Cleaning of fluid-infused surfaces in microchannels - Langmuir (ACS

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Cleaning of fluid-infused surfaces in microchannels Yongjian Li, Xiangyu Hu, Shuaishuai Liang, Jiang Li, and Haosheng Chen Langmuir, Just Accepted Manuscript • DOI: 10.1021/acs.langmuir.8b02237 • Publication Date (Web): 26 Sep 2018 Downloaded from http://pubs.acs.org on September 28, 2018

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Cleaning of fluid-infused surfaces in microchannels Yongjian Li,† Xiangyu Hu, † Shuaishuai Liang, ‡ Jiang Li,‡ Haosheng Chen*,† †State Key Laboratory of Tribology, Tsinghua University, Beijing 100084, China

‡Mechanical Engineering School, University of Science and Technology Beijing, Beijing 100083, China KEYWORDS: cleaning, fluid-infused, microchannel, transverse grooves

ABSTRACT: When an immiscible fluid is flowing over a fluid-infused surface with transverse grooves in a microchannel, the infused fluid is either left in or cleaned away from the grooves by the flowing fluid. The cleaning status depends on the geometric parameters of the groove and the contact angle of the flowing fluids. The critical width of the grooves for the infused fluid enclosed in or driven out of the grooves are derived. This study helps to understand the stability of the Cassie status in a low shear flow where the surface tension plays the key role.

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INTRODUCTION When a secondary immiscible fluid is flowing on a rough or patterned surface infused with a primary fluid, there will be a wetting competition between the two fluids on the surface. In recent years, patterned surfaces are designed to keep the infused fluid from being cleaned by the flowing fluid to form a variety of functional surfaces, which demonstrate remarkable useful properties such as superhydrophobicity,1,2 omniphobicity,3,4 self-cleaning,5-7 fouling resistance,810

drag reduction,11 and promotion of dropwise condensation.12-14 While in many other cases,

such as the washing of the dishware and the cleaning of culture-wells inside microchannels,15 completely cleaning the patterned surface is desirable. The dynamic of the wetting on liquidinfused surface is still a challenge, and the understanding of its mechanism may improve the design of the functional patterns on the surface. The infused fluids could be cleaned away when they are exposed to the external loads,16-19 especially when they are in the flowing system. The cleaning effect of liquid-infused surface by the flowing fluid is usually dependent on the microstructure and chemistry properties of the surfaces.20-22 Recently, the outer shear flow is found to cause the failure of the fluid-fluid interface and lead to the drainage of the fluid inside the patterns.18,19 However, certain amount of the liquid are still left in the dead-end of the patterns. This inspired us to consider whether the patterned microchannel can be cleaned by the shear flow, and how the contact angle affect the cleaning result. In this work, we have performed a series of experiments in microchannels with transverse grooves made on the wall. The fluid infused wall is exposed to an external flowing fluid to form water-on-air, oil-on-air, and oil-on-water boundary conditions on the grooves, and the contact


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angle of the flowing fluid on PDMS surface is varied to change the surface tension of the fluidfluid interfaces. Only the cases that both of the flowing fluid and the infused fluid are able to contact with the wall of the microchannel were investigated in this work. Once the walls are completely wetted by the infused fluid, the flowing fluid can never touch the walls, and the fluid infused surface can never be cleaned.23 Therefore, the contact angles of the fluids on PDMS surface were all less than 180º in this series of experiments. Three kinds of cleaning status of the grooves from uncleaned to cleaned are found in the experiments. The critical widths of the grooves for the transition of the cleaning status are derived, and it agrees well with the experimental results. EXPERIMENTAL SECTION The microchannel is made of polydimethylsiloxane (PDMS) using soft photolithography methods.24 As shown in Fig.1(a1), the microchannel is straight and has rectangular grooves on one side. The height of the channel (hc) is 100 μm. The height of the grooves (hg) are 50 μm, while the width of the grooves (wg) varies from 5 μm to 100 μm. On the direction perpendicular to the plane shown in Fig.1(a1), the depth of the microchannel is 20 μm. The fluids used in the experiments are air, water, paraffin oil (Sigma Aldrich Co.) and silicone oil (Sigma Aldrich Co.). Here we denote the subscript “o” as oil, “w” as water and “a” as air. The viscosity µo = 29.5 mPa⋅s and 19.0 mPa⋅s for paraffin oil and silicone oil, respectively. The surface tension σwa= 72.6 mN/m, σoa(paraffin)= 28.5 mN/m; σoa(silicon)= 20.1 mN/m, σow(paraffin)= 52.0 mN/m. Sodium dodecyl sulfate (SDS, Sigma Aldrich Co.) is added to water, and Span-80 (Beijing Solarbio S&T Co., Ltd.) is added to silicon oil and paraffin oil, respectively, to change the surface tension of the interfaces, and the contact angle θ of the flowing fluid is changed with different concentrations of SDS in the water and Span-80 in the oils. The contact angles of these fluids on PDMS surface are listed in Table 1. To obtained these contact angles, the flowing fluids


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were injected into straight microchannels (without grooves), which were filled with the infused fluids, the fluid-fluid interface were captured by the high-speed camera, and the included angles between the tangent line of the fluid-fluid interface and the wall of the microchannel were measured. Table 1. Contact angle on PDMS surface

Infused

Contact Flowing fluid

fluid

Angle(º) Si. Oil +

Air

12.8±1.0 0.50%Span80

Air

Si. Oil

39.7±6.2

Paraffin + Air

57.7±4.5 0.05% Span80 Paraffin +

Air

65.4±5.9 0.20% Span80

Air

Water

104.9±7.4

Water + 0.10% Air

108.9±3.4 SDS Water + 0.05%

Air

114.9±3.2 SDS Paraffin +

Water

133.1±1.6 1.00% Span80 Paraffin +

Water

138.6±7.2 0.01% Span80


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Before the cleaning tests, the channel is filled with the infused fluid. Then, the flowing fluid is injected into the channel by a pressure controller (MFCSTM, Fluigent Inc.). The flow rate is controlled to be lower than 5 mm/s, and the capillary number, Ca=µU/σ, is lower than 10-3. Thus the surface tension force plays the most important role. The invasion of the flowing fluid and the drainage of the infused fluid are observed using a microscope (Leica Camera Inc.) and a high speed camera (M110, Phantom Co.). RESULTS AND DISCUSSION When the flowing fluid enters the microchannel, it will drive the infused fluid out of the channel, but some of the infused fluid could be enclosed in the grooves. Three kinds of status of the enclosed infused fluid are found in the experiments. The uncleaned status is that the infused fluid is enclosed by the flowing fluid and the infused fluid still occupies the groove (Fig.1(a1) & (a2)). Partially cleaned status is that the flowing fluid enters the groove and contacts with part of the groove wall (Fig.1(b1), (b2) & (b3)). The cleaned status is that the flowing fluid occupies the whole groove and the infused fluid is driven out of the grooves completely (Fig.1(c1) & (c2)). Accroding to the experiment results, the cleaning status is found to be dependent on the contact angle of the fluid on the surface and the size of the grooves, as illustrated in Fig.1(d).


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(a1) Uncleaned

(b1) Partial Cleaned

(c1) Cleaned

Secondary Phase

hc

θ

hg wg

Primary Phase

(a2)

(b2)

50µm

Trailing Edge Leading Edge (b3)

(c2)

50µm

50µm

50µm

(d) 1.0

0.8

0.4

Uncleaned

Partial Cleaned

0.6

Cleaned

Dimensionless Groove Width, wg*

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

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0.2

0.0

30

60

90

120

150

Contact Angle of the Outer Phase, θ(º)

Figure 1. Cleaning status of the fluid infused grooves on the wall of microchannels. (a1) and (a2) are the schematics and image of the “uncleaned” status; (b1)-(b3) are the schematics and images of the “partial cleaned” status; (c1) and (c2) are the schematics and image of the “cleaned” status; (d) is the diagram of the cleaning status controlled by the geometries of grooves and contact angle of the fluids. (wg*=wg/hc, hc=100 μm, hg=50 μm and wg varies from 5 to 100 μm.)

Firstly, we study the critical width of the groove for the uncleaned status. When the flowing fluid is going over the leading edge (as shown in Fig.2(a)) of the groove, the three phase contact point is pinned at the edge, while the contact point on the other side of the channel keeps moving forward. The contact angle at the leading edge of the groove increases gradually until it reaches its advanced contact angle, (θ + 90º). This is the contact angle variation stage, shown by “A” in Fig.2(a). During this stage, once the fluid-fluid interface reaches the trailing edge of the groove before the pinned contact point moves, the flowing fluid will not enter the groove and the infused fluid will be enclosed in the groove to form an uncleaned status.


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But when the contact angle of the flowing fluid reaches its advanced contract angle before the fluid-fluid interface reaches the trailing surface, the pinned contact point at the leading edge will move into the groove, as shown by “B” in Fig.2(a). The variation of the contact angle and the displacement of the contact point are measured, as shown in Fig.2(b). To nondimensionalize this problem, we divide the displacement of the contact point on the groove wall, h(t), by the height of the channel, hc, and get the dimensionless displacement, h(t)/hc. As shown in Fig.2(b), when the contact points moves, the dimensionless displacement of the contact point increases rapidly and the flow fluid occupies part of the groove wall. When the groove is even wider, the interface will reach the bottom, and only a small amount of infused fluid is left at the corners of the groove. Both of these two cases are partially cleaned status, and they are observed in the experiments, as shown in Fig.1(b2) and (b3). The largest groove width that allows the fluids to maintain the uncleaned status is defined as the critical width, wgc, beyond which the cleaning status of the groove will change from uncleaned to partially cleaned status. Here, we analyze the variation of the fluid-fluid interface with a simplified 2D model in which the curvature of the interface in the depth direction and gutters25 along the edge of the channel are ignored. As shown in Fig.2(a) and (b), we find that the fluid-fluid interfaces are in circular shape and sysmetrical to the 45 º line approximately. By analysis of the geometry of these circular fluid-fluid interfaces in the 2D model, we derive the expression of critical width of the groove as ‫ݓ‬௚௖ଵ = 2ℎ௖ /(1 − tanߠ) . Thus, we obtain the ∗ dimensionless critical width, ‫ݓ‬௚௖ଵ = ‫ݓ‬௚௖ଵ /ℎ௖ , for the uncleaned status which is expressed as Eq.

(1). The details of the derivation is provided in Appendix. According to Eq.(1), the critical width for the transition from uncleaned to partially cleaned status can be predicted as the magenta dashed line in Fig. 1(d), and it agrees well with the results of the experiments.


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w g*c1 = 2 (1 − tan θ )

(1)

(a)

A

Contact angle variation stage

B

Contact point variation stage

θ 1

2

hc

θ

Trailing Edge

A hg

B Leading Edge wg

200

0.5

Side of grooved wall

Top of grooved wall Side of grooved wall

0.4 180 0.3

B

160

A 0.2

140 100µm 120

100

0.1

100µm

Dimensionless Displacement, h(t)/hc

(b)

Contact Angle, θ(t), (º )

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

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0.0 0

1

2

3

4

5

6

7

Time, t, (ms)

Figure 2. Cleaning behavior of flowing fluid with contact angle larger than 90º. (a) The schematics of the variation of the fluid-fluid interface; (b) The experiment results of the variation of contact angle and displacement of the contact point on the groove wall. (h(t) is the accumulated displacement of the pinned contact point on the groove wall at time t. θ(t) is the “instantaneous” contact angle at time t. It refers to the contact angle corresponding to the top of the groove before the contact point moves on the side wall of the groove, while it refers to the contact angle corresponding to the side wall of groove after that.)

Secondly, we study the cleaned status. In the experiments, we find that the cleaned status happens only when the contact angle of the flowing fluid on the surface, θ, is less than 90°. In this case, when the flowing fluid is going over the leading edge of the groove, the three phase contact point is also pinned at the edge, while on the opposite wall of the channel the fluid keeps moving forward, as shown by “A” in Fig.3(a). The contact angle at the edge also increases gradually until it reaches its advanced contact angle, θ+90º. However, since θ is less than 90º,


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θ+90º is always less than 180º. Therefore, the fluid-fluid interface cannot reach the trailing edge of the groove within the contact angle variation stage, as illustrated with red dashed line in Fig.3(a). So, the contact point will inevitably keep on moving into the groove, as shown by “B” marked by red line in Fig.3(a). Once the fluid-fluid interface reaches the trailing edge of the groove during the stage “B”, part of the infused fluid will be enclosed in the groove, and the partially cleaned status is formed. When the groove width is larger, the contact point can reach the bottom of the groove, the contact angle corresponding to the bottom of the groove increases to θ+90º again, and then the contact angle decreases rapidly as the contact point moves on the bottom of the groove. This is the stage where both the contact angle and displacement of the contact point vary at the same time (Stage “C” marked by blue lines in Fig.3(a)). A typical variation of the fluid-fluid interface with the change of contact angle and the displacement of the contact point during this stage is shown in Fig.3(b). When the contact point is pinned at the leading edge, the contact angle of the paraffin oil increases from ~60º to ~130º. When the contact point moves on the leading side wall, the contact angle decreases to ~40º, and the displacement of the contact point increases gradually. However, as soon as the contact point reaches the bottom corner of the groove, the contact angle jumps to ~140º and then drops quickly to ~60º, while the displacement of the contact point increases rapidly. The measured contact angle together with the displacement of the contact point are shown in Fig.3(c). The acceleration of the contact point moving on the bottom is attributed to the bending of the interface close to the bottom, as shown in Fig.3(b). The bending interface generates higher Laplace pressure and it causes the contact point to move faster than that on the opposite wall of the channel. It is the accelerated motion of the contact point on the bottom of the groove that


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make it possible to catch up with the contact point on the opposite wall of the microchannel in the direction of the main channel. In this case, all of the infused fluid in the groove can be swept out by the flowing fluid to form the cleaned status.

(a)

A Contact angle variation stage B Contact point variation stage C Dual variation stage

h

A θ

B

hg θ(t)

C wg (b)

A

B

(c) 150

50 µm

C

Side of grooved wall Bottom of grooved wall

1.2

Top of grooved wall Side of grooved wall Bottom of grooved wall

1.0

120

0.8

A

90

C

B

0.6 0.4 0.2

60

0.0 30

0.00

0.05

0.10

0.15

0.20


50µm

Contact Angle, θ(t), (º )

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

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-0.2

Time, t, (ms)

Figure 3. Cleaning behavior of flowing fluid with contact angle less than 90º. (a) The schematics of the fluid-fluid interface variation; (b) The recording of the fluid-fluid interface of a typical process to achieve cleaned status (redrawn according to the photos captured by high-speed camera in the experiment, as shown in the inserted figure); (c) The experiment results showing the variation of contact angle and displacement on grooved side surface of the microchannel.

The smallest groove width that allows the flowing fluids to achieve the cleaned status is defined as the critical width, wgc2, for cleaned status, below which the cleaned status will change


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from cleaned to partially cleaned status. To achieve the cleaned status, the infused fluid needs to be driven out before the fluid-fluid interface reaches the trailing edge. The breakup of the fluidfluid interface at the trailing edge is initiated by the Plateau-Rayleigh instability which is determined by a geometrical criterium.26 The Plateau-Reyleigh instability is considered to arise as the fluid-fluid interface approaches the trailing edge within a critical distance δ0. In the experiment, we find that once the distance between the fluid-fluid interface and the trailing edge, δ, is larger than δ0 at the beginning of the dual variation stage, the cleaned status will happen as shown in Fig.4(b). Partial cleaned status always occurs when the interface has reached the trailing edge before the contact point reaches the right corner of the groove, as shown in Fig.4(c). It is reasonable to infer that the Laplace pressure generated from the bent interface near the bottom will push the infused fluid out of the groove through the gap δ, and it will prevent the contact of the interface and the trailing edge.

(a)

δ0

(b) 50 µm

δ

50 µm

(c) 50 µm

50 µm


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Figure 4. Critical Condition of Cleaned Status. (a) The schematics of breakup induced by Plateau-Reyleigh instability at the T junction; (b) & (c) comparison between the cleaned and partial cleaned status in experiments.

With the 2D geometry model, analyzing the case in which the contact point reaches the bottom of the groove as soon as the fluid-fluid interface contacts with the trailing edge, we can derive a ∗ dimensionless critical width, ‫ݓ‬௚௖ଶ = ‫ݓ‬௚௖ଶ /ℎ௖ , which is expressed as Eq.(2), where cg=hg/hc is

the ratio between the height of the groove and the height of the channel. The details of the derivation of the Eq. (2) is provided in Appendix. As δ0 is relatively small, which is not larger ∗ than about 5 µm in the experiments, we adopt ‫ݓ‬௚௖ଶ as the approximation of the dimensionless

critical width for cleaned status. The predicted critical widths are illustrated as cyan dashed line in Fig.1(d). The prediction copes well with the experimental results.

* wgc 2 ≈

(c

g

(

)

tanθ − 1) + 2cg tan2 θ + 1 − cg − 1 2

tanθ − 1

(2)

CONCLUSIONS

In this work, the cleaning status of the fluid-infused patterned surface is investigated in microchannels. We find three different status of the enclosed fluid in the cleaning processes and they are depending on the groove geometry and the dynamic contact angle of the flowing fluid. It is found that even if the flowing fluid are more wettable than the infused fluid, it cannot clean the enclosed infused fluid when the grooves are in “improper” shape. Motion of the contact point is found to play an important role in the cleaning process. The pinning of the contact point which occurs at the edge of the groove is a necessary condition to achieve the uncleaned status. If the stage of pinning lasts long enough for the interface to reach


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the trailing edge of the groove, the uncleaned status will occur. On the contrary, the acceleration of the contact point at the bottom of the groove is necessary for the cleaned status, and the contact angle of the flowing fluid needs to be less than 90º. It should be noted that, in this study, we focus on the flow with a relatively low flow rate, where the surface tension force plays the most important role. In higher flow rate, and the cleaning status cannot be predicted according to the equations derived in the work.


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AUTHOR INFORMATION Corresponding Author *E-mail: [email protected]. Phone: (086)10-62792741 ORCID Yongjian Li: 0000-0002-3485-4253 Jiang Li: 0000-0001-5443-5550 Notes The authors declare no competing financial interest. ACKNOWLEDGEMENT This work is supported by grants NSFC 51420105006, and NSF (BeiJing) 3172018.


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(16) Preston, D. J.; Lu, Z.; Song, Y.; Zhao, Y.; Wilke, K. L.; Antao, D. S.; Louis, M.; Wang, E. N. Heat transfer enhancement during water and hydrocarbon condensation on lubricant infused surfaces. Sci. Rep. 2018, 8, 540. (17) Wexler, J. S.; Grosskofp, A.; Chow, M.; Fan, Y.; Jacobi, I.; Stone, H. A. Robust liquidinfused surfaces through patterned wettability. Soft Matter 2015, 11, 5023. (18) Wexler, J. S.; Jacobi, I.; Stone, H. A. Shear-driven failure of liquid-infused surfaces. Phys. Rev. Lett. 2015, 114, 168301. (19) Liu, Y.; Wexler, J. S.; Schönecker, C.; Stone, H. A. Effect of viscosity ratio on the sheardriven failure of liquid-infused surfaces. Phys. Rev. Fluids 2016, 1, 074003. (20) Kreder, M. J.; Alvarenga, J.; Kim, P.; Aizenberg, J. Design of anti-icing surfaces: smooth, textured or slippery? Nat. Rev. Mater. 2016, 1, 15003. (21) Kim, P.; Kreder, M. J.; Alvarenga, J.; Aizenberg, J. Hierarchical or not? Effect of the length scale and hierarchy of the surface roughness on omniphobicity of lubricant-infused substrates. Nano Lett. 2013, 13, 1793-1799. (22) Ragesh, P.; Anandganesh, V.; Nair, S.; Nair, A. S. A review on self-cleaning and multifunctional materials. J. Mater. Chem. A 2014, 2, 14773-14797. (23) Preston, D. J.; Song, Y.; Lu, Z.; Antao, D. S.; Wang, E. N. Design of lubricant infused surfaces. ACS Appl. Mater. Interfaces 2017, 9(48), 42383-42392 (24) Fainman, Y.; Lee, L.; Psaltis, D.; Yang, C. Optofluidics: Fundamentals, Devices, and Application; McGraw-Hill Education, 2009.


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(25) van-Steijin, V.; Kleijn, C. R.; Kreutzer, M. T. Flows around confined bubbles and their importance in triggering pinch-off. Phys. Rev. Lett. 2009, 103, 214501 (26) Menetrier-Deremble, L.; Tabeling, P. Droplet breakup in microfluidic junctions of arbitrary angles. Phys. Rev. E 2006, 74, 035303.


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APPENDIX 1. Calculation of the critical width for transition between uncleaned and partial cleaned status. The critical condition for transition between uncleaned and partial cleaned status is illustrated is Fig. A1, where the fluid-fluid interface just reaches the trailing edge of the groove when the contact angle increases to θ on the leading surface of the groove. Assuming that the fluid-fluid ෢ , the blue interface is in perfect circular shape, we can represent the fluid-fluid interface with ‫ܤܣ‬ line in Fig. A1. Here, point A represents the leading edge of the groove and point B is the contact point of the interface on the opposite flat wall of the channel. AO’ is perpendicular to BO’. O is ෢ and R is the radius of ‫ܤܣ‬ ෢ . AA’ and BB’ are tangent to ‫ܤܣ‬ ෢ . So, OA = OB = R the center of ‫ܤܣ‬ and ∠ABO = ∠BAO. ∠A’AO’ = ∠B’BO’=θ and ∠A’AO = ∠B’BO=90º.

Therefore, ∠OAO’ = ∠OBO’=θ-90º. ∠BAO’ =∠OAO’+ ∠BAO =∠OBO’+∠ABO =∠ABO’. ෢ is always on the 45º line through Thus, AO’=BO’, ∠AO’ O = ∠BO’ O=45º. So the center of ‫ܤܣ‬ point O’. According to the geometric relation, as shown in Fig. A1, the following equations can be derived. hc = R sin(θ − 90 o ) + R cos(θ − 90 o ) = − R(cos θ − sin θ )

wgc1 = 2 R sin(θ − 90 o )

(A1)

(A2)

= −2 R cos θ

So,

w∗gc1 = =

wgc1 hc

=

− 2 R cos θ − R(cos θ − sin θ )

(A3)

2 1 − tan θ


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O’

B R

O hc

θ-90

B’

θ A

wgc1

A’

Figure A1. The schematics of critical geometrical relation of transition between uncleaned and partial cleaned status.

2. Calculation of the critical width for transition between cleaned and partial cleaned status. The critical condition for transition between cleaned and partial cleaned status is illustrated is Fig. A2, where the fluid-fluid interface just reaches the trailing edge of the groove when the contact point reaches the bottom of the groove. Assuming that the fluid-fluid interface is in ෢ , the blue line in Fig. perfect circular shape, we can represent the fluid-fluid interface with ‫ܤܣ‬ ෢ is also on the A2. With the similar derivation process, we can also prove that the center of ‫ܤܣ‬ 45º line through point O’. According to the geometric relation shown in Fig. A2, the following equations can be derived. hc + hg = R cos θ − R sin θ

(A4)

wgc 2 = R cos θ −

(A5)

R 2 − ( R sin θ + hg )2


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Langmuir

Give that, hg = cg hc , it can be derived as follows:

∗ w gc 2 =

wgc 2 hc

=

(A6)

(c g tan 2 θ − 1)2 + 2c g(tan 2 θ + 1) − c g − 1 tan θ − 1

෢ turns into a straight line, and wgc 2 = hg (Eq. (A6) is not applicable for θ=45º. When θ=45º, ‫ܤܣ‬ ∗ in that case. So, wgc 2 = c g when θ=45º.)

O’ B

hc

θ

hg

wgc2

R

θ O

θ A

Figure A2. The schematics of critical geometrical relation of transition between cleaned and partial cleaned status.


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For Table of Contents Use Only


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(a1) Uncleaned

Langmuir

(b1) Partial Cleaned

(c1) Cleaned

Uncleaned

Partial Cleaned

Cleaned

Dimensionless Groove Width, wg*

1 Secondary hc 2 Phase θ 3 4 hg 5 wg 6 Primary Phase Trailing Edge Leading Edge 7 (b2) (b3) (c2) 8 (a2) 9 10 11 12 50μm 50μm 50μm 50μm 13 14 (d) 15 1.0 16 17 18 19 0.8 20 21 22 0.6 23 24 25 0.4 26 27 28 0.2 29 30 31 32 0.0 30 60 90 120 150 33 ACS Paragon Plus Environment 34 Contact Angle of the Outer Phase, θ(º) 35 36

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A

Contact angle variation stage

1 2 3 4 5 6 7 8 9 10 11 12 13 14(b) 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31

B

Contact point variation stage

θ 1

2

hc

θ

Trailing Edge

A hg

B Leading Edge wg

200

0.5

Side of grooved wall

Top of grooved wall Side of grooved wall

0.4

180

B

160

0.3

A 0.2

140 100μm

120

100

0.1

100μm

0.0 0

1

3 Plus Environment 4 5 6 ACS 2Paragon

Time, t, (ms)

7


Contact Angle, θ(t), (º)

(a)

Langmuir

A Contact angle variation stage

Contact Angle, θ(t), (º)

B Contact point variation stage 1 2 C Dual variation stage 3 4 5 h 6 A 7 θ 8 9 10 B hg 11 12 θ(t) 13 C wg 14 15 16 17 (b) 18 19 20 21 22 23 A 24 25 26 B 27 28 50μm 50 μm C 29 30 31 (c) 150 Side of grooved wall Top of grooved wall Bottom of grooved wall Side of grooved wall 32 Bottom of grooved wall 33 34 120 35 36 37 A C B 90 38 39 40 41 60 42 43 44 30 45 ACS0.05 Paragon Plus 0.00 0.10Environment 0.15 0.20 46 Time, t, (ms) 47 48

1.2 1.0

0.8 0.6

0.4 0.2

0.0 -0.2


Page 25 of 28 (a)

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(a)

1 2 3 4 5 6 7 8 9 10 (b) 11 12 13 14 15 16 17 18(c) 19 20 21 22 23 24 25 26

δ0

δ

50 μm

50 μm


50 μm

50 μm

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Langmuir

O¶

B R

O hc

©-90

B¶

© A

wgc1

A¶


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O’

B

hc

θ

hg

wgc2

R

θ O

θ ACS Paragon Plus Environment

A

Cleaning of fluid-infused surfaces in microchannels - Langmuir (ACS

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