Hydrodynamics of Two Interacting Liquid Droplets of Aqueous

Subscriber access provided by Queen Mary, University of London

Interface Components: Nanoparticles, Colloids, Emulsions, Surfactants, Proteins, Polymers

Hydrodynamics of two interacting liquid droplets of aqueous solution inside a micro-channel Tapan Kumar Pradhan, and Pradipta Panigrahi Langmuir, Just Accepted Manuscript • DOI: 10.1021/acs.langmuir.8b00184 • Publication Date (Web): 21 Mar 2018 Downloaded from http://pubs.acs.org on March 22, 2018

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

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

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

Langmuir

Hydrodynamics of two interacting liquid droplets of aqueous solution inside a micro-channel. Tapan Kumar Pradhan∗ and Pradipta Kumar Panigrahi Department of Mechanical Engineering, Indian Institute of Technology Kanpur, Kanpur 208016, India E-mail: [email protected]

Abstract We experimentally investigated the effect of a neighboring liquid droplet on fluid convection inside a liquid droplet of aqueous solution present inside a micro-channel using micro-PIV technique. There is no physical contact between the two droplets and the solute concentration of the two droplets are set at different value. Vapor concentration near the interface of the two droplets is different due to the difference in solute concentration. Water vapor evaporates from the low concentration droplet having higher vapor pressure and condenses on the high concentration droplet having lower vapor pressure. Evaporation and condensation induces Rayleigh convection inside the two droplets. Flow pattern shows circulating loop inside both the liquid droplets. The circulation at the interacting adjacent interface of the two droplets are opposite to each other. The strength of flow inside the liquid droplets decreases with time due to decrease in the difference of solute concentration between the two droplets. The flow strength inside the two interacting droplets is also a function of separation distance between the droplets. The flow strength inside the droplets decreases with increase in separation distance. ∗

To whom correspondence should be addressed

1

ACS Paragon Plus Environment

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

Page 2 of 24

Introduction Droplet interaction is observed in many applications like dropwise condensation, droplet coalescence, digital microfluidics etc. Droplet based microfluidics have been widely used in many fields like biomedical application, protein crystallization, micro reactors, synthesis of advanced material etc. 1,2 These devices consist of discrete droplets arrays inside microchannel and provide faster reaction, increased mass transfer due to high surface to volume ratio. In all cases, each droplet is found with other droplets nearer to it. Therefore, it is expected that droplet interaction will be encountered in many microfluidic devices based on droplets. The neighboring droplets may have identical composition as that of the droplet. In many cases, alternative droplets of different compositions and concentrations are found with variable separation distance from each other. One of such example is the protein crystallization in micro-channel. Protein crystallization in droplet based microfluid devices is carried out by two methods: (1) micro-batch method and (2) vapor diffusion method. 3 Microbatch technique in microfluidic system contains droplets of identical composition. Screening of protein crystallization conditions in microfluidics devices leads to array of droplets of different compositions. 4,5 In vapor diffusion method, alternative droplets of protein solution and reservoir solution are placed inside a micro-capillary in a carrier fluid. 6,7 During the crystallization process, water vapor is transported from the droplet containing protein solution to the droplet containing reservoir solution. Alternative droplets of different compositions are also observed in the synthesis of spinel magnetic iron oxide nanoparticles 8 and CdS nanoparticles 9 using microfluidic system. Droplets with different solute concentration are also found in biochemical screening of different sample and indexing of concentrations in droplet based microfluidic devices. 5,10,11 Difference in the composition of two neighbouring droplets may lead to the transfer of water vapor between the droplets due to the vapor pressure difference. 7 The present study investigates convection inside neighbouring droplets with concentration difference between the droplets. Presence of a neighbouring evaporating droplet affects the behavior of a droplet even 2


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

Langmuir

though there is no physical contact between the two droplets. Many researchers 12–18 have studied the effect of a neighboring droplet on the behavior of a droplet. Carles and Cazabat 12 studied the behavior of two neighbouring drops of PDMS and trans-decaline placed on a glass slide. They found that the PDMS drop moves towards the trans-decaline drop due to the surface tension gradient created on the PDMS surface caused by the penetration of trans-decaline vapor on PDMS drop surface. When the PDMS droplet reaches the trans-decaline droplet, PDMS gets mixed with the trans-decaline droplet at the touching point. This leads to surface tension difference between the two ends of the trans-decaline droplet and the trans-decaline droplet moves away from the PDMS droplet. Cira et al. 13 studied both repulsion and attraction between two neighboring droplets of propylene glycol and water, which is caused by the effect of vapor emitted from the neighboring droplet. This vapor-mediated interaction between the droplets causes random motion of droplets on the surface called as dancing of droplets. Karpitschka et al. 19 have studied the substratemediated interaction between two liquid droplets placed on a soft surface. The interaction between the droplets is due to the inverted cheerios effect caused by substrate deformation. 20 They observed repulsion and attraction between the droplets based on the thickness of the substrate. Pradhan and Panigrahi 14 studied the hydrodynamics and deposition pattern of two drying water droplets containing micro-beads placed on a glass substrate. They reported that the presence of a neighbouring droplet affects the flow pattern inside the droplet, which causes weak deposition of micro-beads at the adjacent region of the two droplets. Later, 15 they experimentally and numerically studied the effect of a neighbouring droplet on the internal convection of an evaporating droplet of aqueous NaCl solution. They reported that the symmetric flow pattern inside a single droplet of aqueous NaCl solution becomes asymmetric in the presence of a neighbouring droplet. This is caused by the modification of evaporative flux distribution on the droplet surface in the presence of the neighboring droplet. Shaikeea and Basu 16 experimentally carried out preliminary evaporation study of a pair of droplets of water placed on a hydrophobic surface (PDMS). They observed that the pair droplets

3


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

Page 4 of 24

show asymmetric contact angle as compared to the single droplet. They also found that the presence of a neighboring droplet suppresses the evaporation from the droplet. Later, 17 they studied the evaporation dynamics of two droplets placed on different hydrophobic surfaces. They observed asymmetric contact angle and asymmetric flow pattern for two droplets case contrary to the single evaporating droplet case. They observed that the life time of evaporation increases for pair droplet in comparison to single droplet. Shaikeea and Basu 18 studied the behavior of paired nanocolloidal droplets evaporating on PDMS surface. They observed that vapor mediated interactions between the two droplets affects the behavior of the evaporating nanocolloidal droplet. They found that the pair droplets show contact angle asymmetry, asymmetric flow pattern and different buckling behavior as compared to single droplet. Previous studies on flow inside liquid slugs are limited to the flow pattern inside moving slug through the micro channel. 21–25 These studies reported the circulating flow field generated inside moving slug as a function of capillary number. Few experimental studies have been done on the flow pattern near an evaporating meniscus using micro-PIV technique. 26–28 Buffone et al. 26 reported thermocapillary convection of an evaporating meniscus inside capillary tubes using micro-PIV technique. They observed presence of two contrarotating vortices in one plane and one clockwise vortex in another plane indicating distortion and loss of symmetry inside the liquid slug. Dhavaleswarapu et al. 27 reported 3D convection pattern generated near an evaporating meniscus and observed 3D buoyancy thermocapillary flow with increase in the diameter of the capillary. The above literature survey indicates that no study has been carried out on the effect of adjacent droplet on the internal convection of a liquid droplet inside micro-channel. This paper presents the hydrodynamics of two neighbouring droplets of aqueous solution present inside a micro-channel.

4


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

Langmuir

Experimental Details Aqueous solutions of sodium chloride having concentration 1 M and 2 M have been used in this experiment. Two liquid droplets with different concentrations are introduced into a square glass micro-channel maintaining a separation distance between the two droplets. The two droplets are introduced into the channel using a micro pipette. The volume of each droplet is kept equal to 2.0 µL. The cross-sectional area of the square micro-channel is equal to 1000×1000 µm2 . The length of the micro-channel is equal to 50 mm. The inside surface of the micro-channel is made hydrophobic through OTS treatment so that the droplets do not wet the glass micro-channel which prevents cross contamination between the two droplets. The droplet forms a contact angle of approximately 104 0 inside the micro-channel. Both the ends of the micro-channel are sealed with silicone gel after inserting the two droplets into the micro-channel to avoid any loss of water vapor out of the channel and prevents the influence of ambient condition. The separation distance between the two droplets is maintained at 505 µm for initial experiment. Later, the separation distance between the two droplets is varied between 145 µm to 6720 µm to study the effect of separation distance on internal convection. Images of the liquid droplets are captured by confocal microscope at different instants of time. The velocity field inside the liquid droplets are measured by micro-PIV technique. The schematic of the two droplets and the experimental setup is presented in Figure 1. Polystyrene fluorescent particles having diameter (dp ) 2 µm are added to the solutions of the two droplets. These particles act as tracer particles for the PIV measurement. The concentration of the tracer particles in the solutions is kept equal to 0.02 % volume fraction. The solution is sonicated for 5 min to make homogeneous suspension of the seeding particles and to break the particle agglomerates. The density of the tracer particles (ρp ) is equal to 1050 kg/m3 . Density difference between the tracer particles and the solution may cause the settling of particles due to gravity. The settling velocity of the particles due to the density difference is given by, Ug =

d2p (ρp −ρ) g, 18µ

where, ρ is the density of the solution and µ is the 5


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

Page 6 of 24

Figure 1: Experimental setup for velocity measurement inside the liquid droplets using confocal microscope.

dynamic viscosity of the solution. Density of 1 M and 2 M solutions is equal to 1038 kg/m3 and 1074 kg/m3 respectively. 29 Dynamic viscosity of 1 M and 2 M solutions is equal to 1.09 × 10−3 Pa · s and 1.20 × 10−3 Pa · s respectively. 30 The settling velocity of the particles is equal to 2.4 × 10−8 m/s and 4.4 × 10−8 m/s for 1 M and 2 M solution respectively. These values of settling velocities are well below the measured velocity magnitude i.e. 1.0×10−5 m/s obtained from the experiment. Hence, error caused by settling of particles is negligible. The particles follow the fluid flow faithfully. The induced flow observed from the experiment prevents settling of particles maintaining homogeneous suspension. The relaxation time ρp . The value of relaxation time is equal to for the tracer particles is given by τs = d2p 18µ

2.1 × 10−7 sec and 1.9 × 10−7 sec for 1 M and 2 M solution respectively indicating quick adjustment of tracer particles with respect to the change in flow pattern without any phase lag.

6


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

Langmuir

Imaging for the micro-PIV measurement is done by the confocal microscope. The fluorescent particles are illuminated by a Ar-ion laser source having wavelength of 488 nm. The emission from the fluorescent tracer particles are captured by the PMT present in the confocal microscope. The images in the confocal microscope are captured by point scanning of object using a scanner present in the confocal microscope. Background noise of the images is significantly reduced as confocal microscope uses pinhole. The images are captured at an interval of 1.29 sec. The size of each image is equal to 1024 × 512 pixels. The field of view of each image is equal to 3.10 mm × 1.55 mm. The images are processed by a PIV evaluation software called Dynamic Studio from Dantec to obtain the velocity vector field. The interrogation area for PIV processing is kept at 32 × 32 pixels with 25 % interrogation area overlap. Adoptive cross correlation is used in the PIV evaluation. The vector fields are averaged over several measurements (five measurements) to reduce the error caused by Brownian motion of the tracer particles. 31,32 The velocity vector field has a spatial resolution of 74 µm × 74 µm.

Results and discussion The velocity vector field inside the two interacting liquid droplets placed inside the microchannel is presented in Figure 2 at 200 µm and 800 µm from the bottom wall of the channel. The left hand side droplet has higher concentration (2M) as compared to the right hand side droplet (1 M). The two droplets are separated by an air gap of 505 µm. Figure 2 shows opposite flow direction of the left condensing droplet from the right evaporating droplet. The direction of the fluid motion at the upper plane ( z = 800 µm) is opposite to that at the lower plane (z= 200 µm) for both condensing and evaporating droplet. The flow visualization inside the two interacting droplets is presented in supplementary movie 1. The complete visualization of the flow pattern inside both interacting droplets has been presented in Figure 3. The convective motion inside the droplet is significant near the adjacent interface

7


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

Page 8 of 24

of both the condensing (Figure 3(a) and Figure 3(c)) and evaporating (Figure 3(b) and Figure 3(d)) droplet. Figure 3(a) and (c) present the velocity vector fields inside the left side droplet having higher concentration (2 M) at Z= 200 µm and Z= 800 µm from the bottom wall. Figure 3(b) and (d) present the velocity vector fields inside the right side droplet having lower concentration (1 M) at Z= 200 µm and Z=800 µm from the bottom wall. The fluid in the left side droplet moves towards the interacting interface present nearer to the neighboring droplet along the bottom wall at Z=200 µm from the bottom surface of the channel and the fluid near the top wall (Z=800 µm) moves away from the interface nearer to the neighboring droplet. The right side droplet shows the opposite flow behaviour. In case of right droplet, the fluid near the bottom wall moves away from the interacting interface present on the side of neighboring droplet and fluid moves towards the interface nearer to neighboring droplet along the top channel wall. The flow visualization inside the condensing and evaporating droplet is presented in supplementary movie 2 and supplementary movie 3 respectively.

Figure 2: Velocity vector field in X-Y plane inside the two interacting droplets at (a) Z = 200 µm and (b) Z = 800 µm from the bottom wall of the channel. 8


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

Langmuir

Figure 3: Velocity vector field in X-Y plane inside both the condensing and evaporating droplets at (a,b) Z=200 µm and (c,d) Z=800 µm after 15 min of placing the droplets inside the channel. The velocity vector field presented in Figure 2 and Figure 3 are 2D velocity field in a horizontal plane (X-Y plane) parallel to the bottom wall of the channel. These velocity fields provide x-component (u) and y-component (v) of velocity. Similar velocity measurements in X-Y plane have been carried out at 20 different Z-locations. The 3D velocity field has been reconstructed using continuity equation (equation 1) and the 2D velocity fields at these 20 z-locations. 33,34 ∂u ∂v ∂w + + =0 ∂x ∂y ∂z

(1)

The unknown z component of velocity (w) has been calculated by numerical integration of the above continuity equation using finite difference method. The reconstructed velocity vector field is presented in Figure 4 along a vertical plane at Y=0. Figure 4 shows strong wvelocity near the adjacent interface of both condensing and evaporating droplet. Fluid flow inside both the droplets show circulating flow pattern. The recirculating flow in both the

9


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

Page 10 of 24

droplets is anti-clockwise. However, the w-velocity at the interacting interfaces of both the droplets are opposite in direction to each other i.e. w-velocity is upward for the condensing droplet and downward for the evaporating droplet.

Figure 4: Velocity vector field in X-Z plane at Y=0 for (a) condensing droplet and (b) evaporating droplet.

Figure 5: Depiction of flow phenomenon inside both the interacting droplets. The solute concentration in both the droplets are different i.e. 2 M (left droplet) and 1 M (right droplet). The vapor concentration at the liquid-air interface of a solution depends on the solute concentration. According to Raoult’s law, vapor concentration at the liquid-air interface is given by, Cs = Xsol Cs0 . Here, Xsol is the mole fraction of solvent and Cs0 is the saturated vapor concentration corresponding to the ambient temperature. The experiment is conducted at an ambient temperature of 20 0 C with 50 % relative humidity. The value of saturated vapor concentration corresponding to 20 0 C is equal to 1.73 × 10−2 kg/m3 . 35 The vapor concentration at the interface of the liquid droplet having concentration 2 M (left droplet) is equal to 1.67 × 10−2 kg/m3 and the vapor concentration at the interface of the liquid droplet having concentration 1 M (right droplet) is equal to 1.61×10−2 kg/m3 . Hence, 10


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

Langmuir

the vapor concentration at the interface of the right droplet is higher as compared to the vapor concentration at the interface of the left droplet. Therefore, water vapor is transported from the interface of the right droplet with less solute concentration to the interface of the left droplet with more solute concentration due to the gradient of vapor concentration inside the air gap. This leads to evaporation from the right droplet having lower solute concentration and condensation on the left droplet having higher solute concentration. The evaporation and condensation phenomena of the two interacting droplets is depicted in Figure 5. Evaporation from the right droplet increases the solute concentration at the evaporating interface adjacent to the neighboring droplet. Higher concentration fluid with higher density slides down along the interface of the evaporating droplet due to gravity. The fluid at the opposite end of the droplet moves upward to maintain the continuity of flow creating a recirculating flow pattern in the vertical plane. This internal convection of the evaporating droplet is similar to the evaporation of aqueous NaCl solution droplet reported by Pradhan and Panigrahi 15 , Kang et al. 36 . They reported that Marangoni convection and thermal effect have no influence on the fluid convection of evaporating droplet of NaCl solution. The evaporation from the liquid droplet has been attributed to the buoyancy driven Rayleigh convection. Hence, it is expected that the flow inside the evaporating droplet is only due to buoyancy driven Rayleigh convection and Marangoni convection is absent in the present study. In our previous work 34 on single droplet located at different distance from the atmosphere, we have observed that evaporation from only one meniscus causes one circulating loop inside the droplet. In the present study, evaporation only occurs at the interacting adjacent interface of the evaporating droplet. The opposite interface of the evaporating droplet present inside the extended channel does not show any evaporation. The extended closed channel region beyond the droplet suppresses the evaporation from the opposite interface. 34 The higher density region of the evaporating droplet develops a stratification with higher NaCl concentration in the bottom wall region. This is likely to reduce the net driving force in the air gap region due to equilibrium between the vapor

11


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

Page 12 of 24

pressure difference of the adjacent interface at later time instant. Similarly, condensation only occurs at the adjacent interface of the condensing droplet. Hence, only one circulating loop is observed similar to the evaporating droplet. The flow inside the condensing droplet is only due to Rayleigh convection. Condensation on the left droplet decreases the solute concentration at the interface nearer to the neighboring droplet. Less concentration fluid with less density rises upward along the condensing interface due to buoyancy. Fluid at the inner region moves downward to maintain continuity creating a circulating loop. The strength of flow inside the condensing droplet (Figure 4 (a)) is higher than the flow strength inside the evaporating droplet (Figure 4(b)). This is because of the higher solute concentration inside the condensing droplet as compared to the evaporating droplet. 37 The Peclet number is given by P e = HU/Dc , where H is the height of the channel, U is the maximum velocity inside the droplets and Dc is the solute diffusivity of NaCl in the solution. The value of H is equal to 1000 µm. The maximum velocity (U ) is approximately equal to 15 µm/s and 12 µm/s inside the condensing and evaporating droplet respectively. The value of Dc is equal to 1.6 × 10−9 m2 /s. 38 The value of Peclet number is found equal to 12.5 and 7.5 for condensing and evaporating droplet respectively. For this value of Peclet number, the solute transport inside the droplets occurs by convection. The decrease and increase in solute concentration at the interacting interfaces of both the droplets is refreshed by the inner fluid through convective solute transport. This helps in continuing the condensation and evaporation process at the interacting interfaces. The transport of water vapor between the condensing and evaporating droplets occurs through diffusion process. 39–41 The air gap between the two droplets are confined by channel wall in the lateral directions. Hence, the diffusion of vapor can be considered as one dimensional as given by: ∂ 2C =0 ∂x2 12


(2)

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

Langmuir

Figure 6: Variation of droplets volume with time for (a) condensing droplet (left hand side droplet) and (b) evaporating droplet (right hand side droplet). Where, C is the concentration of water vapor in air. The solution of this diffusion equation gives a linear distribution of vapor concentration in the air. The transport of vapor from evaporating droplet to condensing droplet can be given by:

J = −Dv

CS,1M − CS,2M ∂C ≈ Dv ∂x S

(3)

Where, Dv is the diffusivity of water vapor in air and S is the separation distance. Due to 13


Langmuir

0.08

Evaporation/Condensation rate (µL/hr)

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

Page 14 of 24

0.07

Condensation rate Evaporation rate

0.06 0.05 0.04 0.03 0.02 0.01 0

0

5

15

10

20

25

30

Time (hour)

Figure 7: Variation of evaporation and condensation rate of the droplets with time. evaporation, the volume of the evaporating droplet decreases with time. The instantaneous volume of the evaporating droplet as a function of time is presented in Figure 6(b). The volume of the droplet is calculated by capturing the image of the droplets at different time and image processing. It shows a decrease in the volume of the evaporating droplet with time. The evaporation rate of the evaporating droplet is presented in Figure 7 with time. The evaporation and condensation rate of the droplets are calculated by taking the slope of the curve fitted curves shown in Figure 6. The evaporation rate is higher at initial time as compared to later time. The volume of the condensing droplet increases with time due to condensation on the droplet. The instantaneous volume of the condensing droplet is presented in Figure 6(a) with time which shows increase in volume of the droplet. Figure 7 shows that the rate of condensation gradually decreases with time similar to the evaporating droplet. The concentration of the condensing droplet near the interface region decreases due to addition of water and the concentration of the evaporating droplet increases due to extraction of water. Hence, difference in vapor pressure at the two interacting interfaces (CS,1M − CS,2M ) decreases. This leads to decrease in the condensation and evaporation rate 14


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

Langmuir

from the two droplets based on the equation 3. Evaporation and condensation from the droplets cease when the concentration of the evaporating and condensing droplets becomes equal. The volume of the evaporating droplet becomes constant at 1.33 µL after 30 hr. The concentration of the evaporating droplet at this value is equal to 1.50 M. The volume of the condensing droplet becomes constant at 2.60 µL after 30 hr which corresponds to a solute concentration of 1.53 M. The solute concentration of both the droplets becomes nearly equal. Hence, negligible evaporation and condensation occurs after 30 hr. The two opposite ends of the channel are closed by silicone gel. Hence, negligible water can escape from the channel. The amount of water leaves from the evaporating droplet condenses on the condensing droplet. Hence, the evaporation rate of the evaporating droplet and the condensation rate of the condensing droplet are almost equal as shown in Figure 7. However, there is a small variation in the evaporation and condensation rate. The evaporation rate is slightly higher than the condensation rate. This may be due to very small loss of water vapor due to diffusion through the silicone gel on both the ends. Due to this small loss of water, the evaporation rate gets slightly enhanced and the condensation rate gets slightly suppressed which is visible from the Figure 7. Decrease in the evaporation rate from the evaporating droplet causes reduction in the flow strength. The strength of velocity magnitude inside the evaporating droplet is presented in Figure 8 at different time instants. Here, the strength of the velocity is represented by the root mean square value (Ur ) of all the velocity vectors along X-Y plane at Z= 200 µm. N,M X p 1 Ur = u(i, j)2 + v(i, j)2 N × M i=1,j=1

Here, N and M corresponds to the total number of X and Y grids for velocity measurement. Similarly, the strength of velocity magnitude inside the condensing droplet is presented in Figure 8 at different instants of time. It shows reduction in flow strength inside the condensing droplet with time. The decrease in flow strength inside the condensing droplet is caused by the reduction in condensation rate as shown in Figure 7. In the initial 15


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

Page 16 of 24

Figure 8: Strength of average velocity in the X-Y plane at Z=200 µm with time of the condensing droplet and the evaporating droplet. period, the flow strength inside the condensing and evaporating droplet linearly decreases. At the later period, the flow strength slowly decreases and shows very negligible value towards the end. The flow strength for the evaporating droplet decreases at faster rate as compared to the condensing droplet. This can be observed from the Figure 8 where the difference in flow strength between the droplets slightly increases with time. This is because the size of the condensing droplet increases and the size of the evaporating droplet decreases with time. Rayleigh number increases with increase in droplet size. Lee et al. 37 studied that the strength of Rayleigh convection increases with increase in droplet size. Hence, the flow strength in the condensing droplet decreases at a slower rate as compared to the evaporating droplet. The flow strength inside both the droplets depends on the separation distance between the two interacting droplets. The flow strength inside the condensing and evaporating droplets is presented in Figure 9 as a function of separation distance after 15 min of placing the droplets inside the channel. The evaporation and condensation rate of the interacting droplets are 16


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

Langmuir

Figure 9: Strength of average velocity in the X-Y plane at Z=200 µm with separation distance of the condensing droplet and the evaporating droplet. inversely proportional to the separation distance based on equation 3. With increase in separation distance between the two droplets, the condensation and evaporation rate decreases. Hence, the flow strength inside both the droplets decreases. The overall flow pattern remains same at all separation distance. The flow strength decreases rapidly at smaller separation distance and shows a slow decrease at larger separation distance. For all separation distance, the flow strength inside the condensing droplet is higher than the flow strength inside the evaporating droplet due to higher solute concentration of the condensing droplet.

Conclusion We have studied the hydrodynamics of two interacting liquid droplets of aqueous NaCl solution kept inside a micro-channel. The two liquid droplets are separated by a separation distance filled with air. The concentration of the two droplets are kept at two different concentration (1 M and 2 M). Different solute concentration of the liquid droplets lead to different vapor concentration at the adjacent interfaces of the two droplets leading to trans17


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

Page 18 of 24

port of water vapor between the two droplets. Water evaporates from the droplet of low solute concentration and condenses on the droplet of high solute concentration. Evaporation and condensation from the droplets induces buoyancy driven Rayleigh convection inside the two droplets. Fluid near the evaporating interface of the evaporating droplet moves downward where as the fluid along the condensing interface of the condensing droplet moves upward. Evaporation and condensation rate of the droplets decreases with time as concentration difference between the two droplets reaches equilibrium value. The convective flow strength inside both the droplets decreases with time. The flow strength inside both the droplets is a function of separation distance between the two droplets i.e. it decreases with increase in separation distance. This study indicates interaction between droplets with different concentration inside a micro-channel leading to internal convection which depends on the separation distance. This induced flow due to droplet interaction can be used as a possible micromixing technique in droplet based microfluidics devices.

Acknowledgement Authors acknowledge the Department of Science and Technology, Government of India for the financial support.

Supporting Information Available Supporting Information Available: • Supplementary Movie 1: Flow visualization inside two interacting droplets of aqueous solution (mpg) • Supplementary Movie 2: Flow visualization inside the condensing droplet (mpg) • Supplementary Movie 3: Flow visualization inside the evaporating droplet (mpg) This material is available free of charge via the Internet at http://pubs.acs.org/. 18


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

Langmuir

References (1) Seemann, R.; Brinkmann, M.; Pfohl, T.; Herminghaus, S. Droplet based microfluidics. Rep. Prog. Phys. 2012, 75, 016601. (2) Teh, S. Y.; Lin, R.; Hung, L. H.; Lee, A. P. Droplet microfluidics. Lab Chip 2008, 8, 198–220. (3) Li, L.; Ismagilov, R. F. Protein crystallization using microfluidic technologies based on valves, droplets, and slipchip. Annu. Rev. Biophys. 2010, 39, 139–158. (4) Zheng, B. B.; Roach, L. S.; Ismagilov, R. F. Screening of protein crystallization conditions on a microfluidic chip using nanoliter-size droplets. J. Am. Chem. Soc. 2003, 125, 11170–11171. (5) Zheng, B.; Ismagilov, R. F. A microfluidic approach for screening submicroliter volumes against multiple reagents by using preformed arrays of nanoliter plugs in a three-phase liquid/liquid/gas flow. Angew. Chem. Int. Ed. 2005, 44, 2520–2523. (6) Zheng, B. B.; Tice, J. D.; Ismagilov, R. F. Formation of arrayed droplets by soft lithography and two-phase fluid flow, and application in protein crystallization. Adv. Mater 2004, 16, 1365–1368. (7) Zheng, B. B.; Tice, J. D.; Roach, L. S.; Ismagilov, R. F. A droplet-baed, composite PDMS/glass capillary microfluidic system for evaluating protein crystallization conditions by microbatch and vapor-diffusion methods with on-chip X-ray diffraction. Angew. Chem. Int. Ed. 2004, 43, 2508–2511. (8) Frenz, L.; Harrak, A. E.; Pauly, M.; Colin, S. B.; Griffiths, A. D.; Baret, J. C. Dropletbased microreactors for the synthesis of magnetic iron oxide nanoparticles. Angew. Chem. Int. Ed. 2008, 47, 6817–6820.

19


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

Page 20 of 24

(9) Hung, L. H.; Choi, K. M.; Tseng, W. Y.; Tan, Y. C.; Shea, K. J.; Lee, A. P. Alternating droplet generation and controlled dynamic droplet fusion in microfluidic device for CdS nanoparticle synthesis. Lab Chip 2006, 6, 174–178. (10) Chen, D. L.; Ismagilov, R. F. Microfluidic cartridges preloaded with nanoliter plugs of reagents: an alternative to 96-well plates for screening. Curr. Opin. Chem. Biol. 2006, 10, 226–231. (11) Zheng, B.; Tice, J. D.; Ismagilov, R. F. Formation of droplets of alternating composition in microfluidic channels and applications to indexing of concentrations in droplet-based assays. Anal Chem. 2004, 76, 4977–4982. (12) Carles, P.; Cazabat, A. M. Spreading involving the Marangoni effect: Some preliminary results. Colloids Surf., A 1989, 41, 97–105. (13) Cira, N. J.; Benusiglio, A.; Prakash, M. Vapor-mediated sensing and motility in twocomponent droplets. Nature 2015, 519, 446–450. (14) Pradhan, T. K.; Panigrahi, P. K. Deposition pattern of interacting droplets. Colloids Surf., A 2015, 482, 562–567. (15) Pradhan, T. K.; Panigrahi, P. K. Influence of an adjacent droplet on fluid convection inside an evaporating droplet of binary mixture. Colloids Surf., A 2016, 500, 154–165. (16) Shaikeea, A. J. D.; Basu, S. Insight into the evaporation dynamics of a pair of sessile droplets on a hydrophobic substrate. Langmuir 2016, 32, 1309–1318. (17) Shaikeea, A. J. D.; Basu, S. Evaporating sessile droplet pair: Insights into contact line motion, flow transitions and emergence of universal vaporisation pattern. Appl. Phys. Lett. 2016, 108, 244102. (18) Shaikeea, A. J. D.; Basu, S. Insights into vapor-mediated interactions in a nanocolloidal

20


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

Langmuir

droplet system: evaporation dynamics and affects on self-assembly topologies on macroto microscales. Langmuir 2016, 32, 10334–10343. (19) Karpitschka, S.; Pandey, A.; Lubbers, L. A.; Weijs, J. H.; Botto, L.; Das, S.; Andreotti, B.; Snoeijer, J. H. Liquid drops attract or repel by the inverted Cheerios effect. Proc Natl Acad Sci USA 2016, 113, 7403–7407. (20) Pandey, A.; Karpitschka, S.; Lubbers, L. A.; Weijs, J. H.; Botto, L.; Das, S.; Andreotti, B.; Snoeijer, J. H. Dynamical theory of the inverted cheerios effect. Soft Matter 2017, 13, 6000–6010. (21) Thulasidas, T. C.; Abraham, M. A.; Cerro, R. L. Flow patterns in liquid slugs during bubble-train flow inside capillaries. Chem. Eng. Sci. 1997, 52, 2947–2962. (22) Kashid, M. N.; Gerlach, I.; Goetz, S.; Franzke, J.; Acker, J. F.; Platte, F.; Agar, D. W.; Turek, S. Internal circulation within the liquid slugs of a liquid-liquid slug-flow capillary microreactor. Ind. Eng. Chem. Res. 2005, 44, 5003–5010. (23) King, C.; Walsh, E.; Grimes, R. PIV measurements of flow within plugs in a microchannel. Microfluid Nanofluid 2007, 3, 463–472. (24) Kinoshita, H.; Kaneda, S.; Fujii, T.; Oshima, M. Three-dimensional measurement and visualization of internal flow of a moving droplet using confocal micro-PIV. Lab Chip 2007, 7, 338–346. (25) Ma, S.; Sherwood, J. M.; Huck, W. T. S.; Balabani, S. On the flow topology inside droplets moving in rectangular microchannels. Lab Chip 2014, 14, 3611–3620. (26) Buffone, C.; Safiane, K.; Christy, J. R. E. Experimental investigation of self-induced thermocapillary convection for an evaporating meniscus in capillary tubes using microparticle image velocimetry. Phys. fluids 2005, 17, 052104.

21


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

Page 22 of 24

(27) Dhavaleswarapu, H. K.; Chamarthy, P.; Garimella, S. V. Experimental investigation of steady buoyant-thermocapillary convection near an evaporating meniscus. Phys. fluids 2007, 19, 082103. (28) Chamarthy, P.; Dhavaleswarapu, H. K.; Garimella, S. V.; Murthy, J. Y.; Wereley, S. T. Visualization of convection patterns near an evaporating meniscus using µPIV. Exp. Fluids 2008, 44, 431–438. (29) Pitzer, K. S.; Pelper, J. C. Thermodynamic properties of aqueous sodium chloride solutions. J. Phys. Chem. Ref. Data 1984, 13, 1–102. (30) Kestin, J.; Khalifa, H. E.; Correia, R. J. Tables of the dynamic and kinematic viscosity of aqueous NaCl solutions in the temperature range 20 − 1500 C and the pressure range 0.1-35 MPa. J. Phys. Chem. Ref. Data 1981, 10, 71–87. (31) Santiago, J. G.; Wereley, S. T.; Meinhart, C. D.; Beebe, D. J.; Adrian, R. J. A particle image velocity system for microfluidics. Exp. Fluids 1998, 25, 316–319. (32) Meinhart, C. D.; Wereley, S. T.; Santiago, J. G. PIV measurements of a microchannel flow. Exp. Fluids 1999, 27, 414–419. (33) Pradhan, T. K.; Panigrahi, P. K. Droplet hydrodynamics during lysozyme protein crystallization. Phys. Rev. E 2012, 86, 051602. (34) Pradhan, T. K.; Panigrahi, P. K. Evaporation-induced natural convection of a liquid slug of binary mixture inside a microchannel: effect of confinement. Microfluid Nanofluid 2016, 20, 115. (35) Haynes, W. M. CRC Handbook of Chemistry and Physics; CRC Press, 2012. (36) Kang, K. H.; Lim, H. C.; Lee, H. W.; Lee, S. J. Evaporation-induced saline Rayleigh convection inside a colloidal droplet. Phys. Fluids 2013, 25, 042001.

22


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

Langmuir

(37) Lee, S. J.; Hong, J.; Choi, Y. S. Evaporation-induced flows inside a confined droplet of diluted saline solution. Langmuir 2014, 30, 7710–7715. (38) Riquelme, R.; Lira, I.; Lopez, C. P.; Rayas, J. A.; Vera, R. R. Interferometric measurement of a diffusion coefficient: comparison of two methods and uncertainty analysis. J. Phys. D: Appl. Phys. 2007, 40, 2769–2776. (39) Hu, H.; Larson, R. G. Evaporation of a sessile droplet on a substrate. J. Phys. Chem. B 2002, 106, 1334–1344. (40) Sobac, B.; Brutin, D. Triple-line behavior and wettability controlled by nanocoated substrates: Influence on sessile drop evaporation. Langmuir 2011, 27, 14999–15007. (41) Carle, F.; Sobac, B.; Brutin, D. Experimental evidence of the atmospheric convective transport contribution to sessile droplet evaporation. Appl. Phys. Lett. 2013, 102, 061603.

23


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

Graphical TOC Entry

Internal hydrodynamics of two interacting droplets of aqueous solution.

24


Page 24 of 24

Hydrodynamics of Two Interacting Liquid Droplets of Aqueous

Recommend Documents