Dynamics of Capillary-Driven Flow in 3D Printed Open Microchannels

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Dynamics of Capillary-Driven Flow in 3D Printed Open Microchannels Robert Kevin Lade, Erik J. Hippchen, Christopher W. Macosko, and Lorraine F. Francis Langmuir, Just Accepted Manuscript • DOI: 10.1021/acs.langmuir.6b04506 • Publication Date (Web): 08 Mar 2017 Downloaded from http://pubs.acs.org on March 11, 2017

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Dynamics of Capillary-Driven Flow in 3D Printed Open Microchannels Robert K. Lade Jr., Erik J. Hippchen, Christopher W. Macosko, and Lorraine F. Francis*

Department of Chemical Engineering and Materials Science, University of Minnesota – Twin Cities, 421 Washington Ave. SE, Minneapolis MN, 55455, United States

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Abstract Microchannels have applications in microfluidic devices, patterns for micromolding, and even flexible electronic devices. Three-dimensional (3D) printing presents a promising alternative manufacturing route for these microchannels due to the technology’s relative speed and the design freedom it affords its users. However, the roughness of 3D printed surfaces can significantly influence flow dynamics inside of a microchannel. In this work, open microchannels are fabricated using four different 3D printing techniques: fused deposition modeling (FDM), stereolithography (SLA), selective laser sintering, and multi jet modeling. Microchannels printed with each technology are evaluated with respect to their surface roughness, morphology, and how conducive they are to spontaneous capillary filling. Based on this initial assessment, microchannels printed with FDM and SLA are chosen as models to study spontaneous, capillary-driven flow dynamics in 3D printed microchannels. Flow dynamics are investigated over short (~10–3 s), intermediate (~1 s), and long (~102 s) timescales. Surface roughness causes a start-stop motion down the channel due to contact line pinning while the cross-sectional shape imparted onto the channels during the printing process is shown to reduce the expected filling velocity. A significant delay in the onset of Lucas-Washburn dynamics (a long-time equilibrium state where meniscus position advances proportionally to the square root of time) is also observed. Flow dynamics are assessed as a function of printing technology, print orientation, channel dimensions, and liquid properties. This study provides the first in-depth investigation of the effect of 3D printing on microchannel flow dynamics as well as a set of rules on how to account for these effects in practice. The extension of these effects to closed microchannels and microchannels fabricated with other 3D printing technologies is also discussed.

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Introduction Three-dimensional (3D) printing is a rapidly developing technology with incredible adaptability that has accelerated its adoption across an array of disciplines. Influences of 3D printing can be found in aerospace1 and automotive2 manufacturing, biomedical engineering,3–5 and even modern art and architecture. Recent efforts have also been made to establish 3D printing in the field of micro-scale manufacturing. The design freedom that the technology offers—an ability to print complex and 3D structures with a potentially wide array of materials—is particularly appealing.6 Microchannels are one important feature present in many micro-manufactured devices. These micron-scale capillary structures are particularly important in many microfluidic devices,7 enabling rapid mixing,8,9 separation,10,11 or diagnostic12,13 processes to be carried out using small volumes of sample fluid. Microchannels are also used in micromolding applications,14 heat sinks for small-scale electronics,15 electrospray tips,16,17 capillary chromatography,18 and printed electronics manufacturing.19 3D printing has proven to be an effective alternative for manufacturing devices that contain these microchannels. For example, selective laser melting (SLM) has been used to fabricate capillary columns out of metal, which were successfully integrated into a liquid chromatography device. 20 3D printed microfluidic devices have garnered particular interest as they can be manufactured quickly at a relatively low cost with minimum manual labor, presenting distinct advantages over prevailing methods of microfluidic chip fabrication.7 For example, one device21 printed with stereolithography (SLA) was used to achieve precise, micro-scale mixing and another device,22 fabricated using fused deposition modeling (FDM), was successfully used for nanoparticle synthesis and electrochemical detection. Microchannels were integral components of both of these devices. Open microchannels (also known as microgrooves or U-grooves) are particularly useful in low cost diagnostic devices where flow can be driven entirely by capillarity.7,13 Paper-based microfluidics commonly take advantage of this phenomenon, spontaneously wicking liquid down microchannels bounded by hydrophobic regions printed directly onto the paper.23,24 The evaporation that naturally accompanies flow in open microchannels can also be exploited to coat and functionalize the channel surface. For example, if a conductive ink is flowed through an open microchannel, the ink (upon evaporation) leaves behind a 2 ACS Paragon Plus Environment

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conductive trace, which can act as a wire in a circuit.19,25 This concept has even been used to fabricate entire electronic devices by creating complex patterns of open microchannels and flowing a suite of inks into the different channels.26 A similar approach has also been used to create catalytically active microchannel surfaces.27,28 How fluid flows through these channels and interacts with their surfaces is fundamental to their performance. If the surface properties of the channel are not favorable, flow can be severely inhibited or even prevented. This is a concern particularly in the case of 3D printed microchannels as 3D printed parts are well-known to possess rough and sometimes porous surfaces. In extrusion-based processes, such as FDM, this roughness results from the layer-by-layer nature of the printing process;29 the individual printed strands of material can also be rough. The surfaces of some SLA parts also possess a characteristic roughness associated with the laser path used to cure the printing resin.30 Powder-based processes, such as selective laser sintering (SLS), SLM, and electron beam melting, also produce parts with a characteristic surface roughness.20,31,32 Flow dynamics in smooth microchannels (both open and closed) have been studied extensively; a good review of the literature is provided by Ouali et al.33 During spontaneous capillary filling, a liquid progresses through different flow regimes during which the relationship between the position of the advancing meniscus, x, and time, t, changes. In the limit of "long" times (typically t ≳ 1 ms), x increases proportionally the square root of t: x(t) ~ t1/2 ,

(1)

as described by Lucas34 and Washburn.35 This Lucas-Washburn behavior results from a balance of capillary and viscous forces, and has been investigated and verified for both open23,33,36–38 and closed33,39 microchannels as well as for a variety of cross-sectional geometries.36–38,40,41 The specific impact of 3D printed surfaces on microchannel flow dynamics remains largely unexplored, and previous work has only suggested that 3D printed topography may disturb laminar flow.42 However, surface topography is well-known to alter the liquid-solid contact angle of spreading droplets43– 45

and can lead to contact angle hysteresis and anisotropy.45–50 Surface roughness acts to locally increase an

advancing contact angle above its equilibrium value (that defined by Young’s equation45,51), and can slow 3 ACS Paragon Plus Environment

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or even stop (‘pin’) flow.45,46,52 Pinning can be permanent or temporary, and in the latter case the contact line eventually depins, subsequently ‘jumping’ forward53 and continuing to flow until it hits another pinning point. During capillary filling, local pinning-depinning (or "start-stop") events have been observed along microchannels fabricated with rough walls.54,55 This same phenomenon has also been observed and/or predicted along microchannels patterned with protruding rectangular54,56,57 and triangular54,58 posts. Girardo et al.59 show that even nanoscopic roughness on microchannel walls can lead to friction effects unaccounted for in the Lucas-Washburn equation, resulting in overall slower capillary filling. In this paper, the morphology and surface properties of open microchannels printed with four different 3D printing technologies are evaluated: FDM, SLA, SLS, and multi jet modeling (MJM). FDM and SLA are shown to produce microchannels most conducive to capillary flow. Accordingly, FDM- and SLA-microchannels are assessed with respect to the flow dynamics of the liquids they imbibe. Both printing processes are shown to impart a different surface topography to the microchannels and, accordingly, different flow dynamics during capillary filling. For the first time on 3D printed surfaces, we analyze the effect of surface roughness on contact line motion as well as its influence on the relationship between x and t over time—behavior over five orders of magnitude (10–3–102 s) is investigated. We show that pinning induced by the surface roughness delays the onset of Lucas-Washburn behavior while also reducing the expected flow velocity due to a decrease in the capillary force. Cross-sectional geometry and print orientation are also shown to have a distinct influence on the flow. Based on these findings, a set of recommendations for practically dealing with the unique flow effects in 3D printed microchannels is introduced. Insight into how these recommendations can be extended to closed microchannels and microchannels fabricated with other 3D printing technologies is also presented.

Experimental Microchannel design.

The microchannel computer aided design (CAD) model is shown in Fig.

1a. Channels are 50 mm in length with rectangular cross sections. A circular reservoir is connected to the top of the channel with a diameter such that its volume is equal to or greater than the volume of the channel. Channel widths, W, ranging from 80–1000 µm and channel depths, H, ranging from 16–1000 µm were specified in the CAD models. 4 ACS Paragon Plus Environment

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Microchannel fabrication. Fused deposition modeling (FDM) microchannels were printed on a Dimension 1200es printer (Stratasys, Ltd., Eden Prairie, MN) using acrylonitrile-butadiene-styrene (ABS; P-400, Stratasys, Ltd.) and a 254 µm layer height. Each part was printed in one of three orientations, as illustrated in Fig. 1b. By default, the print head rasters back and forth at 45° or -45° in the x-y plane (alternating between layers) and by rotating the part on the build stage, different microchannel topographies are obtained. These topographies are shown in Fig. 2. As-printed FDM-microchannels are porous and thus were coated with a thin layer of photocurable resin (NOA73, Norland Products, Inc., Cranbury, NJ)) after printing to make the channel watertight. Stereolithography (SLA) microchannels were printed using a Form 1+ printer (Formlabs, Somerville, MA) with a photocurable resin (methacrylic acid esters and photoinitiator, clear color, Formlabs) and a 50 µm layer height. Parts were angled at 10° from the horizontal during printing (Fig. 1c). After printing, parts were soaked in two sequential isopropanol baths for 10 and 8 min, respectively, to remove uncured monomer from the part surface. Parts were then cured under UV light (366 nm, ~1.2 mW/cm2) for 1 h. The 1 h post-cure was found to reduce the tackiness of the part surface. Selective laser sintering (SLS) microchannels were printed offsite60 using an EOS P396 SLS machine and PA2200 Balance 1.0 Nylon 12 powder (EOS GmbH, Krailling, Germany) with an average layer height of 120 µm. Unsintered powder was removed from the channels using a combination of vibration and bead blasting. Multi jet modeling (MJM) microchannels were also printed offsite61 on an Objet 500 Connex 3 or Objet 260 Connex 3 PolyJet 3D printer (Stratasys, Ltd.) using a transparent acrylate resin (VeroClearRGD810, Stratasys, Ltd.) and a 16 µm layer height. Parts were printed either with or without a waxy support material (SUP705, Stratasys, Ltd.) inside the channels, which was removed with water jets after printing. Microchannels were also fabricated via photolithography to provide a standard for comparison against the 3D printed channels. A master microchannel mold was first fabricated in a silicon wafer using standard photolithographic techniques. Then, using a two-step molding process described previously,19 the silicon master mold was used to obtain 92.7 µm deep microchannels embedded in a flexible, plastic substrate (NOA73, Norland Products, Inc.) with widths ranging from 50–500 µm. 5 ACS Paragon Plus Environment

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Additional details on microchannel fabrication using the above-mentioned five technologies can be found in the Supporting Information. Analysis of surface topography.

Microchannel surface topography was measured using a

mechanical stylus profilometer (P-16, KLA-Tencor, Milpitas, CA). Measurements were taken over scan lengths of 1–5 mm and reported roughness values represent averages from measurements on at least three different samples printed with identical parameters. Glycerol solution characterization.

Aqueous glycerol solutions were used for all flow tests

(Table 1). Water concentration was used to adjust viscosity and a sodium dihexyl sulfosuccinate surfactant solution (MA-80, Cytec Industries, Inc., Woodland Park, NJ) was used to adjust surface tension (a change in the equilibrium contact angle was also coupled to this adjustment). Blue food dye (FD&C Blue #1, Target Corp., Minneapolis, MN) was added to each solution (40 µL per 20 mL of solution) to enhance flow visualization. Control tests with liquid containing no dye revealed that the dye did not significantly influence the liquid properties or flow. Solution viscosity was measured using an AR-G2 stress-controlled rheometer (40 mm, 2° steel cone and plate geometry; TA Instruments, New Castle, DE). All solutions are Newtonian over the relevant range of shear rates (0.1–100 s–1). Surface tension and contact angle were measured using pendant drop shape analysis and sessile drop measurements, respectively (DSA-30, Krüss GmbH, Hamburg, Germany). To minimize the influence of surface roughness on the measured contact angles, smooth test surfaces were fabricated. These surfaces were processed to be chemically equivalent to the surfaces of our 3D printed microchannels but with minimal surface roughness. For our FDM material, this was done by pelletizing the ABS printing filament and hot pressing the pellets into small, smooth coupons at the printing temperature (300°C). For our SLA material, a smooth testing surface was fabricated by first curing approximately 2 mL of resin onto a glass slide. The post-printing procedure described above for the SLA-microchannels (isopropanol bath and post cure) was then performed on the resin-coated slide. All surfaces were plasma treated (PDC-32G, Harrick Plasma, Ithaca, NY) with air (0.5–1 torr) for 60 s before testing. Measured solution properties and contact angles on FDM and SLA surfaces are reported in Table 1.


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Table 1. Glycerol solution properties and contact angles on 3D printed surfaces Glycerol conc.a Viscosity Surface tension Solution (w/w) (mPa∙s) (mN/m) Standard 0.86 ± 0.01 81 ± 3 64.7 ± 0.3 Medium viscosity 0.70 ± 0.01 42 ± 1 64.5 ± 0.4 Low viscosity 0.60 ± 0.01 9±1 70 ± 1 Low surface tension 0.86 ± 0.01 81 ± 3 30.1 ± 0.5 a Mass fraction of glycerol in solution b Equilibrium contact angle of glycerol solution on indicated surface

Monitoring capillary flow.

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Contact angleb (°) FDM SLA 38 ± 3 41 ± 2 38 ± 3 41 ± 2 38 ± 3 41 ± 2 19 ± 3 15 ± 2

A digital optical microscope (KH-7700, Hirox USA, Hackensack, NJ)

with a 50–400x lens (Hirox MX(G)-5040Z zoom lens with mid-range adapter) was used to monitor capillary filling. Microchannels were first plasma treated as described above and positioned under the microscope. A liquid drop (with volume equal to that of the reservoir) was then dispensed into the reservoir. Care was taken to dispense the droplet into the center of the reservoir so that, upon deposition, the droplet quickly and uniformly wet the reservoir. Flow was recorded at 1, 7.5, or 15 frames per second (fps) over intervals ranging from 3 to 200 s. The position of the advancing meniscus (taken at the center of the microchannel) in each frame was extracted using ImageJ (v1.48v, NIH). A position of zero was assigned to where the microchannel intersects the reservoir and times of zero were set to coincide with the moment the liquid passed this point. The data in Figs. 5a, 6a, 6b, and 7a, however, are an exception to this convention: the zero point was set relative to an arbitrary starting point, as described in the corresponding figure captions. Videos were also recorded at a higher frame rate to capture the high-speed liquid dynamics. Microchannels were plasma treated as described above, positioned under a lens (Zoom 6000 system with 3 mm FF zoom lens (Model No. 1-6232) and 2x standard adapter (Model No. 1-6030), Navitar, Rochester, NY), and illuminated with a fiber optic light. During flow, video was captured with a high speed camera (Fastcam Ultima APX, Model 120 K, Photron, Tokyo, Japan) at 125 or 250 fps. All visualization experiments were performed at room temperature (23 (± 1)°C). Independent experiments confirm that neither water loss (via evaporation) nor water absorption (due to the hygroscopy of glycerol) have a significant impact on the results.


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Theoretical analysis An exact analytical solution for spontaneous capillary filling in a horizontal microchannel was derived by Bosanquet in 1923:62 𝑥 2 (𝑡) =

2𝑏 (𝑡 𝑎

1

− 𝑎 {1 − exp⁡(−at)}) ,

(2)

which is valid when the microchannel is smooth and possesses a constant depth and width, the properties of the liquid are invariant, and contact line shape and contact angle are static. In Eq. (2), x is the distance of the liquid meniscus from the entrance (x = 0) of the microchannel, t is time, and a and b are coefficients indicative of the strengths of the viscous and capillary forces in the system, respectively, with larger values corresponding to larger forces. Several approximations33,37 for the coefficients a and b have been derived for open microchannels with a rectangular cross-sectional geometry. Assuming the liquid front is a slab moving uniformly down the channel, Ouali et al.33 approximate a and b as: 3η −1 𝑓 (H, W) ρH2

(3)

γ 2𝐻 ) − 1] [cos𝜃𝑒 (1 + ρH 𝑊

(4)

a= b=

where η, γ, and ρ are the liquid viscosity, surface tension, and density, respectively, H and W are channel depth and width, respectively, θe is the equilibrium contact angle, and f is a geometric function dependent on microchannel geometry: f

–1

(H,W) ≈ 1 + 0.671004(H/W) + 4.169711(H/W)2. To account for non-

rectangular cross-sectional geometries, Eqs. (3) and (4) can be expressed more generally as: η

a = ρ 𝑔(𝐻, 𝑊, … ) b=

γ (𝑝 cos𝜃𝑒 − 𝑝𝑓 ) ρ𝐴𝑐 𝑤

(5) (6)

where g, like f, is a geometry-dependent function, Ac is the cross-sectional area of the channel, and pw and pf are the wetted and non-wetted (free surface) perimeter lengths of the channel cross section.24,33,63 In the limit of long times (t >> 1/a), Eq. (2) simplifies to: 𝑥 2 (𝑡) ≈

2𝑏 𝑡 𝑎

= 𝑘𝑡 ,

where k ≡ 2b/a. The velocity, v, in the channel at any given time can thus be expressed as: 8 ACS Paragon Plus Environment

(7)

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𝑣(𝑡) =

𝑘 2√𝑘𝑡

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.

(8)

Eq. (7) is often referred to as the Lucas-Washburn (LW) equation,34,35 and represents the long time limit of capillary flow where viscous and capillary forces are dominant and x increases proportionally to the square root of time (𝑥⁡~⁡𝑡1/2 ). Eq. (2) instead predicts 𝑥⁡~⁡𝑡 at early times64 and 𝑥⁡~⁡𝑡1/2 only at long times (t > 10/a); the difference between Eqs. (2) and (7) is that the former accounts for inertial forces.33,62 For channel depths on the order of 100 µm, the transition to LW behavior is expected to occur after 10–5– 10–3 s, depending on the viscosity of the liquid. Traditionally, Eq. (7) is the standard against which most experimentally measured capillary flows are compared. Given that even the longest “long” time is on the order of 10 ms, most experimentally measured flows do indeed satisfy the long time requirement. While Eq. (7) has been validated for both open23,33,36–38 and closed33,39 channels and for a variety of channel geometries,36–38,40 the assumptions listed above are suspect for 3D printed microchannels. Specifically, the assumptions of a smooth microchannel surface and a constant contact line shape during flow. In the next several sections, we explore capillary filling dynamics in 3D printed microchannels while also framing the results in the context of classic LW theory.

Results and Discussion Microchannel geometry and surface topography. Representative cross sections of microchannels printed with FDM, SLA, SLS, and MJM are shown in Fig. 3. Each printing process imparts a unique crosssectional geometry to the channels. FDM-microchannels have rounded walls due to the circular extrusion nozzle used for printing, with printed strands approximately 400 µm wide and 250 µm in height. Microchannels printed with SLA or MJM (without support) exhibit a characteristic ‘U’ shape due to slight sagging of the printing liquids during fabrication. In contrast, microchannels printed with MJM (with support) and SLS hold their rectangular shapes well. However, walls of channels fabricated using these two technologies are rough. In SLS, this is due to the roughness of the printing powder (diameter ≈ 30–60 µm) and in MJM (with support) the wall roughness arises upon removal of the support, which creates a rough interface where the model and support material droplets overlapped during printing. 9 ACS Paragon Plus Environment

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Using the three print orientations illustrated in Fig. 1b, three different surface topographies can be obtained in FDM-microchannels (Fig. 2). These topographies are dictated by the orientation of the channel walls with respect to the print direction of the layer forming the base of the channel. The printed strands in this base layer may be oriented diagonal to (Fig. 2a), parallel with (Fig. 2b), or perpendicular to (Fig. 2c) the channel walls. The surface topography (measured along the x-axis) associated with each of these print orientations is shown in Figs. 2d-f, along with the corresponding RMS roughness (Rq) values. Coating the channels did not significantly alter measured values of Rq due to the thinness of the coating. The surface roughness in the channels is a superposition of both a large- and small-scale roughness. The large-scale roughness results from the orientation of the printed strands whereas the small-scale roughness is due to the roughness of the plastic itself. Thus, channels printed in a parallel orientation only possess small-scale roughness. Fig. 4 shows representative top views of microchannels printed with each technology as well as the corresponding surface topographies (measured along the x-axis) and associated Rq values. As in the FDMmicrochannels, the surface topography of SLA-microchannels (Fig. 4g) is a superposition of roughness on two different length scales. The large-scale roughness (the parabolic peaks) originates from the Gaussianlike intensity distribution of the laser used to cure the resin, which results in a printed, cured line with a similar parabolic shape.30 The small-scale roughness (Fig. 4g inset) is due to the roughness of the cured resin. On SLS-microchannels, the surface topography (Fig. 4h) was observed to be isotropic and reflects the size of the powder used for printing. The individual powder particles also possess some small-scale topography, but this roughness was not characterized. Channels printed with MJM are relatively smooth compared to channels fabricated with other technologies. Roughness on MJM-microchannels printed with support is small and random (Fig. 4i) whereas the roughness when printed without support is periodic, with 1–3 µm repeating features approximately every 500 µm (Fig. 4j). This repeating topography may be an artifact of the discrete droplets used for printing. SEM micrographs highlighting the small-scale surface topography on microchannels printed with each technology are presented in Fig. S2.


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The dimensional accuracy of channels printed with each technology was assessed as a function of channel width, depth, and print orientation (where applicable). Detailed results are presented in the Supporting Information, along with minimum-printable channel dimensions for each technology. Channel dimensions reported herein are actual, measured values of the printed parts, not dimensions specified in the CAD models, unless otherwise specified. As neither FDM- nor SLA-microchannels are exactly rectangular, widths reported herein are approximations. Widths were approximated by averaging channel width over the entire channel depth in FDM-microchannels. SLA-microchannel widths were approximated by recording the width where channel depth was equal to half of the total channel depth. Assessing viability for spontaneous capillary flow. For a microchannel to be conducive to spontaneous capillary filling, two requirements must be met: the channel must be watertight and the contact angle must be low enough to permit spontaneous filling24,63(𝑐𝑜𝑠𝜃𝑒 > 𝑝𝑓 /𝑝𝑤 ). We found that SLA- and FDM-microchannels satisfied both requirements. However, channels fabricated with our FDM printer required a thin coating before they became watertight, as described above. (Note that, in general, FDMmicrochannels are not necessarily porous, e.g. see Ref. [65]). In contrast, microchannels produced using SLS were very porous (even after coating). Additionally, the resolution limit (~750 µm minimum channel width) was not competitive with what we could achieve with FDM and SLA (~300 µm). MJMmicrochannels printed with support are watertight but the base of the channel is highly hydrophobic (θe = 71° with water after plasma treatment), prohibiting spontaneous capillary filling. MJM-microchannels printed without support satisfy both requirements for flow, but the printing process does not yield channels with a well-defined cross section (see Fig. 3e). Ultimately, FDM and SLA were chosen as model technologies for our study because of their popularity as well as the above-mentioned disadvantages of SLS and MJM. However, as will be discussed, the results of this study can be generalized to microchannels fabricated with other 3D printing technologies. Capillary flow dynamics: Contact line motion.

A distinct contact line behavior was observed for

each of the three FDM-microchannel orientations tested and in SLA-microchannels. These behaviors were captured at a high temporal resolution using high speed video. Fused deposition modeling. Fig. 5a shows a representative plot of meniscus position and velocity vs 11 ACS Paragon Plus Environment

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time for the simplest case of flow in a microchannel with a parallel orientation (i.e. only small-scale roughness present) and Fig. 5b shows an image sequence of this flow. While the average position increases linearly with time (R2 > 0.99), the instantaneous velocity fluctuates widely around an average, vavg, of 0.42 mm/s due to the roughness of the channel surface which induces local pinning and depinning events at the contact line. This pinning causes micro-scale deformations of the contact line and leads to inhomogeneous wetting. This is evidenced by the varying contact line shapes seen in Fig. 5b. A video of flow in an FDMmicrochannel printed with a parallel orientation is shown in Movie S1 in the Supporting Information. Pinning occurs because there is an energetic barrier associated with changing the shape of the contact line as it moves over topography.46,48 As upstream liquid flows to the pinned contact line, the contact angle can locally increase and if a threshold (larger) contact angle is reached, depinning occurs. During depinning, the contact line moves through a series of metastable configurations before either relaxing back to the equilibrium contact angle or pinning on another obstacle. This depinning energy comes from the higher free energy associated with the larger contact angle reached just before depinning.50,53 These pinningdepinning events can occur concurrently in multiple locations along the contact line, causing its shape to fluctuate during flow. Similar behavior has been predicted56,57 and observed experimentally54,55,58 in channels with rough walls. Fig. 6 shows meniscus position and velocity for capillary filling in a microchannel printed in a perpendicular orientation. Here the liquid must interact with both the roughness of the printed plastic and the large-scale roughness imposed onto the microchannel base by the curvature of the printed strands. In Fig. 6a, the relationship between meniscus position and time is again linear overall (R2 > 0.99; vavg = 1.3 mm/s), but there is also a large increase (“pulse”) in the velocity approximately every 0.4 s. Fig. 6b matches the channel topography (top) with the velocity profile (bottom). Dashed lines have been drawn from the bottom of each trough (local minimums in topography) to guide the eye. Each pulse initiates just before the contact line reaches the center of each trough and ends approximately 200 µm downstream. This behavior was observed in all microchannels with a perpendicular orientation, regardless of liquid properties or microchannel size. Fig. 6c shows an image sequence of the flow described in Figs. 6a and 6b. Following the first pulse 12 ACS Paragon Plus Environment

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(t = 0.3 s), the contact line is relatively uniform, except for two small fingers at each edge (i). These fingers are caused by the region of high curvature at the intersection of the wall and the base of the microchannel24,63,66–69. As the contact line approaches a trough (indicated by a vertical dashed line), it maintains this shape (aside from small deviations due to local, random roughness). However, over this time the average flow velocity drops from 1900 (i-ii), to 850 (ii-iii), and finally to 440 µm/s (iii-iv). Once the contact line wets the region just before the trough, the liquid quickly flows forward (v-vi), with an average velocity of 2800 µm/s. This process repeats down the length of the channel and gives a visual effect of a pulsing flow. A video of flow in an FDM-microchannel printed with a perpendicular orientation is shown in Movie S2 in the Supporting Information. Each pulse is caused by the rapid wetting of the trough by the contact line. The trough region is conducive to rapid wetting both due to its high curvature as well as its increased depth with respect to the rest of the channel. Locally increasing channel depth increases the wetted perimeter while leaving the nonwetted perimeter constant, momentarily increasing the capillary driving force (see Eq. (6)).54 During an individual pulse, two flow scenarios can occur. If one liquid finger reaches the trough first (e.g., the bottom finger in Fig. 6c(v)), it bifurcates. Part of that finger continues to flow as before while the rest moves perpendicular to the main flow direction along the trough. For reasons mentioned above, the flow inside the trough is very fast and once it spreads to the other side of the channel, the rest of the meniscus (including the second finger) can quickly wet the trough and the area immediately downstream, causing the contact line to pulse forward. Alternatively, if both fingers reach the trough simultaneously, they both bifurcate and meet in the middle of the channel, again causing the center of the contact line to quickly pulse forward. The contact line behaviors illustrated in Figs. 5 and 6 represents the two extreme cases of flow in FDM-microchannels. Contact line motion in microchannels with a diagonal orientation closely resembles that observed in channels printed with a perpendicular orientation, due to the presence of large-scale topography. The main difference arises due to the large-scale topography being oriented at 45° with respect to the direction of flow in diagonally oriented channels instead of 90°. This causes the fingers to always reach the trough at different times and results in two smaller pulsing events at each trough, separated in 13 ACS Paragon Plus Environment

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time and space. Data similar to those presented in Fig. 6 for flow in diagonal microchannels can be found in the Supporting Information. Note that contact line motion in microchannels with large-scale topography is a superposition of two types of motion: pulsing and local pinning-depinning events. The latter type pervades all three FDMmicrochannel orientations due to the inherent roughness of the printing material. While pulsing dominates the observable motion in channels with perpendicular and diagonal orientations, local pinning-depinning can still influence the overall flow dynamics, as will be discussed later. Stereolithography.

Fig. 7a shows an image sequence of flow in an SLA-microchannel, where a

characteristic pulsing motion is also observed. The contact line is initially relatively even over the width of the channel (i; channel curvature and a high contact angle can suppress finger formation24,33,37). When the bottom of the contact line reaches the trough (ii; indicated by a vertical dashed line), it continues to flow forward but also begins to move inward toward the other side of the channel along the trough, creating a liquid finger (iii; notice the similarities between Figs. 6c(v) and 7a(iii)). When this newly formed liquid finger reaches the other edge of the channel, the contact line quickly pulses forward over the already wetted trough (iv). The contact line then returns to its original shape further down the channel (v). Fig. 7b plots meniscus position and velocity vs time for flow in an SLA-microchannel. The relatively large jump in velocity around t = 0.3 s corresponds to the pulsing event shown in Fig. 7a. Due to the suppression of liquid fingers in the SLA-microchannel, the velocity change with each pulse is less dramatic than in FDM-microchannels. The observed local variation in velocity can again be attributed to local pinning-depinning events caused by small-scale surface roughness. As chemical heterogeneities can also contribute to contact line pinning,45 several tests were conducted to assess the chemical homogeneity of our FDM and SLA surfaces. These tests revealed that neither material possesses a significant degree of chemical heterogeneity. A description of this testing procedure can be found in the Supporting Information. Photolithography.

Microchannels fabricated via photolithography always had a smooth contact line

motion and exhibited no pulsing or pinning. Additional information on contact line shape and motion in channels fabricated via photolithography can be found in the Supporting Information. 14 ACS Paragon Plus Environment

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Capillary flow dynamics: Filling velocities.

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To monitor filling velocities, flow was recorded

over intermediate timescales (1–10 s) at 7.5 or 15 fps. Note the extended timescale of these experiments compared to those in the previous section. Fused deposition modeling. Fig. 8a shows representative plots of meniscus position vs time for capillary filling in diagonally oriented, FDM-microchannels of various widths. Channels of diagonal orientation were chosen for this case study as their topography represents an intermediate configuration between parallel and perpendicular orientations. Again, a distinguishing feature of these flow curves is the presence of a pulsing motion caused by the large-scale channel topography. Wider channels exhibit slower filling velocities and longer times between pulsing events. Figs. 8b-d compare filling velocities in diagonal microchannels as a function of channel depth, liquid viscosity, and liquid surface tension/equilibrium contact angle, respectively. Reported velocities are averages obtained using regression and taking the slope at a distance of 1 mm down the channel (x = 1 mm). For a fixed channel width, larger filling velocities are observed in our experiments when channel depth is increased (Fig. 8b) or when liquid viscosity (Fig. 8c) or surface tension/equilibrium contact angle (Fig. 8d) are decreased. Larger velocities are associated with faster pulsing motions and shorter pinningdepinning events. Though data is only reported at x = 1 mm in Figs. 8b-d, the conclusions made above were found to hold further down the channel as well (Fig. S11). The observed increase in filling velocity upon decreasing viscosity agrees with the predictions of Eqs. (5) and (8) as well as results observed in microchannels fabricated via photolithography (Fig. S8c). Increasing channel depth is also predicted to increase filling velocity, as it decreases viscous resistance while increasing pw (and hence capillary force) in Eq. (6). Both surface tension and equilibrium contact angle are affected by the introduction of a surfactant into the system. The contact angle and surface tension are both reduced by approximately half when surfactant is added (compare ‘standard’ and ‘low surface tension’ solutions in Table 1); given this change, Eqs. (4) and (8) predict a decrease in filling velocity for microchannels with a rectangular cross section due to the associated reduction in b. Filling velocities in microchannels fabricated via photolithography followed this expectation (Fig. S8d). However, we observe the opposite effect in our FDM-microchannels, 15 ACS Paragon Plus Environment

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as shown in Fig. 8d. This anomaly is due to the unique cross-sectional geometry of our FDM-microchannels and, more specifically, to the relative magnitudes of pw and pf in Eq. (6). For example, consider the crosssectional image in Fig. 3a. Because the liquid can wet nearly to the top of the walls, the free surface contribution to the total cross-sectional area (pf) is relatively large. This permits the low surface tension/low contact angle scenario in Fig. 8d to be more energetically favorable, increasing the capillary force (via an increase in b), and hence increasing the flow velocity. As Fig. 8d illustrates, this trend holds for all channel widths tested. Fig. 9a compares flow curves for FDM-microchannels printed in three different orientations. The qualitative differences in contact line motion discussed previously are apparent in the shape of each curve and these differences hold regardless of channel size or liquid properties. Fig. 9b reports filling velocities vs width for channels printed in each orientation (at x = 1 mm). The Fig. 9b inset shows the same data plotted vs aspect ratio (W/H) to help account for small differences in channel depth that arise when printing in different orientations. Despite print orientation strongly influencing contact line motion during capillary filling, it is not observed to have a significant influence on average filling velocity. Similar results are obtained if velocity is measured further down the channel (Fig. S9d). These results suggest that while largescale topography influences the macroscale appearance of the flow and contact line motion, the small-scale roughness (present on all FDM-microchannel surfaces) predominantly governs the average filling velocity. Regardless of channel dimensions, liquid properties, or print orientation, flow in our FDMmicrochannels was always observed to be slower than predicted for rectangular channels with equivalent dimensions (using Eqs. (3) and (4) with same average width and depth). For example, liquid traveling in a 150 µm x 250 µm (W x D) channel (with same liquid properties as in Fig. 9b) is predicted to flow 1 mm in 0.04 s and (at x = 1 mm) possess a velocity of 12 mm/s. In contrast, flow in our FDM-microchannels requires ~1 s to reach x = 1 mm, where we observe a flow velocity of approximately 1.2 mm/s (for the conditions described in Fig. 9b). Part of this observed discrepancy may be attributable to the cross-sectional shape of our FDM-microchannels. By approximating the channel as rectangular with a width equal to the average, pf is greatly underestimated. While pw is also underestimated using this method, the effect is less dramatic. This rectangular approximation results in an overestimation of both the capillary force (via b) and 16 ACS Paragon Plus Environment

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filling velocity. This example illustrates the risk associated with imposing the cross-sectional geometry of the original CAD model onto the 3D printed channel. Surface roughness, contact angle hysteresis, and entrance effects may also play a role in reducing the observed filling velocity in our 3D printed microchannels. This point is discussed more in the next section. Stereolithography.

Meniscus position vs time for capillary filling in SLA-microchannels is shown in

Fig. 10a for several channel widths. Filling velocity in SLA-microchannels exhibits the same dependence on viscosity, surface tension/contact angle (Fig. 10b), and channel depth as is observed in FDMmicrochannels. The ‘anomalous’ change in velocity observed in Fig. 10b when surface tension/contact angle are both reduced can again be attributed to the geometry of the microchannels and the relatively large contribution of pf to the total cross-sectional area. Observed filling velocities are also lower than expected for equivalent rectangular channels for the same reasons as discussed above. Capillary flow dynamics: Filling behavior at long times.

The value of the exponent n in

the relationship between meniscus position, x, and time, t (x ~ tn (Eq. (1))) characterizes a capillary flow regime. As discussed previously, classic LW theory predicts n = 0.5 in the limit of long times whereas Quéré64 showed that n = 1 when t 150 s), flow persists but

continues to decelerate, following the trend predicted by Eq. (8) and observed in Fig. 11. Despite the strong contact line pinning, permanent pinning (stoppage) of the flow was never observed. With sufficient time,


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flow in both FDM- and SLA-microchannels was always observed to reach the end of the 50 mm channels used in this study.

3D printed microchannel flow assessment and recommendations Table 2 summarizes flow effects that can occur during capillary filling in 3D printed microchannels and how to approach them in practice. These guidelines are developed for open FDM- and SLA-microchannels, but can in general apply to other 3D printing technologies as well as closed channels, as discussed below. Table 2. Flow effects in 3D printed microchannels Effect

Description/cause

Recommendations

Nonuniform contact line motion

Roughness causes local pinning of contact line, leading to nonuniformity. Large-scale topography may cause pulsing.

Adjust print orientation to avoid largescale topography, if possible. Avoid applications requiring smooth, uniform flow.

Altered filling velocity

Cross-sectional geometry imparted by 3D printer can influence velocity. Surface roughness and dynamic contact angle effects reduce velocity.a

Plan for velocities lower than predicted by theory. Run tests to identify range of expected velocities. Carefully analyze geometry of printed channel.

Delayed onset of LW behavior (n = 0.5)b

Surface roughness and dynamic contact angle effectsa increase time required to reach LW behavior.b

n ≈ 0.5 requires t > ~106/a.c In many applications, n will likely fall between 0.6 < n < 1.

a

Other factors, such as fingers formed along corners and entrance effects, may also play a role in this effect Lucas-Washburn (LW) behavior means n = 0.5 in the relationship x ~ tn, where t is time and x is meniscus position (see Eq. (1)) c a approximated by Eq. (3) b

Contact line motion is nonuniform due to pinning-depinning events caused by surface roughness and a macroscale pulsing motion may also accompany any large-scale topography. It is important to consider if and how this behavior affects the microchannel’s intended application. For example, if two phase laminar flow with minimal mixing is sought, a 3D printed microchannel may not be appropriate as the surface topography can lead to undesired mixing.74 In other cases, the disturbance of laminar flow induced by the surface roughness may be desirable, e.g. in the case of micro-scale mixers.75,76 For diagnostic tests where liquid must simply be transported around a chip, details of the contact line motion may be irrelevant to the performance of the device. To attain smooth and/or uniform flow, FDM-microchannels printed in a parallel orientation are 20 ACS Paragon Plus Environment

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recommended. However, few will be able to always accommodate such a design constraint. In these cases, surface roughness effects can be alleviated by coating the channel to fill in troughs between printed strands. Solvent treatments77 may also help to smooth out parts; this method is, however, only compatible with some printing materials (e.g. ABS). Employing other 3D printing technologies with naturally smoother surfaces like MJM (see Figs. 4i,j), SLA printers employing digital light projection,75 or multi-photon direct laser writing (DLW)78,79 is also possible. As with FDM and SLA, these printing methods have their own disadvantages7 that must be considered alongside the advantage of a smoother channel surface. Capillary filling velocities in 3D printed microchannels are expected to be different than velocities predicted based on the geometry of the original CAD model. This is due to a combination of imperfectly reproduced channel geometries and surface roughness. Whereas surface roughness is always predicted to decrease velocity, the channel cross section printed by a specific 3D printer could, in theory, either decrease or increase the observed velocity beyond the expected value. For example, the ‘expected’ filling velocity for channels specified by the CAD model in Fig. 1a (a perfectly rectangular channel) is defined by Eqs. (3), (4), and (8). In this study, both our FDM and SLA machines recreated rectangular microchannel geometries such that the observed filling velocity was always lower than this expected value. Channel dimensions were also always different than specified in the CAD models (see Figs. S3–S6). Decreasing viscosity, contact angle, or channel width will increase filling velocity (channel sizes below a minimum aspect ratio (W/H) can reduce velocity) as will increasing surface tension (for a constant contact angle) or channel depth. Eqs. (5) and (6) can be used to predict how filling velocity will scale with specific variables (e.g. viscosity) in 3D printed microchannels, but not to predict actual velocity magnitudes. Caution must be exercised in estimating the values of pf and pw, as they can change with print technology or even print orientation for the same CAD model. In practice, it is recommended to run several tests to identify the range of velocities expected by a specific liquid–channel pairing. Overall, this reduced capillary filling velocity effect is expected to be more severe in rougher microchannels. The observed relationship(s) between contact line position and time in a microchannel will depend on the liquid, the channel surface, and total channel length. Our results suggest that smoother channels exhibit a lower value of n at early times (~0.9 for FDM/SLA channels, ~0.6 – 0.7 for channels fabricated 21 ACS Paragon Plus Environment

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via photolithography, but all channels require t ~ 105/a – 106/a to reach n ≈ 0.5. Depending on the properties of the system, this could equate to times on the order of seconds to tens of minutes. Whether or not the liquid reaches the LW equilibrium state therefore depends on total channel length. Higher viscosity liquids are associated with larger values of a and lower filling velocities, making them more likely to reach n ≈ 0.5 before reaching the end of a channel. In practice, however, microfluidic devices commonly employ low viscosity liquids and channels that are only several millimeters in length. In this case, LW behavior is not expected to be established by the time most liquids reach the end of the channel. As a general rule, n will not reach 0.5 unless (a) the microchannel is long (> 50–100 mm) and the region of interest is near the end of the channel or (b) the liquid has a high (>100 mPa∙s) viscosity. Otherwise, it should be expected that 0.6 < n < 1. Again, this effect is expected to be more dramatic for rougher channels. The effects discussed in Table 2 can be generalized to other 3D printing technologies when the surface roughness and/or cross-sectional geometry of the parts they produce is well characterized. For example, channels printed with powder based processes (e.g. SLS) have an isotropic roughness on the entire channel surface made up of protruding, spherical powder particles. Based on this roughness profile, we can expect an uneven contact line motion over both the base and walls of the channel. Pinning-depinning events on two different length scales are also expected: small-scale pinning on the topography of the individual powder particles and larger scale movements as the contact line jumps from one powder particle to another. Even DLW, where surface roughness has been shown to be on the order of nanometers, 78,80 has a periodic topography that we expect would lead to small-scale pulsing during flow. However, this effect would likely only be noticeable as channel dimensions approached those of the topography (< 100 nm). The recommendations outlined in Table 2 are also expected to apply to closed microchannels fabricated via 3D printing. Altering the channel geometry (closed vs open) does not significantly impact the nature of the surface roughness and flow in both open and closed microchannels is governed by analogous sets of governing equations33 (i.e. Eqs. (5–8)). In practice, this means that those employing closed, 3D printed microchannels are likely to encounter the effects listed in Table 2. While the exact nature of the contact line motion will differ from that observed in this work, the tactics to understand and


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accommodate roughness effects discussed herein should also be effective for 3D printed, closed microchannels.

Summary and conclusions Microchannels were fabricated using four different 3D printing techniques: fused deposition modeling (FDM), stereolithography (SLA), selective laser sintering (SLS), and multi jet modeling (MJM). Microchannels can be fabricated using all four technologies, but each printing method is associated with distinct advantages and disadvantages. Microchannels fabricated via SLA and FDM were found to offer the best compromise between print resolution and surface properties (surface roughness, hydrophilicity, low porosity). FDM-microchannels have rounded walls imposed by the curvature of the printed strands while SLA-microchannels are ‘U’ shaped. Both types of channels possess unique large- and small-scale surface topographies which can be attributed to the different printing processes. Flow dynamics in FDM- and SLA-microchannels were evaluated over short (~10–3 s), intermediate (~1–10 s), and long (~102 s) timescales using high speed visualization. Flow in both types of channels was found to exhibit a characteristic start-stop motion caused by local pinning of the contact line on the smallscale surface roughness (Rq ≈ 2 µm). Superimposed over this pinning is a macroscale pulsing motion of the contact line caused by the large-scale surface topography (Rq ≈ 20 µm); in FDM-microchannels, this largescale topography is a function of print orientation. It was found that the small-scale roughness reduces the capillary force driving flow down the channel and, coupled with the unique cross-sectional geometry of the channels, acts to lower filling velocity at all times. An unexpected exponential relationship between meniscus position, x, and time, t, (where x ~ tn (Eq. (1))) was also observed in our 3D printed channels. Lucas-Washburn (LW) theory predicts n = 0.5 in Eq. (1) after ~ 1 ms whereas we observe 0.6 < n < 1 when t < 10 s with n only approaching 0.5 at long times (t > 30 s). Delays in the onset of LW behavior were also observed in rectangular microchannels fabricated using photolithography and are consistent with observations in the literature by others. Lastly, a set of recommendations for dealing with the unique flow effects (listed in Table 2) caused by 3D printed microchannels was presented. This guide provides details on the origin of each effect as well 23 ACS Paragon Plus Environment

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as strategies for approaching each potential problem. These guidelines can also be extended to channels fabricated with other 3D printing technologies when the geometry and roughness of the parts they produce is known. Analogies can then be drawn between the characteristics of the FDM-and SLA-microchannels presented here. Likewise, these guidelines can also be applied to 3D printed, closed microchannels. This work represents the first comprehensive investigation of flow dynamics in 3D printed microchannels. It should serve as a tool for those designing and employing 3D printed microchannels in practice. By better understanding flow dynamics, microchannel design can be optimized to complement or even augment its functionality.

Associated Content Supporting Information Fabrication details for all microchannels, analysis of small-scale surface roughness on 3D printed surfaces, dimensional accuracy of all printed parts, capillary filling dynamics in microchannels fabricated via fused deposition modeling (diagonal orientation) and photolithography, flow velocity data at distances of x = 3 mm from channel entrance, an evaluation of the chemical homogeneity of our 3D printing materials, and a derivation of capillary imbibition accounting for a roughness- and velocity-dependent dynamic contact angle. This material is available free of charge via the Internet at http://pubs.acs.org.

Author Information Corresponding authors * (L.F.F.) E-mail: [email protected] Notes The authors declare no competing financial interests.

Acknowledgements The authors would like to thank the industrial supporters of the Coating Process Fundamentals Program (CPFP) of the Industrial Partnership for Research in Interfacial and Materials Engineering (IPRIME) for supporting this research. This work was also supported by funding through MnDRIVE at the University of Minnesota. The authors also extend their gratitude to Wieslaw Suszynski for high speed video assistance, Yan Wu for some SEM imaging, Satish Kumar for helpful discussions, and Luke Rodgers and Brian Sabart at Stratasys for printing microchannels with multi jet modeling. Parts of this work were carried out in the Characterization Facility, University of Minnesota, which receives partial support from the NSF through the MRSEC program, and the Minnesota Nano Center, which receives partial support from the NSF through the NNCI program.


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Van Weeren, R.; Agarwala, M.; Jamalabad, V. R.; Bandyophadyay, A.; Vaidyanahan, R.; Langrana, N.; Safari, A.; Whalen, P.; Danforth, S. C.; Ballard, C. Quality of Parts Processed by Fused Deposition. Proceedings of the Solid Freeform Fabrication Symposium, Austin, TX, Aug. 7–9, 1995.

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Garcia, C. R.; McHale, G.; Tsang, H. H.; Barton, J. H. Effects of Extreme Surface Roughness on 3D Printed Horn Antenna. Electron. Lett. 2013, 49, 734–736.

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Ouali, F. F.; McHale, G.; Javed, H.; Trabi, C.; Shirtcliffe, N. J.; Newton, M. I. Wetting Considerations in Capillary Rise and Imbibition in Closed Square Tubes and Open Rectangular Cross-Section Channels. Microfluid. Nanofluid. 2013, 15, 309–326. 26 ACS Paragon Plus Environment

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Kusumaatmaja, H.; Pooley, C. M.; Girardo, S.; Pisignano, D.; Yeomans, J. M. Capillary Filling in Patterned Channels. Phys. Rev. E 2008, 77, 067301.

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Queralt-Martín, M.; Pradas, M.; Rodríguez-Trujillo, R.; Arundell, M.; Corvera Poiré, E.; Hernández-Machado, A. Pinning and Avalanches in Hydrophobic Microchannels. Phys. Rev. Lett. 2011, 106, 194501.

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Mognetti, B. M.; Yeomans, J. M. Capillary Filling in Microchannels Patterned by Posts. Phys. Rev. 27 ACS Paragon Plus Environment

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Chibbaro, S.; Costa, E.; Dimitrov, D. I.; Diotallevi, F.; Milchev, a; Palmieri, D.; Pontrelli, G.; Succi, S. Capillary Filling in Microchannels with Wall Corrugations: A Comparative Study of the ConcusFinn Criterion by Continuum, Kinetic, and Atomistic Approaches. Langmuir 2009, 25, 12653– 12660.

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SLS-microchannels were printed by Xometry, Inc. (www.xometry.com)

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Object 500 parts were printed at Stratasys (Eden Prairie, MN) and Object 260 parts were printed at the Medical Devices Center, University of Minnesota (Minneapolis, MN).

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Dolomite’s ‘Fluidic Factory’ produces parts using FDM that are watertight after printing with no post-processing (http://www.dolomite-microfluidics.com/webshop/fluidic_factory)

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Schumann, M.; Bückmann, T.; Gruhler, N.; Wegener, M.; Pernice, W. Hybrid 2D – 3D Optical Devices for Integrated Optics by Direct Laser Writing. Light: Sci. Appl. 2014, 3, 1–9.

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Malinauskas, M.; Farsari, M.; Piskarskas, A. Ultrafast Laser Nanostructuring of Photopolymers : A Decade of Advances. Phys. Rep. 2013, 533, 1–31.

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Figures

Figure 1. (a) Microchannel schematic, units in mm. Cross section shows slice from z-y plane. Not to scale. (b) Top view of FDM-microchannels on build stage. Indicated orientation is with respect to rotation in the x-y plane. During printing, the print head rasters back and forth at 45 or -45° in the x-y plane. (c) Side view of SLA-microchannel on build stage. SLA parts are printed upside down with the channel facing away from the support.


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Figure 2. Schematic of FDM-microchannel orientations obtainable using print configurations shown in Fig. 1b, where topography of base layer of channel is (a) diagonal to, (b) parallel with, or (c) perpendicular to the wall layer(s). Arrows indicate direction of capillary flow. Surface topography (measured along xaxis) and corresponding RMS roughness (Rq) for (d) diagonal, (e) parallel (inset: same data, expanded scale), and (f) perpendicular print orientations.


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Figure 3. SEM micrographs of cross sections of microchannels printed using (a) fused deposition modeling (FDM; diagonal orientation), (b) stereolithography (SLA), (c) selective laser sintering (SLS) (d) multi jet modeling (MJM; with support), and (e) MJM (without support). Scale bars: 100 µm.


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Figure 4. SEM micrographs of top views of microchannels printed using (a) fused deposition modeling (FDM), (b) stereolithography (SLA), (c) selective laser sintering (SLS), (d) multi jet modeling (MJM; with support), and (e) MJM (no support). Topography and RMS roughness (Rq) values from surface profilometry of microchannel surfaces, measured along x-axis, for microchannels printed using (f) FDM (inset: topography along y-axis), (g) SLA (inset: topography along y-axis), (h) SLS, and MJM (i) with and (j) without support (insets (i,j): same data, expanded scale). (a-e) Scale bars: 1 mm.


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Figure 5. (a) Relative meniscus position and velocity vs time for capillary filling in an FDM-microchannel with parallel orientation (data taken in center of microchannel). Average velocity, vavg, indicated with horizontal dashed line. (b) Image sequence of flow. Arrow indicates flow direction. Scale bar: 200 µm. Times and positions are relative to an arbitrary start point, not the start of flow into the microchannel. Position ‘0’ corresponds to a distance approximately 3 mm from the channel entrance (x ≈ 3 mm). [Channel: W = 324 (± 63) µm, D = 242 (± 16) µm; Liquid: ‘Standard’ solution (𝜂 = 81 mPa∙s, γ = 64.7 mN/m, θe = 38°)].


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Figure 6. (a) Relative meniscus position and velocity vs time for capillary filling in an FDM-microchannel with perpendicular orientation (data taken in center of microchannel). Average velocity, vavg, indicated with horizontal dashed line. (b) Velocity profile of capillary filling (bottom) aligned with approximate channel topography (top). (c) Image sequence of flow. Arrow indicates flow direction. Scale bar: 200 µm. Times and positions are relative to an arbitrary start point, not the start of flow into the microchannel. Position ‘0’ corresponds to a distance approximately 1 mm from the channel entrance (x ≈ 1 mm). In (b) and (c), vertical dashed lines indicate location of a trough and the common trough is indicated with an asterisk [Channel: W = 200 (± 31) µm, D = 285 (± 12) µm; Liquid: ‘Standard’ solution (𝜂 = 81 mPa∙s, γ = 64.7 mN/m, θe = 38°)].


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Figure 7. (a) Image sequence of capillary filling in an SLA-microchannel. Arrow indicates flow direction and vertical dashed line indicates location of a trough. Scale bar: 200 µm. (b) Relative meniscus position and velocity vs time for flow in an SLA-microchannel. Average velocity, vavg, indicated with horizontal dashed line. Times and positions are relative to an arbitrary start point, not the start of flow into the microchannel. Position ‘0’ corresponds to a distance approximately 1 mm from the channel entrance (x ≈ 1 mm). [Channel: W = 352 (± 6) µm, D = 220 (± 4) µm; Liquid: ‘Standard’ solution (𝜂 = 81 mPa∙s, γ = 64.7 mN/m, θe = 41°)].


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Figure 8. (a) FDM-microchannel flow curves for channels of indicated width. Velocity at a distance of 1 mm from channel entrance (x = 1 mm) vs width as function of indicated (b) microchannel depth, (c) liquid viscosity, and (d) surface tension [contact angle]. All microchannels printed in diagonal orientation. In (a), (c), and (d), reported depth is average from all channels represented in plot. Liquid is ‘standard’ solution (𝜂 = 81 mPa∙s, γ = 64.7 mN/m, θe = 38°) unless otherwise indicated.


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Figure 9. (a) Flow curves for FDM-microchannels printed in indicated orientation. Diagonal, parallel, and perpendicular channels have widths of 239 (± 54), 207 (± 55), and 200 (± 31) µm and depths of 243 (± 10), 235 (± 20), and 285 (± 12) µm, respectively. (b) Velocity at a distance of 1 mm from channel entrance (x = 1 mm) vs width for FDM-microchannels printed in indicated orientation. Inset: Same data plotted vs aspect ratio (W/H). In (b), diagonal, parallel, and perpendicular channels have average depths of 245 (± 21), 250 (± 22), and 283 (± 15) µm, respectively. Liquid is ‘standard’ solution (𝜂 = 81 mPa∙s, γ = 64.7 mN/m, θe = 38°).


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Figure 10. (a) Flow curves for SLA-microchannels of indicated widths. (b) Velocity at a distance of 1 mm from channel entrance (x = 1 mm) vs width in SLA-microchannels at indicated liquid surface tension [contact angle]. In (a) and (b), reported depths are averages from all SLA-microchannels [Liquid is ‘standard’ solution (𝜂 = 81 mPa∙s, γ = 64.7 mN/m, θe = 41°), unless otherwise indicated].


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Figure 11. (a,b,c) Long-time flow curves for FDM-microchannels of indicated orientation. (a,b) W = 239 (± 54), 207 (± 55), and 200 (± 31) µm for diagonal, parallel, and perpendicular orientations, respectively. (c) W = 640 (± 47), 530 (± 22), and 609 (± 19) µm for diagonal, parallel, and perpendicular orientations, respectively. In (a), inset shows same data enlarged at early times. (d) Long-time flow curves for SLAmicrochannels at indicated widths and depth. Liquid is ‘standard’ solution (𝜂 = 81 mPa∙s, γ = 64.7 mN/m, and θe = 38°(a,b,c) or θe = 41°(d)).


Dynamics of Capillary-Driven Flow in 3D Printed Open Microchannels

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