, these hybrid systems can be used for classical fluid mechanics tasks, like mixing and separation

28-29

. Xing et al.

30

showed three-dimensional transport on micro-

patterned superhydrophobic textiles (MST) in autonomous, controllable and continuous fashion. A wetting contrast was created by stitching hydrophilic yarns in hydrophobic textiles. Transport on such fibrous assemblies created microfluidic, cloth-based, analytical devices devices having functional capabilities like bio-sensing and drug delivery

31-33

; microfluidic wearable

34-35

have attracted much

attention in recent years due to the ever-increasing demands in the areas of fitness and healthcare 36. Paper-based microfluidic devices offer a promising tool for low-cost, POC diagnostics 22. These are made of paper or fabric materials that easily wick liquids – capillary forces generated by the porous substrate enable liquid transport without an external pump. The biomedical sector has been a prime user of such paper-based substrates 37-39 because of their low-cost, simple fabrication and passive mode of transport. A crucial segment in this area is fabrication of microfluidic sensors, which are used to 3 ACS Paragon Plus Environment

Langmuir 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 4 of 29

transduce physical quantity into measureable electrical signals. Research has been focused on developing different types of paper/fiber based microfluidic transducers, such as pH sensors electrochemical

42

sensors

.

Surfaces

treated

with

45-46

and

cytophilic/cytophobic

(superhydrophilic/superhydrophobic) chemicals have been shown to detect cancer cells bacteria

40-41

43-44

and

. In wound healing, accumulation of wound fluid might lead to bacterial overgrowth

47

.

Wettability-patterned porous substrates can be used as an ideal dressing material that can directionally transport and absorb wound fluid and maintain the sensitive surface dry. Thus, biological applications are a great arena for wettability-patterned porous surfaces. Li et al.

48

published an exhaustive review

article in 2012 summarizing prior studies on such paper-based devices and their possible applications and future trends. Recent surveys clearly indicate a rising interest 49 on market potential of such paperbased systems 50. Classically, interaction of liquids with air and solid has been investigated as a rich three-phase contact line problem 51. Surfaces with rendered domains of hydrophobicity or hydrophilicity create wettability patterns which provide useful applications for open-surface fluid transport 52. Water droplet transport on superhydrophobic grooves using external forces, like gravity or electrostatic forces, has been shown by Mertaniemi et al. 53. Microfluidic paths where water was confined and transported by surface tension alone (a.k.a. surface-tension confined tracks) possessed the ability to pumplessly transport low surface tension liquids without an external force 54. Khoo et al. 55 introduced the idea of high-speed transport on a solid surface through the use of triangularly-patterned, wettable tracks on superhydrophobic substrates, prepared through elaborate micropatterning and nanotexturing methods. Such triangular patterns harnessing pressure gradient due to curvature of liquid are observed in cactus spines which are shown to be efficient fog collector systems56-57. In Nature, directional water collection from air is also exhibited by spider silk using a unique fiber structure as is shown by Zheng et al.58 The concept was further explored by Ghosh et al.

59

to achieve pumpless rapid transport on a wide range of substrates,

from metals to polymers, by using a facile fabrication technique of spraying a fluoro-polymer nanocomposite and ultraviolet radiation through a photo mask. The Laplace pressure-driven transport of liquid on the wettability-confined tracks surpassed the Washburn speed, the typical transport speed encountered in capillary wicking or hemiwicking flows. Ghosh et al. 59 also demonstrated complex liquid manipulation tasks, like liquid merging, splitting, metered dispensing and even transport against gravity, using different shapes of wettable patterns on superhydrophobic backgrounds on versatile substrates. The transport speed for a wedge-track design is well characterized in a recently accepted manuscript for different types of fluids

60

. A linear relation is observed between the liquid front and time which is 4 ACS Paragon Plus Environment

Page 5 of 29 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

double the Washburn speed. Higher liquid volumes of ~1L/min can also be transported by this design on fibrous substrates as has been shown by Sen et al.61 Chen et al.

62

demonstrated a fluidic diode and a

delay valve that offered directional liquid permeation in two-dimensional plane of a paper-based substrate. As highlighted in the foregoing sections, several designs have been attempted to attain controlled, unidirectional liquid transport either on the surface or through the thickness of fibrous substrates. However, combining these two modes of unidirectional transport has not been explored to date. Here, we examine transport of metered volumes of liquid on paper-based permeable substrates. We demonstrate controlled liquid manipulation with simultaneous deployment of rapid, horizontal transport on the surface along with permeation in desired regions of a paper towel using different designs of wettability-confined tracks. Our designs, which feature different wettability contrast patterns, can be applied on any substrate (paper/nonwovens), as long as there is transverse permeability (i.e. matrix wettability). The main substrate is a high density paper towel (HDPT), chosen because of its widespread use and homogeneity in porosity. The methodology discussed in this work uses directional transport in a unique way, which provides more control over the diodic nature of coated porous substrates. The present fabrication process is facile and scalable. Moreover, different design modules can be realized with minor modifications, lending flexibility in the liquid-handling capability of the device. We integrate wettability features to increase water transport rates on different fundamental design modules. Further, we develop a semi-analytical model to explain droplet penetration through a porous sheet and explore how that is affected by a wettability-confined wedge-shaped track on the surface directly underneath. The results expand the foundation for liquid manipulation strategies in paper and fabric-based microfluidic devices, wearable healthcare and personal hygiene products.

2. Materials and methods 2.1 Substrate preparation with wettability contrast A facile patterning technique, based on our previous approach of wettability patterning on solid impermeable surfaces 59, was adopted. High-density paper towel of 300 µm thickness (Kleenex Hard Roll Towel 50606, 38 GSM, Kimberly-Clark) was used as the porous substrate. HDPT samples of size 4 cm x 9 cm were coated with a hydrophobic nanocomposite matrix of titanium (IV) dioxide nanoparticles (anatase, < 25nm, 99.7% trace, Sigma Aldrich) dispersed in a water-soluble fluoroacrylic copolymer (PMC; Capstone® ST-100, 20 wt. % in water; DuPont). A typical nanocomposite dispersion was formed

5 ACS Paragon Plus Environment

Langmuir 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

by first suspending 1.5 g of TiO2 in 14 g of ethanol by probe sonication (for 1000 J energy input at 750 W, 13mm probe diameter, 40% amplitude, 20 kHz frequency, Sonics and Materials Inc., Model VCX-750), and then by adding 2.5 g of PMC and shaking mechanically at room temperature. The nanocomposite suspension was spray-deposited using an airbrush (Paasche, 30 PSI) on one or both sides of the HDPT samples. The uniformly-coated samples were then air-dried in an oven (Model 10GC; Quincy Lab, Inc.) at 80oC for 2 hrs, when they turned superhydrophobic (CA ~ 153 ±3o; Contact Angle Hysteresis ~ 5o; See Fig. 1A). Superhydrophilic patterns were laid on one or both surfaces (depending on the design) of the HDPT by selectively exposing the coated substrate to UV radiation (Dymax 5000 EC, 400 W, 390 nm UV Source) through a photomask (a PET film with printed black negative patterns using an office laserjet printer) for ~60 minutes (see Fig. 1B). UV light that passed through the transparent (unprinted) sections of the mask struck the coated superhydrophobic substrate, rendering the exposed areas superhydrophilic (CA < 5 o) 63. Exposure to UV does not alter physical texture as is well known in the literature 64. For the Janus surfaces (superhydrophobic on one side and superhydrophilic on the other side) used in this work, both sides of the sample were first coated superhydrophobic, and then one side was exposed to UV to render it superhydrophilic. The fiber distribution and the pores in the fiber mesh were observed via scanning electron microscopy. As seen in Fig. 1C, high-aspect ratio fibers with width ranging from 10 – 50 µm lay in an inter-woven manner on a planar matrix, which is dotted with pores of varying diameter and orientation.


Page 6 of 29

Page 7 of 29 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

Figure 1: (Color online) Schematic of the substrate preparation process. (A) Spraying of TiO2-PMC dispersion on HDPT using an airbrush; (B) Selective UV treatment of the coated HDPT sample using a PET photomask; (C) Typical SEM of HDPT substrate.

2.2 Surface characterization Liquid permeability of the spray-coated and wettability-patterned HDPT substrates was determined by a custom-made hydrohead measurement apparatus

10

(see Fig. 2). The sample substrate (a circular

substrate with diameter 1 cm) is mounted at one end of the hydrohead tube in a water-tight fashion and the height of the water column in the hydrohead tube is increased until the water shows the first sign of penetration across the substrate. The liquid, after coming in contact with the porous material, needs to overcome a penetration pressure to emerge at the air-side (Fig. 2 inset). The hydrohead H, quantifying the penetration pressure required for achieving z-directional transport across the paper towel, is shown in Fig. 2. Substrates requiring lower penetration pressure allow easier fluid permeation. By rendering the porous substrate superhydrophobic, it can be made to withstand a finite hydrostatic pressure before the liquid starts penetrating across its thickness to the absorbent side. The hydrohead H 7 ACS Paragon Plus Environment

Langmuir 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

depends on whether the superhydrophobic dispersion is sprayed on one or both sides of the substrate. Figure 2 shows the hydrohead measurement (H) for four different coating configurations of the HDPT. When both sides of the HDPT sample are coated superhydrophobic, the required penetration pressure is the greatest, as observed in the topmost data point in Fig. 2 (case A). For samples that have one side superhydrophobic, and the other side superhydrophilic (through UV exposure on the entire surface), the hydrohead depends on the orientation of the coated side in the hydrohead setup. In the arrangement where the water in the hydrohead column encounters the superhydrophobic coating first, penetration to the other side occurs at a lower H (case C) compared to that when the liquid encounters the superhydrophilic side first (case B). For the surface treatment protocol described in Section 2.1, the hydrohead data for cases A, B and C are 762.3 N/m2 (7.8 cm ± 0.33 cm), 357.8 N/m2 (3.65 cm ± 0.3 cm) and 62.2 N/m2 (0.95 cm ± 0.13 cm), respectively. When both sides of the substrate are superhydrophilic, the penetration pressure is zero (Case D).

Figure 2: (Color online) Hydrostatic pressures (hydrohead) required for water-column penetration through HDPT samples with different coating configurations; A: Both air and water sides of the HDPT are coated superhydrophobic; B: Air side of HDPT is coated superhydrophobic, water side is superhydrophilic; C: Air side is superhydrophilic and water side is superhydrophobic; D: Both air and water sides are superhydrophilic. Inset shows the hydrohead measurement setup, as in [4].


Page 8 of 29

Page 9 of 29 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

2.3 Experimental Each HDPT substrate was mounted horizontally between a stationary and a movable clamp; the substrates were rendered taut by applying slight tension via the movable clamp, which was mounted on a rack and pinion assembly as shown in Fig. 3. In order to synchronously image both the side and top views using a single camera, a mirror was placed over the HDPT at 45° angle with respect to the substrate. Droplets were dispensed from a syringe and each event was recorded using a DSLR camera (Canon EOS Rebel T5i) at 30 frames per second.

Figure 3: (Color online) Schematic of experimental setup. A single camera is used to capture simultaneously the side view (direct view) and the top view (in the 45o inclined mirror) during each experiment.

2.4 Numerical In order to develop a theoretical expression of the overall liquid transport (comprising of permeation across the HDPT thickness and transport on the top and bottom surfaces of the sample), we first need to evaluate the Laplace pressure inside the curved liquid volumes formed at either side of the sample, as the fluid was dispensed on the superhydrophobic coating or accumulated on the wettability-confined domains. Since the liquid permeation rate through the HDPT is much slower than the Laplace pressuredriven free-surface flow on the HDPT (as we shall see later in Section 3.2), the overall transport is restricted primarily by the top-to-bottom liquid permeation rate. Therefore, a quasi-static 9 ACS Paragon Plus Environment

Langmuir 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 10 of 29

approximation has been adopted for the liquid pools accumulated on the wettability-confined regions of the HDPT. For spherically-shaped droplets, the Laplace pressure has been obtained analytically

65

.

However, evaluation of Laplace pressure for more complicated liquid shapes, viz., those on the wettability-confined regions underneath the HDPT, warranted a numerical solution, which implemented an open source surface energy-minimization software, Surface Evolver - Fluid Interface Tool SE-FIT 66. SEFIT computes the shape of a given volume of liquid so as to minimize the total energy (due to surface tension and other conservative force fields, e.g., gravitational force, electrostatic force, etc.) using a gradient descent method 67. In SE-FIT, the initial condition of the liquid pool is rendered in the form of a block of a given volume of the liquid (equal to the dispensed volume), deposited on the narrow end of the superhydrophilic track underneath the HDPT. After successful convergence of the iterative procedure, the liquid evolves into a steady shape, which exhibits minimum energy. In order to validate the SE-FIT simulations, the Laplace pressure in hemispherical liquid droplets of different volumes collected on a circular wettability-confined area on the substrate was estimated by SE-FIT and compared with analytical results (details in Supplementary Information). After validation, spreading events of water droplets on different designs of superhydrophilic tracks (elaborated in Section 3.1) on superhydrophobic background were studied. The gravity effect was incorporated in these simulations; gravity acted in an outward normal direction from the wedge track. Grid- (or number of facets) independence checks of the numerical implementation were also performed. In SE-FIT, facets are used to approximate the surface. Hence, using the “refinement feature,” the number of facets can −

gradually be increased from ∼104 to ∼1.2×105 until the converged normalized energy difference ( E ) between the finally-chosen grid and the previous (coarser) grid fell below ∼10-4. The normalized energy −

difference is E =

| En+1 − En | , where E denotes the total energy of the liquid on the wedge. The grid | En |

independent SE-FIT solution was used to estimate the Laplace pressure in the liquid volumes on the wettable tracks of the substrate.


Page 11 of 29 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

Figure 4: (Color online) (A) When a water droplet is dispensed on the superhydrophobic-coated, top side of the HDPT sample, the liquid penetrates after a few seconds and spreads radially on the superhydrophilic bottom surface. If the dispensed volume exceeds a critical value, the penetrating liquid drips from the bottom without any lateral shift. (B) Liquid transport with wettability-patterned HDPT substrates, coated superhydrophobic on both sides and superhydrophilic domains (wedge track, end reservoir) on the top and/or bottom surfaces; three different design configurations are shown: (i) Case I: superhydrophilic wedge track laid on the bottom surface. (ii) Case II: superhydrophilic wedge track patterned at the topside and superhydrophilic, circular reservoir patterned at the bottom aligned with the top-side reservoir. (iii) Case III: superhydrophilic wedge tracks with end reservoirs patterned on both top and bottom surfaces with perfect alignment.

3. Results and discussion 3.1 Design configurations Our study intends to demonstrate improved flexibility in manipulating liquid using wettabilitypatterned HDPT substrates by directionally transporting the liquid in three dimensions, namely, along the surface (x-y plane in Fig. 4A), as well as across the thickness of the porous substrate (z in Fig. 4A). The wettability contrast between the superhydrophobic and superhydrophilic domains, and the shapes of the wettability-confined tracks on the substrate control the liquid transport on the open surface. We seek designs where a known liquid volume, dispensed at one point on the substrate, comes out the other side with a lateral shift, i.e., at a distance offset from the original point of injection. For a HDPT substrate with a superhydrophobic top and superhydrophilic bottom (achieved by uniform UV exposure


Langmuir 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

at the bottom face of the substrate without a photomask), a liquid droplet dispensed atop the substrate first penetrates to the bottom surface and radially wicks underneath, as shown in Fig. 4A. This mode of liquid transport is akin to the “passing” mode (Case C in Fig. 2) of the fluid diode, as also discussed by Mates et al.10 As expected, directional lateral transport of the liquid is not achieved in this case. Although the liquid permeates down through the HDPT and spreads radially outward through fibers at the lower surface, it emerges right on the underside of the dispensing location, eventually pinching off in the form of dropping droplets upon adequately large supply from the top (about 52 µL). More complex transport modes are observed using the design configurations shown in Fig. 4B, where superhydrophilic tracks are laid on the top, bottom or both surfaces of the HDPT substrate. The wedge-shaped wettable tracks offer a sharp wettability contrast, so that liquid dispensed (or accumulated due to permeation from the other side of the substrate) remains confined within the wettability contrast lines. The resulting curvature of the wettability-confined liquid meniscus creates a Laplace pressure gradient along the length of the tracks, leading to a rapid, planar, unidirectional transport of the liquid from the narrower to the wider end of the track 59. Thus, the vertical, directional (akin to a liquid diode 10) penetration of the liquid to the other side of the HDPT is coupled with rapid, directional (laterally guided 59) transport along the wedge-shaped track, as driven by Laplace pressure gradients 59. Three different design configurations, discussed in Fig. 4B, exhibit different rates at which liquid is transported horizontally and vertically. The vertical transport is dependent on the z-direction penetration pressure, whereas the lateral (x-y) transport is governed by the Laplace pressure gradient formed from the curvature of the liquid/gas interface. In Case I, the superhydrophilic wedge track is laid at the bottom surface; a wide circular superhydrophilic region (end reservoir), is also laid at the end of the wedge track to facilitate liquid accumulation and disposal (by pinch-off after sufficient accumulation at that location). In Cases II and III, a superhydrophilic wedge track (with superhydrophilic reservoir at its wider end) is laid on the top superhydrophobic surface, whereas the bottom surface is rendered superhydrophilic at different regions (Fig. 4B). For Case II, the bottom is made superhydrophilic only under the circular end reservoir. In Case III, the bottom surface has a superhydrophilic wedge track and an end reservoir aligned with those on the top surface. In all present cases, the wedge design used to demonstrate the flow behavior has fixed length (8 cm), wedge angle (4o) and narrow-end width (5 mm). These values were designated based on prior experience with Laplace driven transport along such wettability-confined wedge tracks 59.


Page 12 of 29

Page 13 of 29 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

3.2 Flow behavior The liquid transport mechanisms in the lateral (x-y) and z-directions are different for each case of Fig. 4B. The wedge-track transports the liquid laterally to the end reservoir; for a wedge-track in the lower surface of the HDPT, the accumulated liquid hangs in the form of a pendant drop, eventually detaching from the substrate when the weight of the accumulated liquid exceeds the retaining surface tension force. Dripping of liquid from the bottom reservoir is observed in all cases of Fig. 4B, but the design designates the exact timing and outcome, as elucidated by the different time stamps after drop deposition in Fig. 5 and Supplementary Movies 1, 2 and 3. Besides the permeation through the HDPT, we identified three intermittent qualitative events of liquid transport on the surface between deposition and pinch off: A) wicking/wetting of the track, B) liquid accumulation at the bottom reservoir, and C) first pinch-off of liquid from the bottom reservoir. Initially, for a fixed volume of dispensed liquid, we observed both A and B, but the liquid volume was not high enough to cause pinch-off. Therefore, additional liquid was deposited to attain pinch-off. We compared this additional volume required for liquid pinch-off for the three Cases I, II and III. All uncertainties listed below have been calculated over three experiments conducted with identical protocols. •

In Case I, the liquid was deposited dropwise (1.6 µL per drop) on the superhydrophobic top of the sample over the narrow end of the wettable track laid underneath; the configuration is akin to Case C in Fig. 2, where the resistance to permeation is low (62.2 ± 12.7 N/m2). At first, when 16 µL of water were deposited atop the sample, the initial Laplace pressure inside the deposited volume (assuming that all water stayed atop, forming a droplet of radius r∼1.56 mm, thus pd = 2σ/r ≈ 89.6 N/m2, where σ is the surface tension of water) exceeded the permeation hydrohead for this substrate configuration. Thus, the liquid started penetrating through the paper at the dispensing point, but the imbibition rate was very small due to the flow resistance of the porous HDPT matrix. Underneath the substrate, at the narrower end of the hydrophilic wedge-track (Fig. 5A1), the liquid experiences a Laplace pressure gradient59, which transports the fluid to the wider end of the track (Fig. 5A2). The narrow end of the track showed no liquid build-up in this process, which indicates that the transport was limited by the liquid permeation rate through the HDPT, and not by the lateral transport on the wedge track underneath the sample. As the liquid droplet penetrates from the top to the bottom surface, the track propels the fluid to the reservoir end and forms a hanging droplet there. Figure 5(A3), which shows the liquid accumulation at ∼22s, reveals that the dispensed droplet volume (16 µL) is not enough to cause 13 ACS Paragon Plus Environment

Langmuir 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

dripping at the reservoir end. Hence, an additional 16 µL was dispensed at the same location at the top. The added liquid followed the same path from top to bottom and along the track laterally to the reservoir end, until the first pinch-off occurred after 80±3 s (Fig. 5A4, uncertainty based on 3 runs performed with the same protocol). •

In Case II, the same liquid volume (16 µL) is dispensed dropwise on the superhydrophilic track over the superhydrophobic bottom surface – a configuration similar to Case B in Fig. 2 – which presents a higher penetration resistance (357.8 ± 29.8 N/m2) than the Laplace pressure in this volume (89.6 N/m2). Therefore, unlike Case I, the liquid cannot penetrate down across the HDPT at the point of deposition. Instead, the liquid transports laterally along the superhydrophilic wedge track to the end reservoir (Fig. 5B1), which has hydrophilic surfaces at both top and bottom, thus offering negligible resistance (c.f., case D in Fig. 2). There, the liquid easily penetrates to the bottom side, where it accumulates and hangs off from the bottom reservoir. The liquid traversed to the reservoir very fast (∼5 ±1 s after dispension of the first droplet), see Fig. 5B2. The vertical penetration at the end of the track happened much faster than in Case I, primarily due to the negligible penetration resistance and also because of the much larger footprint of wettable passage for permeation (the end reservoir has much larger footprint than the deposited droplet). The liquid accumulated at the bottom side reservoir in 8 ±1 s (Fig. 5B3), indicating that the entire transport process occurred faster than in Case I. The fluid holding capacity within the fibrous substrate in this configuration is larger because of the two aligned superhydrophilic reservoirs. Therefore, the first pinch-off in this case required a larger volume of liquid (36.8 µL total) to be deposited compared to Case I (32 µL). Ultimately, in Case II, the first pinch-off occurred at ∼43 ± 2 s after the first deposition (Fig. 5B4).

•

In Case III, both the top and bottom surfaces had superhydrophilic wedge tracks aligned with each other (akin to Case D of Fig 2, which again offers negligible penetration resistance). Once deposited on the narrow end of the top track (Fig. 5C1), the liquid (16 µL) was transported to the wider end as a film (Fig. 5C2). At the same time, the liquid penetrated in the vertical direction through the thickness of the substrate. The transport times in this configuration are similar to Case II, as seen in Fig. 5C3. However, since the superhydrophilic area coverage is maximum in this case, higher volume (24 µL over and above the initial deposit of 16 µL, for 40 µL total) was required to be deposited for the liquid to pinch-off from the bottom end reservoir (Fig. 5C4).


Page 14 of 29

Page 15 of 29 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

Figure 5: (Color online) Vertical (permeation) and transverse transports and pinch-off of liquid in a superhydrophobic-coated HDPT for the three wettability design configurations described in Fig. 4B. The top views are observed synchronously with the side views through the mirror inclined at 45o. Case I: Vertical permeation followed by lateral transport; Case II: Lateral transport followed by vertical permeation; Case III: Lateral transport of liquid occurs as a film through the thickness of the substrate. Snapshots of distinct intermittent events with time stamps leading to pinch-off are shown for the different configurations.


Langmuir 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Figure 6: (Color online) (A) Synchronous top and side views of a dispensed droplet in Case I. Water droplets (3 µl) are dispensed over the left end of the wedge where they penetrate to the opposite (bottom) side. Temporal variation of radius (r) and height (h) are measured from these images. Scale bar denotes 5 mm. (B) Schematic side and bottom views near the liquid deposition point for Case I, marking the droplet Laplace pressure (pd) and back pressure (pb) caused by liquid confinement on the track laid on the bottom surface. The liquid permeates through the substrate to the superhydrophilic backside of the substrate (bottom view) and forms a film, spreading over the superhydrophilic wedge track (to the right). SHPB indicates the superhydrophobic region.

3.3 Case I drop penetration: Comparison with model Case I in Figs. 4 and 5 describes a complex and interesting transport process – the liquid first permeates in the vertical direction at the dispensing point and then gets transported laterally along the wettable track at the underside of the sample. This mechanism helps to maintain the top surface (where the liquid is first deposited) dry, which is important for several Point of Care (POC) applications. For example, such transport, if envisaged in bandages would help maintain the oozing, body-contact points of bandages dry – the liquid can be transported across the fabric to the outer side and away from the point of injury68. A similar strategy can also be adopted to deliver water soluble drugs to the wound location from an outer dispensing location on the bandage69. Because of the practical relevance of Case I, we developed a mathematical model for predicting the liquid transport rate. We validated this model


Page 16 of 29

Page 17 of 29 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

not only against the type of transport described in Section 3.2 and tracks featuring different wedge angles. As explained earlier for Case I, when liquid is dispensed atop the sample on the opposite side of the narrow end of the wedge track, it first forms a droplet on the superhydrophobic substrate; this droplet gradually permeates through the substrate as the Laplace pressure inside the curved liquid/gas interface exceeds the required hydrohead (Case C in Fig. 2). Once the drop emerges at the narrow end of the track on the bottom surface, the fluid gets laterally transported to the wider end driven by the Laplace pressure gradient on the track 59. When the liquid penetrates the substrate, the time varying radius (r) and height (h) of the droplet atop the surface are measured from the top and side views respectively, as shown in Fig. 6A. As shown in Fig. 6B, the Laplace pressure inside the droplet (pd = 2σ/r) assists the liquid permeation. The permeated liquid develops a film on the wettability-confined track at the underside of the substrate; the curvature of this liquid meniscus gives rise to another Laplace pressure, which now resists the downward liquid transport. We term this opposing pressure as back pressure (pb). Since the liquid volumes at both sides change over time due to the liquid transport (described in Fig. 6B), both pd and pb also vary with time. The pressure differential

∆P ( t ) = pd ( t ) − pb ( t )

(1)

at any instant provides the net driving force for permeation of the liquid through the porous HDPT substrate. The effect of gravity on estimating the pressure pd inside the droplet has been neglected here; this assumption is valid when the droplet equivalent diameter is near or below the capillary length of the water (2.7 mm). Thus, all comparisons between the model and experiments were made for initial droplet diameters near 3mm or below. Even when the initial droplet size exceeded the capillary limit (thus making the effect of gravity non-negligible, as in some cases with α=2o), the liquid penetration into the porous matrix caused drop size reduction, bringing it into the capillary regime. Following Darcy’s law 70

, the instantaneous flow rate (

) of the drop penetrating the porous substrate is related to the

pressure differential via

(2) where k, A, µ and L denote, respectively, the permeability of the porous substrate, the cross-sectional area for the permeating flow ( A = π ri2 , where ri is the initial footprint radius of the droplet obtained


Langmuir 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 18 of 29

from the side view), the viscosity of the liquid, and the thickness of the substrate. The volume V of the droplet atop the substrate is modeled as a spherical cap (an assumption supported by the volume being in the capillary regime) and hence is a function of radius r and height h (see Fig. 6A), both of which are time dependent because the droplet is gradually permeating through the substrate. Thus, Eq. 2 can be expressed as

(3)

where K =

kA is a constant that depends on material and geometric properties of the system. Porosity µL

of the substrate at the location of the permeating fluid may differ from the intrinsic porosity (85.5 %) of the uncoated substrate, since (i) the TiO2 polymer coating may have changed the effective pore diameter, and (ii) the liquid infusion might have altered porosity due to swelling of the paper fibers 71. Therefore, the value of K was evaluated from a separate experiment considering a simpler configuration (where pb = 0), as described in Supplementary Information 2.

Figure 7: (Color online) Temporal variation of droplet radius (atop the substrate) for six separate dispensing events, each with different initial volume. Colored circles of different size indicate the different initial radius of the droplets. The colored vertical lines mark the start of each curve, with all curves following the same trend r(t).


Page 19 of 29 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

The temporal size variation of each droplet dispensed atop the HDPT was monitored for different initial droplet volumes. As seen from Fig. 7, the radius reduction (due to liquid permeation) follows the same temporal curve irrespective of initial radius. This confirms the experimental consistency in measuring the radius change with time from the experimental images. It is important to note, however, that droplets with r >1.5mm in Fig. 7 are affected by gravity, as they exceed the capillary limit. On the other hand, when the droplets get small enough (due to mass loss through their base), they operate in the capillary regime and gravity effects are then negligible. Because of the complex shape of the liquid on the wedge track under the sample, the back pressure pb cannot be computed analytically. Instead, we estimate this back pressure numerically, using SE-FIT 66. It was verified earlier that the liquid spreads much faster on the track at the bottom surface than it permeates through the thickness of HDPT. Thus, the temporally developing liquid volume on the back surface may well be represented by a sequence of quasi-static liquid pool of monotonically increasing volumes. This assumption allows evaluation of the liquid meniscus shapes at this location, and the corresponding values of pb by using the SE-FIT simulations for different volumes (VW) of liquid pool on the wedge-track. Since VW is the total volume of liquid that has traversed from the top side of the sample at any time t from the moment of dispension (t=0) and before pinch-off, then

(4)

under the assumption that the liquid volume retained in the fibrous material is negligible. In Case I described in Sections 3.1 and 3.2, we used tracks of wedge angle α = 4o. For a given length of track, α has been found to influence the Laplace pressure gradient and the resulting liquid transport along the wedge track 59. To evaluate the performance of the Case I design, we used tracks of different wedge angles. The temporal variation of pb in Eq. (3) will, therefore, not only depend on the instantaneous VW , but also on α (see Supplementary Information for details). It is noted that the SE-FIT calculations included the effect of gravity, as the fluid volume accumulated under the substrate had dimension well above the capillary limit. Based on the above analysis and the simulation results, we used the following algorithm for comparing the experimental results with the model predictions:


Langmuir 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

•

We measure

dr ( t ) dt

and

dh ( t ) dt

Page 20 of 29

from experiments (Figure S3 in Supplementary Information)

with an HDPT substrate with superhydrophobic top and superhydrophilic bottom (see Fig. S2 in Supplementary Information). The experimental results were used to estimate the permeability parameter K using Eq. 3 with pb=0. The process is described in detail in the Supplementary Information. The permeability value (6×10-10 m2) thus obtained was used for other cases with a wedge on the bottom surface. •

We obtain a database of the back pressure for different VW (fluid volume hanging from the sample) and α from a series of SE-FIT simulations. Reckoning that the instantaneous volume V(t) of the liquid atop the substrate is related to VW and the initially dispensed liquid volume Vi by

()

()

V t =Vi −VW t

(5)

The empirical correlation for pb in terms of VW and α as drawn in the Supplementary Information (Eq. E6) may be expressed as

1 pb = 6.62[Vi − π h 2 (t ) r (t ) − π h3 (t )]0.48 α −1.06 3

(6)

Substituting this expression of the back pressure in the right hand side of Eq. 3, a differential equation of the following form ensues 0.48      σ dr(t)  dh 2 1 2 2 3 −1.06   π h (t) + 2π r(t)h(t) − π h (t) = −K + K 6.62Vi − π h (t)r(t) − π h (t) α  (7) dt  dt 3 r(t)     2

which is solved numerically for r(t) in Mathematica using the experimentally-observed values of h(t) and dh(t ) , the latter as estimated from a quadratic fit to the experimentally-obtained h(t). Figure 8 dt

compares the experimentally-obtained r(t) with the values obtained from the semi-analytical study. The experimental data were averaged over 5 experiments (5 different sample substrates) with equal droplet sizes deposited atop the substrate. The mean deviation was estimated, and is shown by the shaded band in Fig. 8. The narrowest width (5mm) and total length (8 cm) of the wedges were kept constant for the different tracks with different wedge angles. As seen in Fig. 8, the semi-analytically obtained results closely match the experimental data.


Page 21 of 29 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

The prior analysis of predicting r(t) takes the experimentally-measured h(t) as input. To produce an independent prediction of r(t) without any experimental data, we consider the spherical section approximation of the liquid volume atop the substrate. As the fluid atop the substrate permeates, its height declines, and under the assumption of spherical section, the volume can be calculated using a fixed contact angle (θ ). In such a scenario, the volume of liquid can be written as

1 3 V = π {r (t )} (2 − 3cos θ + cos3 θ ) . This volume expression modifies Eq. 7 to 3 dr (t ) 2σ 2 − 3cos θ + cos3 θ } = − K { dt r (t ) 1 + K [6.62(Vi − π r 3 (t ) {2 − 3cos θ + cos3 θ })0.48 α −1.06 ] 3

π r 2 (t )

(8)

Equation 8 was solved numerically to obtain the temporal variation of radius for different wedge angles (α). Figure 8 shows this variation and compares it with that obtained from the semi-analytical model using the h(t) and dh(t ) data from experiments. Both the predictive constant contact angle model dt

(Eq. 8) and semi-analytical model (Eq. 7) fall within the error zone of the experimental data (± 1 standard deviation). Hence, the constant contact angle model can be used in Case I to predict the overall liquid transport rate, with nearly the same level of accuracy as the experimental results. In the presence of larger wedge angles, the liquid at the bottom track is pushed away from the injection point faster (as the Laplace pressure gradient is larger, being proportional to the wedge angle 59

). This, in turn, induces lower values of pb, resulting in faster top-to-bottom permeation for larger

wedge angles, as observed both in the experiments and the model predictions in Fig. 8.


Langmuir 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Figure 8: Comparison between experimental, semi-analytical model (Eq. 7) and constant contact angle analytical model (Eq. 8) in terms of temporal variation of radius of the liquid droplet atop the HDPT. Note that the fluid volumes in these cases were mostly (except the early points in (A)) in the capillary regime, thus justifying the assumption of negligible gravity effects for the transport atop the sample.

4. Conclusions The present work used spatially-tunable wettability to examine pumpless, directional liquid transport in three dimensions on and through porous materials. The work was motivated by fundamental design configurations for controlled three-dimensional liquid transport in thin porous matrices. The approach allows liquid volumes, deposited dropwise on the top side of a thin porous sheet, to be dispensed from another location on the opposite side and at distances of the order of centimeters from the dispensing location. Apart from standard wicking mechanisms of transporting liquid across a porous substance, the current approach leverages wettability-contrast patterns on the surface to invoke Laplace pressure gradients to transport the liquid directionally along the upper or lower surface of the porous substrate. Also, by creating a widened patch of superhydrophilic region (end-reservoir), the liquid is disposed from the substrate from a desired location away from the original dispensing spot. Three different designs are 22 ACS Paragon Plus Environment

Page 22 of 29

Page 23 of 29 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

described, which transport liquid either on and through, or through and under a porous sheet. The designs vary in terms of the liquid being transported in the horizontal direction either only on the bottom surface (Case I), only on the top surface (Case II), or on both top and bottom surfaces (Case III). The vertical penetration location can also be tuned based on the laid wettability pattern. The present wettability-controlled designs can be used as fundamental blocks of pumpless liquid-manipulating systems based on porous substances. Further, we presented an analytical model to study the rate of liquid permeation through the porous substance in Case I. The analytical model was validated with experimentally-observed data on the temporal variation of the liquid droplet shape atop the substrate. The liquid volume at the wettable track underneath imposes a backpressure – resisting the liquid permeation – which is numerically estimated using SE-FIT, an open source surface evolver software. Based on different simulations, an empirical relation was obtained for the back pressure, wedge angle and volume of liquid present on the track. The empirically-obtained back pressure was used in the analytical formulation along with experimental height variation to estimate the temporal behavior of droplet radius, which was very close to the values measured experimentally. The model was further extended with a constant contact angle assumption for the permeating liquid droplet (atop the substrate) to estimate the temporal variation of liquid droplet radius, eliminating the need of any experimental data. Hence, the model offers an independent tool to predict the liquid permeation rate, which is crucial for design purposes.

Supplementary Information Validation of SE-FIT numerical model Figure showing Laplace pressure and contact angle variation for a droplet shaped as a spherical section and pinned on a circular superhydrophilic spot laid on a superhydrophobic background. Estimation of substrate permeability Schematic showing liquid wicking radially outward after vertical penetration in the absence of wettability confinement on the bottom surface. Plots showing temporal variation of radius and height for a droplet permeating a substrate having a superhydrophobic top and superhydrophilic bottom surface with quadratic fits. Graph showing permeability values as estimated for different volume droplets on the same substrate. Back pressure estimate by SE-FIT


Langmuir 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Figure showing snapshot of SE-FIT simulation of liquid pool hanging from wedge and back pressure estimates for different volumes of liquid accumulated on wedge track for two different wedge angles. Case-I video demonstrating droplet permeation from superhydrophobic side to narrow side of superhydrophilic wedge track followed by lateral transport to the wider end and pinch off from downstream superhydrophilic reservoir (avi).

Acknowledgements The authors are grateful to Kimberly-Clark Corporation for the generous financial support during the course of this study. The scanning electron microscope of the Nanotechnology Core Facility at UIC was used for sample characterization. The authors would also like to thank David Mecha of the Engineering Machine Shop at UIC for assistance with experimental setup. Finally, the authors thank Aritra Ghosh of the UIC Micro/Nanoscale Fluid Transport Laboratory for providing resources on the state-of-the-art in open-surface microfluidics.

References 1. Su, X.; Zhang, M.; Han, W.; Guo, X., Experimental study on the heat transfer performance of an oscillating heat pipe with self-rewetting nanofluid. International Journal of Heat and Mass Transfer 2016, 100, 378-385. 2. Fries, N.; Odic, K.; Dreyer, M., Wicking of perfectly wetting liquids into a metallic mesh. In 2nd International Conference on Porous Media and its Applications in Science and Engineering, Kauai, Hawaii, 2007. 3. Leelamanie, D. A. L.; Karube, J., Effects of hydrophobic and hydrophilic organic matter on the water repellency of model sandy soils. Soil Science & Plant Nutrition 2009, 55 (4), 462-467. 4. Chapman, R., Applications of Nonwovens in Technical Textiles. Woodhead Publishing: 2010, 9096. 5. Brown, P. S.; Bhushan, B., Bioinspired, roughness-induced, water and oil super-philic and superphobic coatings prepared by adaptable layer-by-layer technique. Sci Rep 2015, 5, 14030. 6. Li, C.; Boban, M.; Snyder, S. A.; Kobaku, S. P. R.; Kwon, G.; Mehta, G.; Tuteja, A., Paper-Based Surfaces with Extreme Wettabilities for Novel, Open-Channel Microfluidic Devices. Advanced Functional Materials 2016, 26 (33), 6121-6131. 7. Wang, H. X.; Ding, J.; Dai, L. M.; Wang, X. G.; Lin, T., Directional water-transfer through fabrics induced by asymmetric wettability. J. Mater. Chem. 2010, 20 (37), 7938-7940. 8. Zhou, H.; Wang, H. X.; Niu, H. T.; Lin, T., Superphobicity/philicity Janus Fabrics with Switchable, Spontaneous, Directional Transport Ability to Water and Oil Fluids. Sci Rep 2013, 3, 6. 9. Tian, X.; Li, J.; Wang, X., Anisotropic liquid penetration arising from a cross-sectional wettability gradient. Soft Matter 2012, 8 (9), 2633-2637. 10. Mates, J. E.; Schutzius, T. M.; Qin, J.; Waldroup, D. E.; Megaridis, C. M., The Fluid Diode: Tunable Unidirectional Flow through Porous Substrates. ACS Applied Materials & Interfaces 2014, 6 (15), 1283712843. 24 ACS Paragon Plus Environment

Page 24 of 29

Page 25 of 29 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

11. Tian, X.; Jin, H.; Sainio, J.; Ras, R. H. A.; Ikkala, O., Droplet and Fluid Gating by Biomimetic Janus Membranes. Advanced Functional Materials 2014, 24 (38), 6023-6028. 12. Comanns, P.; Buchberger, G.; Buchsbaum, A.; Baumgartner, R.; Kogler, A.; Bauer, S.; Baumgartner, W., Directional, passive liquid transport: the Texas horned lizard as a model for a biomimetic ‘liquid diode’. Journal of The Royal Society Interface 2015, 12 (109). 13. Toley, B. J.; McKenzie, B.; Liang, T.; Buser, J. R.; Yager, P.; Fu, E., Tunable-Delay Shunts for Paper Microfluidic Devices. Anal. Chem. 2013, 85 (23), 11545-11552. 14. Giokas, D. L.; Tsogas, G. Z.; Vlessidis, A. G., Programming Fluid Transport in Paper-Based Microfluidic Devices Using Razor-Crafted Open Channels. Anal. Chem. 2014, 86 (13), 6202-6207. 15. Li, S. H.; Huang, J. Y.; Ge, M. Z.; Cao, C. Y.; Deng, S.; Zhang, S. N.; Chen, G. Q.; Zhang, K. Q.; AlDeyab, S. S.; Lai, Y. K., Robust Flower-Like TiO2@Cotton Fabrics with Special Wettability for Effective Self-Cleaning and Versatile Oil/Water Separation. Advanced Materials Interfaces 2015, 2 (14). 16. Cao, M. Y.; Xiao, J. S.; Yu, C. M.; Li, K.; Jiang, L., Hydrophobic/Hydrophilic Cooperative Janus System for Enhancement of Fog Collection. Small 2015, 11 (34), 4379-4384. 17. Wang, H.; Zhou, H.; Yang, W.; Zhao, Y.; Fang, J.; Lin, T., Selective, Spontaneous One-Way OilTransport Fabrics and Their Novel Use for Gauging Liquid Surface Tension. Acs Applied Materials & Interfaces 2015, 7 (41), 22874-22880. 18. Song, Y.-Y.; Schmidt-Stein, F.; Bauer, S.; Schmuki, P., Amphiphilic TiO2 Nanotube Arrays: An Actively Controllable Drug Delivery System. Journal of the American Chemical Society 2009, 131 (12), 4230-4232. 19. Guo, T. Q.; Han, K. Y.; Heng, L. P.; Cao, M. Y.; Jiang, L., Ordered porous structure hybrid films generated by breath figures for directional water penetration. RSC Adv. 2015, 5 (107), 88471-88476. 20. Masoodi, R.; Pillai, K. M., Wicking in Porous Materials: Traditional and Modern Modeling Approaches. Taylor & Francis: 2012. 21. Obeso, C. G.; Sousa, M. P.; Song, W.; Rodriguez-Pérez, M. A.; Bhushan, B.; Mano, J. F., Modification of paper using polyhydroxybutyrate to obtain biomimetic superhydrophobic substrates. Colloids and Surfaces A: Physicochemical and Engineering Aspects 2013, 416, 51-55. 22. Martinez, A. W.; Phillips, S. T.; Butte, M. J.; Whitesides, G. M., Patterned paper as a platform for inexpensive, low-volume, portable bioassays. Angew. Chem.-Int. Edit. 2007, 46 (8), 1318-1320. 23. Martinez, A. W.; Phillips, S. T.; Carrilho, E.; Thomas, S. W.; Sindi, H.; Whitesides, G. M., Simple telemedicine for developing regions: Camera phones and paper-based microfluidic devices for real-time, off-site diagnosis. Analytical Chemistry 2008, 80 (10), 3699-3707. 24. Martinez, A. W.; Phillips, S. T.; Whitesides, G. M., Three-dimensional microfluidic devices fabricated in layered paper and tape. Proc. Natl. Acad. Sci. U. S. A. 2008, 105 (50), 19606-19611. 25. Wang, X.; Hagen, J. A.; Papautsky, I., Paper pump for passive and programmable transport. Biomicrofluidics 2013, 7 (1), 11. 26. Li, X.; Tian, J.; Shen, W., Thread as a Versatile Material for Low-Cost Microfluidic Diagnostics. ACS Applied Materials & Interfaces 2010, 2 (1), 1-6. 27. Reches, M.; Mirica, K. A.; Dasgupta, R.; Dickey, M. D.; Butte, M. J.; Whitesides, G. M., Thread as a Matrix for Biomedical Assays. ACS Applied Materials & Interfaces 2010, 2 (6), 1722-1728. 28. Safavieh, R.; Zhou, G. Z.; Juncker, D., Microfluidics made of yarns and knots: from fundamental properties to simple networks and operations. Lab on a Chip 2011, 11 (15), 2618-2624. 29. Morrissette, J. M.; Mahapatra, P. S.; Ghosh, A.; Ganguly, R.; Megaridis, C. M., Rapid, Self-driven Liquid Mixing on Open-Surface Microfluidic Platforms. Scientific Reports 2017, 7 (1), 1800. 30. Xing, S. Y.; Jiang, J.; Pan, T. R., Interfacial microfluidic transport on micropatterned superhydrophobic textile. Lab on a Chip 2013, 13 (10), 1937-1947. 31. Guan, W. R.; Zhang, C. S.; Liu, F. F.; Liu, M., Chemiluminescence detection for microfluidic clothbased analytical devices (mu CADs). Biosens. Bioelectron. 2015, 72, 114-120. 25 ACS Paragon Plus Environment

Langmuir 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

32. Guan, W. R.; Liu, M.; Zhang, C. S., Electrochemiluminescence detection in microfluidic clothbased analytical devices. Biosens. Bioelectron. 2016, 75, 247-253. 33. Liu, M.; Zhang, C. S.; Liu, F. F., Understanding wax screen-printing: A novel patterning process for microfluidic cloth-based analytical devices. Analytica Chimica Acta 2015, 891, 234-246. 34. Yang, Y.; Xing, S.; Fang, Z.; Li, R.; Koo, H.; Pan, T., Wearable microfluidics: fabric-based digital droplet flowmetry for perspiration analysis. Lab on a Chip 2017, 17 (5), 926-935. 35. Yeo, J. C.; Kenry; Lim, C. T., Emergence of microfluidic wearable technologies. Lab on a Chip 2016, 16 (21), 4082-4090. 36. Zhao, Y.; Wang, H.; Zhou, H.; Lin, T., Directional Fluid Transport in Thin Porous Materials and its Functional Applications. Small 2017, 13 (4), 1601070-n/a. 37. Derda, R.; Laromaine, A.; Mammoto, A.; Tang, S. K. Y.; Mammoto, T.; Ingber, D. E.; Whitesides, G. M., Paper-supported 3D cell culture for tissue-based bioassays. Proceedings of the National Academy of Sciences 2009, 106 (44), 18457-18462. 38. Rodriguez, N. M.; Linnes, J. C.; Fan, A.; Ellenson, C. K.; Pollock, N. R.; Klapperich, C. M., PaperBased RNA Extraction, in Situ Isothermal Amplification, and Lateral Flow Detection for Low-Cost, Rapid Diagnosis of Influenza A (H1N1) from Clinical Specimens. Analytical Chemistry 2015, 87 (15), 7872-7879. 39. Dutta, S.; Mandal, N.; Bandyopadhyay, D., Paper-based alpha-amylase detector for point-of-care diagnostics. Biosens. Bioelectron. 2016, 78, 447-453. 40. Curto, V. F.; Fay, C.; Coyle, S.; Byrne, R.; O’Toole, C.; Barry, C.; Hughes, S.; Moyna, N.; Diamond, D.; Benito-Lopez, F., Real-time sweat pH monitoring based on a wearable chemical barcode micro-fluidic platform incorporating ionic liquids. Sensors and Actuators B: Chemical 2012, 171, 1327-1334. 41. Wang, H.; Ding, J.; Dai, L.; Wang, X.; Lin, T., Directional water-transfer through fabrics induced by asymmetric wettability. J. Mater. Chem. 2010, 20 (37), 7938-7940. 42. Nie, Z.; Nijhuis, C. A.; Gong, J.; Chen, X.; Kumachev, A.; Martinez, A. W.; Narovlyansky, M.; Whitesides, G. M., Electrochemical sensing in paper-based microfluidic devices. Lab on a Chip 2010, 10 (4), 477-483. 43. Nagrath, S.; Sequist, L. V.; Maheswaran, S.; Bell, D. W.; Irimia, D.; Ulkus, L.; Smith, M. R.; Kwak, E. L.; Digumarthy, S.; Muzikansky, A.; Ryan, P.; Balis, U. J.; Tompkins, R. G.; Haber, D. A.; Toner, M., Isolation of rare circulating tumour cells in cancer patients by microchip technology. Nature 2007, 450 (7173), 1235-1239. 44. Liu, H.; Li, Y.; Sun, K.; Fan, J.; Zhang, P.; Meng, J.; Wang, S.; Jiang, L., Dual-Responsive Surfaces Modified with Phenylboronic Acid-Containing Polymer Brush To Reversibly Capture and Release Cancer Cells. Journal of the American Chemical Society 2013, 135 (20), 7603-7609. 45. Tomšič, B.; Simončič, B.; Orel, B.; Černe, L.; Tavčer, P. F.; Zorko, M.; Jerman, I.; Vilčnik, A.; Kovač, J., Sol–gel coating of cellulose fibres with antimicrobial and repellent properties. Journal of Sol-Gel Science and Technology 2008, 47 (1), 44-57. 46. Vilčnik, A.; Jerman, I.; Šurca Vuk, A.; Koželj, M.; Orel, B.; Tomšič, B.; Simončič, B.; Kovač, J., Structural Properties and Antibacterial Effects of Hydrophobic and Oleophobic Sol−Gel Coacngs for Cotton Fabrics. Langmuir 2009, 25 (10), 5869-5880. 47. Schwartz, S. I., Principles of Surgery: Companion Handbook. McGraw-Hill: 1994. 48. Li, X.; Ballerini, D. R.; Shen, W., A perspective on paper-based microfluidics: Current status and future trends. Biomicrofluidics 2012, 6 (1), 011301. 49. Gomez, F. A., The future of microfluidic point-of-care diagnostic devices. Bioanalysis 2012, 5 (1), 1-3. 50. Yetisen, A. K.; Akram, M. S.; Lowe, C. R., Paper-based microfluidic point-of-care diagnostic devices. Lab on a Chip 2013, 13 (12), 2210-2251. 51. Shikhmurzaev, Y. D., Motion of a three-phase contact line along a wet surface. Fluid Dynamics 27 (6), 818-823. 26 ACS Paragon Plus Environment

Page 26 of 29

Page 27 of 29 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

52. Quéré, D., Wetting and Roughness. Annual Review of Materials Research 2008, 38 (1), 71-99. 53. Mertaniemi, H.; Jokinen, V.; Sainiemi, L.; Franssila, S.; Marmur, A.; Ikkala, O.; Ras, R. H. A., Superhydrophobic Tracks for Low-Friction, Guided Transport of Water Droplets. Adv. Mater. 2011, 23 (26), 2911-2914. 54. Schutzius, T. M.; Elsharkawy, M.; Tiwari, M. K.; Megaridis, C. M., Surface tension confined (STC) tracks for capillary-driven transport of low surface tension liquids. Lab on a Chip 2012, 12 (24), 52375242. 55. Khoo, H. S.; Tseng, F.-G., Spontaneous high-speed transport of subnanoliter water droplet on gradient nanotextured surfaces. Applied Physics Letters 2009, 95 (6). 56. Liu, C.; Xue, Y.; Chen, Y.; Zheng, Y., Effective directional self-gathering of drops on spine of cactus with splayed capillary arrays. Scientific Reports 2015, 5, 17757. 57. Ju, J.; Bai, H.; Zheng, Y.; Zhao, T.; Fang, R.; Jiang, L., A multi-structural and multi-functional integrated fog collection system in cactus. Nature Communications 2012, 3, 1247. 58. Zheng, Y.; Bai, H.; Huang, Z.; Tian, X.; Nie, F.-Q.; Zhao, Y.; Zhai, J.; Jiang, L., Directional water collection on wetted spider silk. Nature 2010, 463, 640. 59. Ghosh, A.; Ganguly, R.; Schutzius, T. M.; Megaridis, C. M., Wettability patterning for high-rate, pumpless fluid transport on open, non-planar microfluidic platforms. Lab on a Chip 2014, 14 (9), 15381550. 60. Sen, U.; Chatterjee, S.; Ganguly, R.; Dodge, R.; Yu, L.; Megaridis, C. M., Scaling laws in directional spreading of droplets on wettability-confined diverging tracks. Langmuir 2018, Accepted. 61. Sen, U.; Chatterjee, S.; Mahapatra, P. S.; Ganguly, R.; Dodge, R.; Yu, L.; Megaridis, C. M., Surfacewettability patterning for distributing high-momentum water jets on porous polymeric substrates. ACS Applied Materials and Interfaces 2018, Accepted. 62. Chen, H.; Cogswell, J.; Anagnostopoulos, C.; Faghri, M., A fluidic diode, valves, and a sequentialloading circuit fabricated on layered paper. Lab on a Chip 2012, 12 (16), 2909-2913. 63. Tadanaga, K.; Morinaga, J.; Matsuda, A.; Minami, T., Superhydrophobic−Superhydrophilic Micropatterning on Flowerlike Alumina Coating Film by the Sol−Gel Method. Chemistry of Materials 2000, 12 (3), 590-592. 64. Emeline, A. V.; Rudakova, A. V.; Sakai, M.; Murakami, T.; Fujishima, A., Factors Affecting UVInduced Superhydrophilic Conversion of a TiO2 Surface. The Journal of Physical Chemistry C 2013, 117 (23), 12086-12092. 65. de Gennes, P. G.; Brochard-Wyart, F.; Quere, D., Capillarity and Wetting Phenomena: Drops, Bubbles, Pearls, Waves. Springer New York: 2003. 66. Chen, Y.; Schaffer, B.; Weislogel, M.; Zimmerli, G., Introducing SE-FIT: Surface Evolver - Fluid Interface Tool for Studying Capillary Surfaces. In 49th AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition, American Institute of Aeronautics and Astronautics: 2011. 67. Brakke, K. A., The surface evolver. 1992, 141-165. 68. Cohen, B.; Jameson, L. K.; Quincy, R. B., Z-directon liquid transport medium. US5695487 A: 1997. 69. Matloub, H.; Lynch, W., Method and device for topical delivery of therapeutic agents to the skin. US7316817 B2: 2005. 70. Çengel, Y. A.; Cimbala, J. M., Fluid Mechanics: Fundamentals and Applications. McGraw-Hill Higher Education: 2010. 71. Shakeri, A.; Ghasemian, A., Water Absorption and Thickness Swelling Behavior of Polypropylene Reinforced with Hybrid Recycled Newspaper and Glass Fiber. Applied Composite Materials 2010, 17 (2), 183-193.


Langmuir 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Page 28 of 29

g

Page 29 of 29

Case II

Langmuir

Case III

time

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Case I

Superhydrophilic top

ACS Paragon Plus Environment Superhydrophilic bottom

Superhydrophobic

Water

Precise liquid transport on and through thin porous materials

Recommend Documents