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Evaporative Lithography in Open Microfluidic Channel Networks Saifullah Lone, Jia Ming Zhang, Ivan U Vakarelski, Er Qiang Li, and Sigurdur T. Thoroddsen Langmuir, Just Accepted Manuscript • DOI: 10.1021/acs.langmuir.6b03304 • Publication Date (Web): 24 Feb 2017 Downloaded from http://pubs.acs.org on February 26, 2017

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Evaporative Lithography in Open Microfluidic Channel Networks Saifullah Lone, Jia Ming Zhang, Ivan U. Vakarelski, Er Qiang Li and Sigurdur T. Thoroddsen* Division of Physical Sciences and Engineering, King Abdullah University of Science & Technology (KAUST), Thuwal, 2355-6900, Saudi Arabia.

*Corresponding Author: Sigurdur T. Thoroddsen, Email: [email protected] Division of Physical Sciences & Engineering 4700 King Abdullah University of Science and Technology Thuwal 23955-6900, Kingdom of Saudi Arabia Tel: +966 2 808 2160

ABSTRACT We demonstrate a direct capillary-driven method based on wetting and evaporation of various suspensions to fabricate regular two-dimensional wires in an open microfluidic channel, through continuous deposition of micro- or nano-particles under evaporative lithography, akin to the coffee-ring-effect. The suspension is gently placed in a loading reservoir connected to the main open microchannel groove on a PDMS-substrate. Hydrophilic conditions ensure rapid spreading of the suspension from the loading reservoir to fill the entire channel length. Evaporation during the spreading and after the channel is full, increases the particle concentration towards the end of the channel. This evaporation-induced convective-transport brings particles from the loading reservoir towards the channel end where this flow deposits a continuous multi-layered particle structure. The particle-deposition front propagates backwards over the entire channel length. The final dry deposit of particles is thereby much thicker than the initial volume fraction of the suspension. Deposition depth is characterized by 3D imaging profiler, whereas the deposition topography is revealed by scanning electron microscope (SEM). The patterning technology described here is robust and passive, hence operates without an external field. This work may well become a launching pad to construct low cost and large-scale thin optoelectronic films with a variable thickness and inter-spacing distances.

Keywords: Capillarity, Wetting, Evaporation, PDMS, Hydrophilic, Suspension, Transport, Deposition

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1. INTRODUCTION Particle-laden droplet on a smooth solid surface transports particles from the interior of the drop towards the periphery due to evaporation-induced radial capillary flow along the free surface. In combination with a pinned contact line, this leaves behind a ring-like morphology of closely packed particles, by what is known as the coffee-ring effect.1-3 The effect is attributed to nonuniform evaporation and gradient of surface tension, which induces surface-flow from the middle of the droplet to replenish the solvent lost at the periphery where evaporation is highest due to the wedge geometry.1,3-5 Coffee-ring and related effects have attracted considerable attention in assembly of nanoparticles (NPs),6-10 and blockcoplymers,11,12 in patterning technologies,14-18 to produce photonic crystals19-21 and for deposition of large-scale aligned DNA nanowires,22 DNA/RNA microarrays,23,24 as well as manufacturing electronic25 and optical materials26 along with thin films and coatings.27-30 Uncontrolled coffee-ring effect suffers from inherent inhomogeneous deposition of particles, which has detrimental effects on uniformity of coatings, in many patterning applications such as high-resolution inkjet-printing.1,31 To date, significant progress has been achieved in understanding the underlying mechanisms of coffeering formation,1-3,5 as well as controlling the particle deposition. 27-29, 32-35 However, exploiting the coffee-ring effect to fabricate uniform and large scale multifarious functional patterns is still a challenging task.36-40 One possible approach, pursued herein, is to use wettability or geometric patterning of the solid surface to guide the liquid spreading. In this work we report such capillary-driven deposition of particulate-formed networks, based on evaporative lithography in open polydimethylsiloxane (PDMS) channels, by utilizing various nano- and micro-particle suspensions. This approach successfully fabricates high quality two-dimensional (2D) continuous metal patterns at room temperature from various suspensions and in different geometries. The process begins by placing a millimetre size drop of the colloidal suspension onto plasma treated loading reservoir connected to a channel or a network of interconnected channels. Hydrophilic condition enables rapid spreading of the suspension along the channel length. Subsequent evaporation-driven particle motions within the channel lead to the formation of a deposition/drying front and eventual de-wetting. This particle deposit begins at the channel dead-end and proceeds to move along the channel length back to the reservoir. This spreading and deposition is accomplished passively, i.e. does not require any external power source, such as syringe pumps, but requires strong surface wettability and controlled channel geometry. The entire fabrication process (see Fig. 1) is divided into three regimes: (i) rapid wetting flow of the suspension from the reservoir to fill the entire length of the microchannel, (ii) evaporation induced convective flow of the suspended particles towards the evaporation site (channel deadend) and (iii) slow back-trajectory of the particle-deposition front, which continuously sediments the particles to form a regular wire-structure. The dynamics within each flow regime are examined by high-speed video imaging to determine the velocities and deposition mechanism. Deposition topography is revealed by scanning electron microscope (SEM), whereas, the deposition thickness is characterized by 3D imaging profiler. The technology described here is simple, yet versatile to fabricate various defect-free 2D structures. In addition to various geometrical channel-patterns, we show that the system also


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Figure 1. Schematic representation of an open PDMS-based microchannel surface-tensiondriven evaporative lithography system. (a) Loading reservoir connected to a meandering microchannel. The channel wetting drives flow from the reservoir (blue arrow) until particles jam and fill the channel, with a deposition front moving backwards (gray arrow). (b) Stepwise schematic of the particle-suspension in the reservoir (top); The suspension spreads along the hydrophilic channel through wetting (middle); Evaporation continues to pull in new suspension until the particles concentrations becomes sufficiently high to jam and form a deposit, thereby constructing a continuous regular 2D structure, with a deposition/drying front moving towards the reservoir (bottom). works efficiently for both aqueous- and organic-solvent-based nano- and micro-particle suspensions. This self-driven patterning technology has a potential to be tailored for continuous flow applications for micro-devices at industrial scale. In addition, our method could well replace or perform in conjunction with existing technologies41-43 to create transparent and conductive coatings of metallic structures to overcome the challenges associated with transparent conductive films. These earlier approaches have been based on evaporation-driven particle assembly from suspensions driven by ordered templates, formed by either pre-fabricated evaporative masks,44 ordered latex particles crystals,45-48 micro-wire screens,49,50 or photoresist templates.51 Furthermore, our new method may be important for promoting particle accumulation and concentration in bio-chemical assays.

2. EXPERIMENTAL 2.1. Materials & Reagents The patterning of the solid surface was accomplished with PDMS photolithography. PDMS Sylgard 184 elastomer was purchased from Dow Corning (Midland, MI, USA). SU-8 negative tone photoresist and propylene glycol methyl ether acetate developer (PGMEA) were supplied by MicroChem Corp. (Newton, MA, USA). Both nano- and micro-particles were used in the experiments. The nano-particle suspensions were the following: Silver ink containing ≤50 nm silver nanoparticle (AgNP) of 30-35 wt % in triethylene glycol monomethyl ether and CdSe quantum dots of an average size of 2.3 nm and concentration of 5 mg/mL in toluene were


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purchased from Sigma Aldrich and used as received. Water suspension of 10 to 20 nm gold nanoparticle (AuNP) of about 2 wt % was synthesized using a sodium citrate and poly (vinyl pyrrolidone) assisted protocol reported earlier.51 Magnetic nanoparticles (with a concentration of 10 mg/mL and average size of 500 nm) were purchased from Micromod Partikeltechnologie GmbH, Germany. For the larger micro-particles we used Latex microspheres (1 µm size) purchased from Sigma Aldrich. The microsphere-suspension used in this work was washed twice in Deionized (D.I.) water, each time being sonicated for 30 minutes to remove excess surfactant and break up particle-particle aggregations. The particles were dried overnight under vacuum at room temperature, and re-dispersed (1 wt.%) in D.I. milliQ water. DI water was used throughout the micro-particle experiments. The reason for selecting big-size microspheres, in addition to the nano-particle suspensions, was to allow for tracking of the particle motions within the liquid bulk, which is difficult to investigate in the case of NP suspensions. 2.2. PDMS Device Fabrication Two main channel-configurations were used in the experiments. First, a single continuous channel, to study the dynamics of particle motions and secondly, square wire-networks for assessing potential applications. Master moulds with the desired patterned channels are fabricated by conventional photolithography using SU-8 photoresist on a silicon wafer. Multiple copies of the PDMS-replica containing the microchannel grooves can be fabricated from a single lithographic master. Figure 1(a) illustrates the schematic experimental set-up of a PDMS-based continuous meandering microchannel. The dimensions of various PDMS-channel based networks used in this work are given in Electronic Supplementary Information (ESI-1). These microchannels consist of two main regions, a long curved channel and a circular loading reservoir. The patterned PDMS-substrate is supported on a flat glass-slide with the open channels facing away from the glass surface into free air. Prior to deposition of the suspension, which initiates the flow, the originally hydrophobic surface of the microfluidic device is plasma treated (Harrick PDC-002) to render the channels hydrophilic. The PDMS devices were then used within 30 s of the surface modification. Plasma exposure time of 30 s was kept constant throughout the course of the experiment. Hydrophilic and hydrophobic surface modifications were characterized by contact angle measurements on both untreated, and plasma treated PDMS surfaces. 2.3. Transport and Deposition Characterization The flow of the suspension from the circular loading reservoir into the PDMS micro-channels and the evaporation-driven deposition of particles inside the channels were recorded at different frame rates, with a high-speed CMOS video camera (Phantom V1610) mounted on an optical microscope, operating between 50 to 25,000 fps. The topography of the resulting deposits is revealed by scanning electron microscope (SEM), whereas, the deposition thickness is characterized by 3D profiler (Scanning White-light Interferometry (SWLI), Zygo New View 7200/7300).


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Figure 2. Optical images extracted from a high-speed video representing evaporation-induced convective flow of microspheres. The particles are advected downwards in the direction of the white arrow, whereas the deposition front moves in the opposite way, indicated by the black arrow, leaving behind the particle deposit.

3. RESULTS AND DISCUSSIONS 3.1. Microsphere deposition Figure 1(a, b) illustrates the core concept of the liquid spreading and particle deposition process in this work, in a long meandering open PDMS microchannel connected to a loading reservoir. This involves the capillary-driven wetting of the suspension and subsequent evaporation-induced particle deposition (supplementary video file-1 for spreading). The dry channel is drawn in light blue, while the dark-blue colour indicates the wet channel following the spreading of the suspension from the reservoir into the main channel to fill its entire length. During and after the spreading the continuous evaporation concentrates the particles and keeps pulling more liquid/particles from the circular reservoir, until eventually the particles aggregate to form a deposit, which is indicated by the gray color. This deposition front propagates backwards leaving behind the dry particle deposit. The channel widths were in the range 5-10 µm and channel depth is 5.6 µm. We study first the flow in a single 10 µm wide meandering channel, using micron-sized particles to allow detailed tracking of the particle dynamics, while showing results for channel networks at the end. Each experiment begins by exposing the patterned PDMS-substrate to plasma, thereby, turning it hydrophilic. The deposition of microspheres into multi-layered structures over the entire channel length is confirmed by high-speed camera, Figure 2(a-h) (see also supplementary video file-1). The suspended particles under evaporation are randomly accumulated into a continuous wire-deposition. Figure 3(a, b) shows optical microscopic images of the microchannel before and after particle deposition. The particle deposition is confirmed by SEM (Figure 3c). In some isolated cases we observe hexagonal arrangements of 1µm latex particles, as revealed by optical and SEM images (Figure 3d-e). Figure 3e shows one of the many closely


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Figure 3. (a) Optical micrograph of a grooved microchannel before suspension injection, (b) microchannel with deposited 1 µ size microspheres with a concentration of 1 wt.% in D.I. water and (c) SEM micrograph of a small section of deposited structure as shown in panel (b). The SEM image in panel (c) is taken at 40ᴼ tilt, Inset: Height profile of microsphere deposition across the microchannel length, characterized by 3D profiler (Scanning White-light Interferometry (SWLI), Zygo New View 7200/7300. (d) High magnification top-view optical image of closely packed particles after evaporation and (C) top SEM image of regularly deposited microspheres in microchannel (as shown in panel d), the image is captured at 0ᴼ tilt. The channel width is 10 µm, whereas the channel depth is 5.6 µm. packed patches within the channel, which are interspersed by more random segments. From this SEM image, one may speculate that some attractive forces (particle-particle and particle-PDMS attractive forces) may play a role, when the particles are pushed close to each other. The amount of suspension available in the reservoir is critical for continuous deposition. Insufficient supply of suspension results in partial deposition in the channel (ESI-2). The loading reservoir connected to the channel/channel network gives this approach a potential to construct patterns based on various suspensions under low concentration, which may not be possible otherwise. We can continuously feed the reservoir with supply of suspension to attain desired results.


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3.2. Wetting phase For the spontaneous spreading of the suspension within an open channel on the PDMS-substrate we require it to be hydrophilic to allow for rapid wetting.52-54 This was achieved with the wellknown technique of plasma treatment, explained above. This is best demonstrated in supplemental information, ESI-3, where we show the resulting contact angle which decreases from ~86o, before surface treatment, while immediately following the plasma treatment it reduces drastically to ~6o, supporting rapid spreading along the channel. Similar wetting behaviour is observed for the nano-particle suspensions discussed in later sections. The total spreading dynamics is investigated in a meandering microchannel with a total length of 5.7 mm Fig. 4 (see also supplementary video file-2), using high-speed video to first track the motion of the spreading liquid front. Figure 4(a) shows this liquid front velocity as a function of distance from the liquid reservoir, for three different liquids, with their properties listed in Table 1. In all cases, the front decelerates when it travels further along the channel. Also our channel is open to the air and the channel geometry clearly effects the wetting, as is demonstrated by the liquid tongues, which move along the bottom corners well ahead of the central wetting line. This confines the spreading within the channel, even though the surrounding PDMS is also equally hydrophilic. The insets in Fig. 4a show close-up images of the spreading front at = 1.2 mm and = 2.6 mm. The local meniscus length in the corners, in the latter is about 3 times that of the former. Liquid

Surface tension σ (N/m)

Viscosity µ (Pa.s)

Water

0.0721

0.00100

3/1 (v/v) Water/Glycerol

0.0703

0.00235

5 cSt Silicone oil

0.0193

0.00458

Table 1. Properties of the D.I. water, water/glycerol mixture and silicon oil used in the experiments. Room temperature was kept at 21 °C. Generally, the capillary-driven motion of a liquid in a small tube follows the Lucas-Washburn law (Lucas (1918)55; Washburn (1921)56), which states = √ with = 2 cos /μ,

(1)

where is the distance of capillary rise, is the time, is the liquid surface tension, is a characteristic channel length scale, like its width, is liquid dynamic viscosity and is the contact angle. This law holds with the assumptions that gravity is insignificant, as well as the constancy of the contact angle . Recently Qúeré́ and co-workers57,58 gave a universal scaling law for the meniscus rise, for different geometries with a corner, showing indefinite rise even against gravity, progressing as a power-law ⁄ ~ ⁄ /, where = / is the


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Figure 4. (a) Velocity of the wetting front as a function of spreading distance . Inset shows the spreading front images at = 1.2 mm and = 2.6 mm. Blue arrows mark the length of the meniscus, which travels fastest along the corner within the channel. (b) Measured liquid spreading distance , normalized by the effects of surface tension and viscosity, versus √. (c) Measured spreading front velocity , versus √. (d) Particle velocity as a function of distance from liquid reservoir. Liquid is 1 wt.% of 1 µm diameter particles in D. I. water. = 0 is here set as the moment when the spreading front reaches = 1 mm. The end of each curve represents the x-location of the particle deposit. (e) Particle velocities relative to deposition front. The distance from reservoir x is shifted to the right, so the deposit fronts overlap at x=6 mm, by adding !, where ! is the length of the channel section with dense packing of particles. (f) Velocity of the deposition front as a function of distance from the reservoir. The arrow indicates the direction of the front with time.


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capillary length based on liquid density and the acceleration of gravity . Herein, gravity is not considered, as we have a horizontal channel configuration. Also, the suspension fully wets the channel after plasma treatment (~6°), the balance between the driving capillary pressure and viscous friction therefore justifies our use of the basic Lucas-Washburn law (1), i.e. ~2 ⁄ .

(2)

Consequently the spreading velocity should follow ~ ⁄2

(3)

Figure 4(b) shows the relationship between measured spreading distance L versus time. Data for the three different liquids follow eq. (2) quite well and collapse on a single curve, with a fitting pre-factor of 0.25. Figure 4(c) shows the corresponding relationship between measured spreading velocity versus time. Again, the data must follow eq. (3) and collapse on a single curve, using the same pre-factor of 0.25. The wetting front eventually reaches the end of the channel and stops. 3.3 Particle motions and the deposition front The spreading and particle deposition phenomenon is not only characterized by the wetting velocity, but three fundamentally different velocities must be considered. Besides the above spreading velocity of the wetting line, there is also the separate velocity of the particles within the suspension, as well as the retracting velocity of the deposition front of particles, which eventually fills up the channel to form the wire-structure. After the channel is fully filled with the suspension, the much slower process of solvent evaporation, from the channel surface, becomes the driving force for pulling new suspension into the channel from the circular reservoir. The particle deposition and eventual drying is initiated from the dead-end of the channel. The reason why the particle-deposition front is initiated at the channel dead-end is owing to the continuing liquid evaporation in the channel during the spreading phase, which effectively increases the particle concentration toward the end of the channel, where the liquid has travelled the longest distance and thus has had the most time to evaporate. This effect is demonstrated in the Figure 5, which shows snapshots taken, shortly after the channel is fully filled with the microsphere-based suspension (Fig. 5a) and AuNP-based suspension (Fig. 5b). The gradient in the colour of the suspension along the channel in this figure is due to the increase in the particle concentration, with dark liquid at the end having evaporated and concentrated for longer time then lightercoloured liquid which has just enter the channel. We also note that particles are often attracted by the hydrophilic meniscus towards the walls, see theoretical treatment in Refs. [59-61]. We do therefore not expect any particle-free zone at the dead-end of the channel, were the particle deposit starts to form, for both 5 and 10 µm wide channels. We expect the same dynamics to apply for even wider channels, if they are smaller than the capillary length.


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Figure 5. Optical images extracted from video tracking of evaporation-driven deposition of (a) latex particle-based suspension and (b) AuNP-based suspension inside a 10 µm wide channel. The snapshots are taken shortly after the channel has filled with the spreading suspension. (c,d) Optical images of a long square-shaped microchannel, showing the effects of continuous open air evaporation. (c) The suspension front has stopped spreading midway in the channel after traveling two full circles. (b) Image at a later time, after evaporation-driven concentration of the deposition and full drying of a dark layer of nano-particles. The feeding reservoirs in (c) and (d) are in the lower-left corners. In the above setup, the suspension fills the entire channel before deposition of the particles begins. However, with an even longer channel the tip of the spreading suspension is often observed to pin and stop the spreading. This is understood by the continuing evaporation during the spreading phase, which for sufficiently long channels allows the particle concentration at the front to reach some critical level, where deposition or contact-line pinning can occur. Figure 5 (a,b) and supplemental videos (1 and 2) show such a case, where the increased particle concentration is evident during the spreading phase. We conclude that for very long channels one may need to reduce the evaporation rate during the spreading phase. This can be accomplished by adding a solid covering over the grooved surface without touching the liquid, or by temporarily saturating the air above the channel during the spreading phase only, while one


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Figure 6. Close-up view of concave meniscus captured during the wetting of nanoparticle-ink suspension flowing through a microchannel with a width of 10 µm (a) before plasma and (b) modified by plasma for 30 s. The video for monitoring the meniscus motion was captured at 50 fps. (c) Optical microscopic image of microchannel after the deposition, spreading and drying of silver-ink (30-35 wt% of AgNPs in triethylene glycol monomethyl ether). The uniformity of the silver color demonstrates the continuous nature of the deposit. (d) SEM image of the dried channel with deposited silver-ink, (e) magnified SEM image of the random nanoparticle deposition as shown in panel (d). (f) Height profiles characterized by 3D profiler (SWLI), across the micro-channels, before and after the deposition and drying of the AgNP-deposition. would remove the cover during the evaporative phase. In Fig. 5(c) we have shown a case where the spreading liquid has travelled two whole circles (∼2.8 mm), but stops in a sharp corner in the lower left of the image, where the geometry may help pin the meniscus. Having characterized the spreading velocity of the liquid front, we now focus on the velocities inside the suspension by following micro-particles in high-speed video sequences, taken under


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the microscope. Supplementary video file-3 illustrates the particle motions in a close-up region of a channel area of 400 µm in length, taken at 200 fps. Figure 4(d) shows the velocity of the particles moving inside the liquid. We assume the particles follow approximately the local liquid flow and we measure particles near the center of the channel where the velocity is largest, away from the no-slip boundary condition at the walls. Each curve shows the particle velocities, at a particular instant in time, as a function of the distance along the channel. All data show linear decrease in particle velocity further along the channel, which are here plotted in terms of the distance from the reservoir. The velocities approach zero where they encounter the deposition front. All these data collapse on a single curve (Fig. 4e) after they are shifted to represent the distance relative to the deposition front where the depositing particles accumulate. This is done by adding !, where ! is the length of the channel section with dense packing of particles. Here x is the variable, while ! is constant for each curve. Let’s assume there is a uniform rate of evaporation along the entire liquid section of the channel, up to the point of the assembled deposit. Since the flow rate of solvent from the reservoir replenishes the liquid evaporating from the channel surface, we see that the flow-rate at some location x must be proportional to the remaining distance from x to the front of the deposit which is currently at Ltot - S, where Ltot is the total length of the channel. For Fig. 4(d) Ltot ∼ 6 mm. At any particular time we therefore expect a linear decrease in the flow velocity with distance x away from the reservoir, as measured by the particles traveling along the channel. This is clearly confirmed by the linear decrease of particle velocity in Figure 4(d,e). The slope of these curves is determined by the evaporation rate. Finally, Figure 4(f) shows the slow retreating velocity of the deposition front, from the dead-end of the channel towards the reservoir. The figure shows a linear decrease in this velocity as the front approaches the reservoir, i.e. small x. This can be understood by the exit velocity of the liquid from the reservoir. Figure 4(e) showed that this exit velocity is proportional to the length of channel from the reservoir to the deposition front. In other words, a longer wet channel, which has larger area available for evaporation, will demand more influx of liquid from the reservoir into the channel. When the wetted section of the channel is longer, more particles are therefore pulled along with this flow per time and the channel cross-section will fill faster and the deposition front thereby grows and moves faster in the direction against the particle flow. We also note that for the particle velocities dup/dx ≠ 0 and therefore the particle density is “compressible”, thereby increasing the number of particles per unit volume as the flow approaches the deposition front. Note that the typical deposition front velocity (∼50 µm/s) is three orders of magnitude slower than the original wetting speed of the liquid front of ∼40 mm/s. Typical particle velocities are between these two extremes, of the order of 2 mm/s. Figure 2 showed a close-up sequence of video frames of the propagation of the deposition front within the channel. It is important to highlight that deposition rates for our configuration are determined by the length of the channel from the reservoir to the deposition front. This is controlled by the strong evaporation from the narrow channel, acting as a line-source. This differs fundamentally from the deposition of monolayers at the “contact line” of an evaporating drop, or of a film on a flat surface, where the local dynamics at the edge of the evaporating film determine the particle deposition rates [59-61]. In that configuration the rate of evaporation from the drop is fairly constant and much lower than that in the thin precursor film. The precursor film pulls in liquid and with it particles. Interstitial liquid between the particles has curved menisci, with increased


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free-surface area and negative capillary pressure which both enhance evaporation in the monolayer film. The capillary pressure also pulls in more liquid from the drop into the thin film, while being counteracted by Darcy friction in the flow between the particles. The edge of our particle deposit is also wet and adds to the evaporation, pulling in some liquid into the porous particle network. However, we think this is a secondary effect, which is likely to remain approximately constant while the deposition front moves closer to the reservoir. Indeed if evaporation from the surface of the porous particle deposit were setting the liquid flow-rate then the liquid/particle velocities along the entire un-obstructed wet channel would be constant, not linearly decreasing with x, as is seen in Figure 4(d). The question remains: what is driving the flow from the reservoir along the channel, once the rapid wetting phase has stopped. Evaporation itself could simply dry the entire channel at the same time, depositing particles vertically onto the channel floor, until it is all dry with a thin layer of particles. This is not observed and we suggest two driving mechanisms, both of which likely play a role. Evaporation cools the liquid elements, progressively so as they move further along the channel. As colder liquid has stronger surface tension, this can set up gradients of surface tension σ, promoting Marangoni stresses with dσ/dx > 0, similar to the proposed driving force in the coffee-ring effect [1-3]. Alternatively, the evaporative loss of liquid along the channel pulls the meniscus down in the middle of the channel width, while hydrophilicity pins the meniscus at the lip of the channel. This will generate a capillary suction pressure, also producing a driving force through a pressure gradient dp/dx

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