Millimeter-Sized Hole Damming - Langmuir (ACS Publications)

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Millimeter sized holes damming So Hung Huynh, Dwayne Chung Kim Chung, Murat Muradoglu, Oi-Wah Liew, and Tuck Wah Ng Langmuir, Just Accepted Manuscript • DOI: 10.1021/acs.langmuir.7b03290 • Publication Date (Web): 08 Nov 2017 Downloaded from http://pubs.acs.org on November 9, 2017

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The damming effect is exhibited by hydrophilic and superhydrophobic substrate with holes, but the different underlying wetting mechanics has an upward jet supplied in the former causing drainage (left) whilst in the latter resulting in its subsumation (right). 164x120mm (96 x 96 DPI)

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Millimeter sized holes damming So Hung Huynh1, Dwayne Chung Kim Chung1, Murat Muradoglu1, Oi Wah Liew2, Tuck Wah Ng1,* 1

Laboratory for Optics and Applied Mechanics, Department of Mechanical & Aerospace

Engineering, Monash University, Clayton, VIC3800 Australia. 2Cardiovascular Research Institute, Yong Loo Lin School of Medicine, National University of Singapore, National University Health System, Centre for Translational Medicine, 14 Medical Drive, Singapore 117599. KEYWORDS. Hydrostatic, Torricelli’s Law, Drainage, Superhydrophobic.

ABSTRACT. Valves used to control liquid filling and draining processes from storage typically need to be actuated. Here, we show that similar flow enabling and restricting operations can be achieved through millimeter scale holes that function according to the amount of hydrostatic pressure applied without any other intervention. This phenomena is exhibited using receptacles where the base is made of either a hydrophilic or superhydrophobic substrate with hole sizes ranging from 1.0 – 2.0 mm. The construction is such that the drainage flow velocities are of the same order in both substrates and follow Torricelli’s law trends. Nevertheless, the primary mechanisms responsible for resisting the onset of flow in each substrate are different; nonbreaching of the advancing contact angle threshold in the former, and stable maintenance of an elastic-like deformation of the liquid-gas interface that is connected to the surrounding plastron in


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the latter. These differences are demonstrated using an upward jet of water delivered to the orifice, where a discharging flow from the hydrophilic base occurred before the threshold hydrostatic pressure condition was attained, while liquid from the jet is subsumed into the liquid body of the receptacle with the superhydrophobic base without any leakage. These findings portend advantages in simplicity and robustness for a myriad of liquid-related processes.

INTRODUCTION. The operation of a flow system for liquid storage is simple; supply of water when the level is low and release of water before there is any danger of an overflow. Valves used to control the filling and draining processes typically need to be actuated mechanically, hydraulically, or electrically. In addition sensors are needed to determine the water levels for filling and draining. When liquid of low viscosity drain from a receptacle that is filled to a height of h, the speed of efflux v through a bottom orifice (Fig. 1A) under gravitational acceleration g is widely accepted to be governed by Torricelli’s Law, which from Bernoulli’s principle, yields

v = 2 gh

(1)

The nature of the orifice’s geometry is often ignored in the scheme of things. Yet liquids that interact with sufficiently small cavities are strongly affected by capillarity. This phenomenon arises from two opposing forces, solid-liquid adhesion that tends to spread the liquid, and cohesive surface tension that acts to reduce the liquid-gas interfacial area. Studies of the ascent of liquid in capillary tubes have a long history1, and remain a subject of interest today, particularly on the effect played by contact angle hysteresis2. The essential governing equation is one where


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hydrostatic pressure as defined by h, g, and the density of the liquid ρ, balances capillary pressure which is determined by the inner diameter of the tube d, surface tension γ, and contact angle of the meniscus θ, such that (see Fig. 1B)

Figure 1 - Influence of capillary pressure on draining from a receptacle. In the typical situation of water draining from a receptacle (A), the velocity is related to the height h according to Torricelli’s equation. A capillary tube (B) with a hydrophilic inner surface such that the contact angle θ < 90o at the meniscus allows upward ascent of liquid into it. For a receptacle with an orifice that is sufficiently small for capillarity to come into play and thick enough for a meniscus to form so that the apparent contact angle θa > 90o (C), resistance to liquid flow from the orifice can be developed when the meniscus M (inset) shifts to bottom plane of the orifice allowing the apparent contact angle θa to exceed the advancing contact angle θ.

1  ρg  = h d  4γ cosθ 

(2)

It is clear that Eq. (2) holds true on condition that the inner surface of the tube has a hydrophilic (θ < 90o) wetting characteristic, otherwise liquid cannot ascend the tube. Yet, capillary pressure can develop at any orifice without a tube as long as it has finite thickness for a meniscus to form.


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The behaviour of a hole at the hydrophilic base of a receptacle (Fig. 1C) mimics that of a closed valve in a reservoir by allowing capillary pressure to act in an upward direction against gravitational flow when significant change in the advancing contact angle develops and the edges of the hole permit larger apparent contact angles than would be obtained on flat surfaces3 to materialize such that θ > 90o. This offers the prospect of utilizing simple openings as valves that respond solely to the amount of hydrostatic pressure present. The dependence of capillary pressure on wetting invites exploration with highly non-wetting surfaces that are often described as superhydrophobic (SH). They were first observed in the flora and fauna of nature4, 5 and now replicable via various chemical treatment methods6, 7. Liquids placed on SH surfaces are characterized by the presence of a thin film of air (plastron), where sessile drops exhibit high contact angles (> 150o) at the three phase contact line8. The strong degree of water repellence permits large sessile drops to remain on the surface even with a hole underneath it9,10. The premise of high drag reduction in flows remains an enduring motivation for using SH surfaces11, 12. In this work, we demonstrate the capability of hydrophilic and superhydrophobic substrates that have holes of sizes ranging from 1.0 – 2.0 mm on them to act as valves, allowing the automatic filling and discharge of water from a receptacle controlled only by the amount of hydrostatic pressure present. Attention is paid to elucidating the underlying mechanisms involved as well as to query the drainage flow velocities with hydrostatic pressure vis a vis Torricelli’s law. The ability of the liquid retaining “reservoir” effect to be maintained when an upward jet of water is delivered to the orifice is also probed. MATERIALS AND METHODS


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Substrate Preparation The SH substrate used for the main experiment was prepared from copper sheet of 550 µm thickness. Hole sizes ranging from 1 - 2 mm were created on 25 x 25 mm sized pieces using a tungsten carbide drill bit operated at 10,000 revolutions per minute. The samples were polished using 240, 320 and 400 grit sandpaper in succession under running water, then ultra-sonicated in ethanol (70% v/v) and acetone for 3 minutes, and subsequently in deionized (DI) water for another 15 minutes. This creates the hydrophilic substrates. To generate SH substrates, some of these hydrophilic pieces were oxidized in a solution containing 2M NaOH and 1.5 M (NH4)2S2O8 for 5 minutes. The samples were then allowed to synthesize in an oven at 180oC for 120 minutes. At the end of the reaction, the substrate was taken out of the solution, rinsed several times with DI water and ethanol and then dried with compressed air. The as-obtained product was dried at 180oC for 2h to complete the phase transfer from hydroxides to oxides. In the final step, the substrates were silanized using FAS (1H,1H,2H,2H-perfluorodecyl-triethoxysilane) to obtain a low-surface energy layer with good corrosion resistance and thermal stability. The substrate was immersed in FAS-ethanol solution for 30 minutes and then dried in an oven at 150oC for 10min.


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Figure 2 - Schematic description of setup to establish draining and stability characteristics of substrates used. The receptacle created using hydrophilic or superhydrophobic substrates to form the base with a hole, was filled with distilled water for the drainage experiments. The velocity of flow from the hole was determined by imaging and analysing the water level position in the receptacle. In order to eliminate possibilities of parallax error, the probe end of a digital height meter was lowered to allow the pixel readings from the camera and the positional values from the height meter to be correlated. This was a one-time calibration process as long as the positions of the setup are not altered. A conventional video camera was used to record the draining experiments, while a high speed camera was used to record fast liquid level change behavior. Substrate Examination To ensure proper surface modification, samples of the SH pieces prepared were placed on stubs using conductive adhesive and examined by scanning electron microsopy (FEI, NovaNanoSEM 430) operated in vacuum. The extent of wetting modification of the hydrophilic and SH pieces were assessed by taking static side images of sessile drops dispensed on these surfaces and measuring the contact angles using an analysis software (Tracker). The substrates were slowly tilted in order to determine the angle wherein slippage occurred. The sequence of images leading to this were then used to ascertain the critical advancing and receding contact angles. Water Retention and Drainage Characteristics The pieces prepared (hydrophilic and SH) were attached to one end of hollow cylindrical plexiglass substrates with outer and inner diameters of 24.4 mm and 19 mm, and lengths of 58.6 mm using adhesive silicone to create receptacles for the drainage experiments. Every receptacle was tested for non-leakage from the sides before usage. In the experiments related to acquiring data on drainage, the cylindrical receptacle was filled with distilled water using a syringe pump (New Era Pump Systems, NE-1000X) programmed to operate at 1 mL/min. A video camera (Moticam 3) fitted with a microscopic lens was used to furnish water height level information in the receptacles.


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In experiments to interrogate liquid retention stability with the hydrophilic and superhydrophobic substrates, the upward liquid jet was created by passing distilled water from the same syringe pump programmed to operate at 1 mL/min. The image sequences relating to the commencement and cessation of drainage, as well as to liquid retention stability were recorded using a high speed camera (Fastec, TS1000ME) at 250 frames per second. The velocity of discharge was determined via measurements of the rate of descent on the liquid level in the receptacle and applying the conservation of flowrate before and after the orifice. Minimal parallax error was ascertained by comparing the digital pixel readings with that obtained using a digital height meter (Mahr, Digimar CX1) with 1 µm resolution. The setup details of these experiments are depicted in Fig. 2. Liquid Gas Interface at the Superhydrophobic Hole The setup details of the experiment to determine the elastic nature of the liquid-gas interface on the SH substrate is depicted in Fig. 3A. A 26 gage flat tip needle with inner diameter 0.26 mm was mounted on a motorized linear actuator such that its axis of movement coincided with the central axis of the hole. The receptacle filled with water to a specific hydrostatic pressure setting level. Blue food dye was carefully dispensed out of the tip of probe such that the dye is visible but extruding out from the tip. The probe was controlled using a motorized linear stage (Zaber Technologies, T-LS13-SM) and moved at steps of 1 µm displacements towards the hole. The bottom position of the liquid-gas interface was located once colour was observed in the liquid body of the receptacle (Fig. 3B and C).


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Figure 3 - Schematic description of setup to establish the minimum position fo the liquid-gas interface at the hole on the superhydrophobic substrate. A flat tip needle, attached the motorized linear stepper, was carefully arranged to align with the centre of the hole in the substrate (A). A small amount of blue dye was continuously injected out of the needle through a syringe pump while a camera located above the receptacle was used for monitoring the liquid in it. The tip was then progressively moved towards the hole. The lowest position of the liquid-gas interface was determined when the first signs of bleed-through of blue dye was observed (C) in the originally clear water in the receptacle (B).

RESULTS AND DISCUSSION Surface Characterization Fig. 4A provides an illustrative SEM image of the hydrophilic substrate surface. Due to the lack of hierarchical microscale and nanoscale structures, the equilibrium contact angle of a 10 µL sessile drop of deionized water placed on it (inset) was 78o ± 3o. The drop was retained on the substrate even when tilted to 90o illustrating the inherent stickiness of the surface. In contrast, the SEM image of the SH substrate (Fig. 4B) shows prismatic hierarchical microscale and nanoscale structures that resulted in a sessile drop of the same volume exhibiting equilibrium contact angles


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of 157o ± 4o (inset), critical advancing and receding angles of 166o ± 3o and 150o ± 2o respectively, and tilt angle for slippage at 1.9o ± 1o. These results indicate significant non-wetting and slippery characteristics obtained from the surface treatment. The SEM images also reveal no unusual surface features (e.g. depositions etc.) that would be responsible for altering the wetting behaviour of the substrates13.

Figure 4 - Surface characterization. The raw copper substrate prior to treatment (A) do not have any surface structures that will allow plastrons to develop. Following treatment (B), needle-like hierarchical structures ranging from the micro to nano scale that give rise to superhydrophobic characteristics. Damming Effect by Hydrophilic Substrate with Hole A hole on a hydrophilic substrate of finite thickness acts like a stop valve and the mechanism underlying this phenomena is exemplified by the liquid bulging out from the hole beyond the bottom plane of the substrate as shown in Fig. 5A. In this situation, the edges of the hole resulted in an apparent contact angle exceeding that of the advancing contact angle so that capillary pressure exerts an upward acting force. Thus water is able to fill the receptacle up to height h1 above which it begins to flow out of the receptacle. The linear characteristic of the plot of 1 / d against h1 (Fig. 6) affirms Eq. (2), and the slope of the relationship translates to an average apparent contact angle of 180o. This indicates that the resistance to flow is offered by the meniscus assuming


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increasingly spherical shapes until a threshold limit is reached where no more hydrostatic pressure can be accommodated.

Figure 5 - Drainage characteristics with the hydrophilic substrate. Side view images show that at liquid level near h1 (A), the formation of a small plug-like meniscus is able to exert sufficient capillary force to resist flow. During the initial stages when drainage flow occurs (B) the liquid quickly assumes the form of drops (C) when Rayleigh breakup conditions are attained. The last drop before cessation of flow at liquid height h2 (D) develops from a pinch-off process of the liquid bridge that regenerates the plug-like meniscus. In the initial stages of the ensuing flow (when liquid height h1 was achieved), kinetic energy overcomes surface energy in the system to initiate a jet of liquid out of the orifice (Fig. 5B) which quickly progresses to a cascade of drops when ‘Rayleigh breakup’ conditions was attained14 (Fig. 5C). With progressive hydrostatic pressure reduction (due to continued drainage from the receptacle), the flow of drops transitioned to a dripping mode15, and finally to complete cessation at liquid height h2 with a final pinch off process (Fig. 5D) to form the plug-like meniscus that generates sufficient capillary pressure to balance the hydrostatic pressure. The linear relationship of 1 / d against h2 (see Fig. 6) confirms capillarity action with an apparent contact angle of 121o. With the apparent contact angle now below 180o, this would imply that the system has been brought back closer to the equilibrium state. When the receptacle is subsequently filled with water to height h1, the same mechanism of liquid flow is initiated and drainage from the receptacle resumes. Thus, the capability of small orifices of sufficient thickness to function as hydrostatic


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pressure-controlled valves to govern liquid flow in a manner akin to flow balancing of a reservoir is demonstrated. The plot of flow speed at various liquid heights reveals behavior that follows Torricelli’s Law (Fig. 7) but with (i) reduced velocities (~40%) ascribed to losses from flow contraction and (ii) unsteady fluctuations that can be attributed to instantaneous inertia effects16.

Figure 6 - Damming characteristics using hydrophilic and superhydrophobic substrates. The plots relate orifice diameters (d) on the substrate to the liquid heights in the receptacle associated with the start (h1) and end (h2) of flow drainage and show a strong linear relationship (R2 values > 0.985 for all plots) that points to the role played by capillarity. The results were based on repeating each liquid drainage and filling cycle 5 times.


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Figure 7 – Example water drainage velocity traces with the substrates. The velocity of flow during discharge from a 1 mm diameter orifice at liquid height h (which lies between h1 and h2) in the receptacle with either a hydrophilic or superhydrophobic substrate base displayed behaviour that is consistent but of lower magnitude and with significant fluctuations than predicted by Torricelli’s law. The marginally higher velocities and lesser fluctuations observed with the superhydrophobic substrate compared with the hydrophilic substrate indicate the influence of wetting in the discharge process.

Damming Effect by Superhydrophobic Substrate with Hole The capabilities of SH substrates with holes achieving similar flow behaviour at height levels h1 and h2 (Fig. 6) cursorily suggest similar operating mechanisms with that of hydrophilic substrates. Yet, the liquid behaviour corresponding to height levels approaching h1 indicate otherwise. Rather than wetting through the hole and harnessing the bottom edges to create apparent contact angles that can sustain higher hydrostatic pressures as in case with the hydrophilic substrate, the liquidgas interface at the vicinity of the SH hole remains almost at the same level as the bottom plane of the receptacle (Fig. 8A). There are two possible mechanisms in action. In the first, which we reckon


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to be most likely, the liquid body essentially treats the hole as an extension of the plastron. Liquid that is subsequently added to the receptacle generates a pressure increase that is easily accommodated by the plastron on the SH surface by adopting metastable states17, 18. However, the lack of a solid phase at the orifice forces the liquid-gas interface to respond by undergoing an almost elastic elongation process to form a liquid bulge (see illustration in inset of Fig. 9). Since this interface is visually hidden from the side view (by the thickness of the substrate), a customized probe setup devised to locate the lowest position of the interface corresponding to the amount of hydrostatic pressure confirms the elastic elongation action (see graph of Fig. 9). Despite this, the resistance to flow remains offered by a meniscus-like form as in the hydrophilic substrate case. Another mechanism can be envisaged as one in which the hole serves as some form of channel that resists wetting such that with any increase in hydrostatic pressure the liquid simply progressively extends into it. This then infers that with longer depths of the hole, the extent of resistance to drainage should be greater. Since it is difficult to treat the wall of a hole that is deep but has a small diameter to be superhydrophobic uniformly, it is will a considerable challenge to prove the action of this mechanism. Once liquid starts to flow from the orifice, the Rayleigh breakdown condition leading to the formation of a cascade of drops is also quickly attained (Fig. 8B). This contrasts with an erstwhile method of generating streams of drops by driving liquid filaments through substrate strips that depend strongly on wetting at the contact line19. The difference can be better appreciated when considering that as the liquid flow ensues and hydrostatic pressure decreases with drainage, the plastron, and thus the predominant Cassie wetting state, is restored (as has been demonstrated to be possible in other contexts20, 21) by the passage of air that axially envelopes the draining liquid body at the hole. While the air flow in this case is naturally limited, it provides an antithetical


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condition to the physical schemes that have been used to aid capillary jetting22. The elastic characteristic is also demonstrated in the stages leading to flow stoppage at h2, where the last drop formed is elongated and retracts strongly back into the hole (see Figs. 8C-D and movie S1). These characteristics parallel the behaviour of drops, which when released from heights to impact on SH surfaces, flatten out radially first before recoiling upwards through an elastic rebound23. The plots of flow speed at various liquid heights again reflect behaviour that follows Torricelli’s Law (Fig. 7). Marginal increases in the velocities and dampening out of the unsteady fluctuations compared to the case with the hydrophilic substrate are observed. This phenomena can be attributed to SH surface not being predominantly parallel to the direction of flow, as opposed to the condition of having the SH surface parallel to the direction of flow that is widely investigated in studies that link air cushions to drag reduction24.

Figure 8 - Drainage characteristics with the superhydrophobic substrate. Side views of the experimental receptacle where no visible meniscus was observed to protrude beyond the bottom plane of the base at liquid level near h1 (A). Liquid flow exhibits a cascade of drops during initial drainage (B). The last stages of flow is denoted by an elastic-like liquid body that protrudes from the orifice beyond the bottom plane (C) and then contracts back up into the hole upon detachment of the drop (D).


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Figure 9 - Liquid-gas interface at the hole for the superhydrophobic substrate. Plot of the lowest positions of the liquid-gas interface at the hole on the superhydrophobic substrate subjected to hydrostatic pressure of liquid height h. As illustrated in the inset figure, this position (denoted by the red circle) is based on the distance y referenced to the bottom of the receptacle which has 550 µm thickness. This illustrates the ability of the interface to extend itself under hydrostatic pressure by connecting with the plastron present on the substrate since it does not have ability to adopt metastable wetting states at the areas away from the hole.

Stability from Upward Jet Perturbation The somewhat similar liquid retention (in h1 and h2 values) and flow characteristics of the hydrophilic and SH substrates (when the hole sizes are similar) also belie the improved isolation features of the latter. The physical presence of a liquid body bulging below the hole of the hydrophilic base plate, which dictates the balance of forces through its wetting states, allowed a simple upward jet of water impinging on it to cause perturbations that initiated a discharging flow despite h1 not yet being attained (Fig. 10 left and Movie S2). This affords the means to devise an emergency discharge of sorts in practical scenarios. Such a behaviour, however, does not occur with the SH surface, where liquid from the jet is absorbed instead into the liquid body of the


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receptacle, leading to the appearance of a upward acting fountain, provided that the liquid level is below h1 (Fig. 10 right and Movie S3). This affords immunity from external liquid sources interrupting the liquid retention behaviour. Unlike the situation where the liquid column is delivered in the direction of gravity, there is absence of a transient cavity with air entrainment. Since the Froude (Fr = 13.97), Weber (We = 7.5), and Reynolds (Re = 1174) numbers in this case do not depart significantly from conditions where this has been previously observed25, it indicates a heightened capability of the liquid-gas interface to dissipate any local air entrainment through its connection to the surrounding plastron (for superaerophilicity is the converse of superhydrophobicity). This same capability then permits liquid from the jet to coalesce well with the liquid body in the receptacle, resulting in the liquid-gas interface at the hole exhibiting high stability (from leakages). It is also noteworthy that this provides a tandem demonstration of a fluid diode effect without the use of microscale porous substrates or channels26, 27, and the transport of liquid against gravity in free space sans the use of any intervening pipes. The linkage between the liquid-gas interface at the hole with the plastron offers additional avenues to extend the longevity of plastrons28, 29.

Figure 10 - Upward jet of liquid directed at the hole on hydrophilic and superhydrophobic substrates. For the hydrophilic substrate there is initially a plug-like meniscus extending beyond


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the bottom plane of the substrate. The jet disrupts the meniscus and results in discharge of liquid from the receptacle even when the liquid level is below the threshold height h1. The drop in water level in the receptacle after 1.17s is noticeable. For the superhydrophobic substrate there is no initial plug-like meniscus that extends beyond the bottom plane of the substrate. In addition, a jet of liquid directed at the orifice is absorbed directly into the receptacle. An increase in water level can be seen in the image after 5.63s. CONCLUSIONS The ability of 1-2 mm sized holes to store and discharge water from a receptacle governed solely by the amount of hydrostatic pressure is demonstrated here. The use of larger opening sizes lowers the capillary pressure influence and thus renders the damming effect to be negligible. The use of smaller orifice sizes alternatively results in flow velocities that are so low that they limit practical uses. The liquid retention behaviour can be extended to the case when many holes of the same size are present on the substrate. When arranged in a regular matrix, these holes then offer the possible use as an array dispenser for microtiter plates in the laboratory without any advanced flow control mechanisms. That not all liquid is discharged allows serial dilution schemes to be incorporated. In biology and medicine, serial dilution, despite its long history30, remains widely used to reduce the concentration of macromolecules, microscopic organisms or cells in samples in a more manageable way31. Since the flow characteristics at each hole follows Torricelli’s law trends, adjusting the number of holes may also allow for simple scaling of the overall drainage flowrate without any loss in the liquid retention behaviour. This offers new vistas in microfluidic reactor processes involving liquid chemicals32. The sensitivity of liquid flow through superhydrophobic orifices to hydrostatic pressure may also provide added insights into mechanisms of insect underwater breathing. Studies on the ability of these anthropods to do this have mainly focused on the sustainability of plastrons on the cuticle surface under hydrostatic pressure33, 34 without much consideration of the openings that may be present.


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AUTHOR INFORMATION Corresponding Author *[email protected] Author Contributions The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. Funding Sources SHH and TWN appreciate funding support from the Joint Research Engagement Program for this work. ACKNOWLEDGMENT This work was performed in part at the Melbourne Centre for Nanofabrication (MCN) in the Victorian Node of the Australian National Fabrication Facility (ANFF). The assistance of G. Gervinskas in SEM imaging is appreciated. REFERENCES (1)

Jurin, J. An account of some experiments shown before the Royal Society; With an enquiry into the cause of the ascent and suspension of water in capillary tubes, Phil. Trans. 1718, 30, 739-747.

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Athukorallage, B.; Iyer, R. Investigation of energy dissipation due to contact angle hysteresis in capillary effect, J. Phys.: Conf. Ser. 2016, 727, 012003.


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Millimeter-Sized Hole Damming - Langmuir (ACS Publications)

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