# Vapour mediated interactions and study of microscale flow in sessile droplets

Eshaan Arora

Department of Mechanical Engineering, National Institute of Technology, Hamirpur, Himachal Pradesh 177005

Prof. Saptarshi Basu

Department of Mechanical Engineering, Indian Institute of Science, Bengaluru, Karnataka 560012

## Abstract

Evaporating sessile droplets display an internal motion. This motion can be exploited to implement a mixing assay. As a result of the internal fluid motion, dispersed particles in the droplet are convectively driven towards deposition at selective locations on the substrate. In applications where such segregation is undesirable, in situ mixing inside the evaporating droplet becomes extremely important. However, the mixing rate in droplets evaporating under diffusion controlled evaporation is low due to the low value of Reynolds number. Bi-component droplets display a higher order of Marangoni velocity arising out of the concentration gradient due to the preferential accumulation of the more volatile components near the surface of the droplet. In scenarios, where adding a foreign component to the assay may not be possible, the same volatile component may be introduced in the vicinity of the droplet of interest. The vapours of the volatile fluid are adsorbed asymmetrically over the surface of the droplet which creates a gradient in the concentration and therefore, the surface tension over the droplet surface. This is termed as vapour mediated interaction. The flow induced by this vapour mediated interaction is an enhanced flow (by a factor of 103). The droplets are deployed over a hydrophobic substrate (i.e. the contact angle > 90). The flow field is then visualized by seeding the droplet with a correct amount of polystyrene particles and illuminating with laser light. The light is then scattered by the polystyrene particles and is acquired using DSLR cameras. For quantification of the flow, micro particle image velocimetry is used.

Keywords: reynolds number, marangoni flow, hydrophobic substrate, micro particle image velocimetry

## Abbreviations

Abbreviations
 CCR Constant Contact Radius CCA Constant Contact Angle PDMS Polydimethylsiloxane

## INTRODUCTION

Capillary flow is the radial flow which follows mass conservation at the edge where evaporation rate is higher. For example, Deegan et al. ​Thomas A. Witten, 1997 [1]​showed that the ring formation in the particle suspended water droplet was due to the radial flow towards the outer edge of the droplet where evaporation flux was higher. On the other hand, Marangoni flow is the flow induced due to a surface tension gradient which may be due to a temperature gradient or a concentration gradient. Kim et al. ​Wang-Cheol Zin, 2011 [2]​found that the capillary flow is stronger than the Marangoni flow when the substrate is heated, or even at room temperatures. In contrast, the Marangoni flow is more significant than the capillary flow in the case of cooled substrates. Both these flows co-exist but Marangoni flow generally has less contribution Dileep Mampallil, 2014 [3]. Buoyancy-driven Rayleigh-B´enard convection ​Suresh V. Garimella, 2014​ results either from a temperature- or concentration-induced density gradient inside the droplet. This flow can be seen inside a droplet on a hydrophobic substrate which basically evaporates in the CCA mode. The evaporation flux is low near the edge of the droplet due to a hindrance provided by the substrate. Therefore, less evaporation leads to a higher temperature at the edges as compared to the apex. This induces a density gradient and a double toroidal flow is observed (​see ​Fig 2​​). The flow patterns inside a droplet on a hydrophilic substrate evaporating in CCR or mixed mode have been studied well but the literature available on the droplets evaporating in CCA mode on hydrophobic substrates is limited. But the absence of the capillary flow inside a droplet on hydrophobic substrate can be attributed to the unpinned contact line and a reduced evaporation flux near the edges.

## LITERATURE REVIEW

A sessile droplet is a droplet which is isolated and lies on a substrate (any base surface). Evaporation may seem a simple phenomenon, but on microscale, as in the case of sessile droplets, it has been a subject of great interest for quite a few decades. There are four modes of evaporation in a droplet ​[4]​.

• Constant Contact Radius (CCR): The contact line is pinned, and the contact angle and height reduce. It is generally seen on rough and hydrophobic substrates.
• Constant Contact Angle (CCA): The contact angle remains constant. It is observed on hydrophilic substrates.
• Mixed Mode: The mode changes between CCR and CCA, or they occur simultaneously.
• Stick-Slip Mode: CCR changes to CCA after reaching a threshold value of contact angle.

Evaporating droplets display an internal flow. The flow may be categorised into three:

• Capillary Flow
• Marangoni Flow
• Buoyancy Driven Flow

Capillary flow is the radial flow which follows mass conservation at the edge where evaporation rate is higher. For example, Deegan et al. ​Thomas A. Witten, 1997 [1]​showed that the ring formation in the particle suspended water droplet was due to the radial flow towards the outer edge of the droplet where evaporation flux was higher. On the other hand, Marangoni flow is the flow induced due to a surface tension gradient which may be due to a temperature gradient or a concentration gradient. Kim et al. ​Wang-Cheol Zin, 2011 [2]​found that the capillary flow is stronger than the Marangoni flow when the substrate is heated, or even at room temperatures. In contrast, the Marangoni flow is more significant than the capillary flow in the case of cooled substrates. Both these flows co-exist but Marangoni flow generally has less contribution Dileep Mampallil, 2014 [3]. Buoyancy-driven Rayleigh-B´enard convection ​Suresh V. Garimella, 2014​ results either from a temperature- or concentration-induced density gradient inside the droplet. This flow can be seen inside a droplet on a hydrophobic substrate which basically evaporates in the CCA mode. The evaporation flux is low near the edge of the droplet due to a hindrance provided by the substrate. Therefore, less evaporation leads to a higher temperature at the edges as compared to the apex. This induces a density gradient and a double toroidal flow is observed (​see ​Fig 2​​). The flow patterns inside a droplet on a hydrophilic substrate evaporating in CCR or mixed mode have been studied well but the literature available on the droplets evaporating in CCA mode on hydrophobic substrates is limited. But the absence of the capillary flow inside a droplet on hydrophobic substrate can be attributed to the unpinned contact line and a reduced evaporation flux near the edges.

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Capillary flow (a) without Marangoni flow (b) with Marnagoni flow ​[4]​.
Evaporation-Induced Rayleigh Convection in a bi-component droplet (NaCl and water)  [7] .

This evaporation induced internal flow can be used for various applications. One such application is the mixing of particles inside the fluid on micro scale. In lab-on-a-chip devices, the chemical reactions which are dependent upon the mixing, are limited by mass diffusion. Such reactions can be enhanced by enhancing the mixing on micro scale. But the flow inside a droplet (buoyancy driven or capillary) has very small Reynolds number which hinders the task of mixing. Here, an induced Marangoni convection plays the role. When two droplets of different volatility (for example, water and ethanol) are placed aside each other, one of the droplet vapours are adsorbed on the other, and that too asymmetrically.

Induction of Marangoni Convection due to asymmetric adsorption of ethanol vapors over water droplet ​[8].

As shown by Hegde et al. [8](​see Fig 3​), since the mass transfer of ethanol vapours is equivalent to the heat transfer, and considering steady state 1-D mass flow in spherical coordinate system

$\frac{1}{{r}^{2}}\frac{d}{dr}\left({r}^{2}\frac{dC}{dr}\right)=0$

where, r is the radial distance from the centre of the ethanol droplet and C is the concentration of the ethanol vapours. Solving this differential equation:

$C=\frac{k}{r}$

Using the boundary conditions:

C=0 at r=∞; C=Cs at r=R

where R is the radius of the ethanol droplet, and Cs is the saturated vapour concentration of ethanol,

$C=\frac{{C}_{s}R}{r}$

which shows the asymmetric adsorption of ethanol. Its concentration is more on the near side and less on the far side. This concentration gradient results in a surface tension gradient (surface tension being lower at the near side) which is responsible for the solutal Marangoni convection (see ​Fig 3​). Hegde et. al [8] showed that the flow velocity induced due to this Marangoni convection in water droplet was 103 times higher than the flow velocity in an isolated water droplet showing capillary or buoyancy driven flow. Therefore, this Marangoni convection can be used to enhance mixing in various biological and chemical fluids. This has been demonstrated by using glycerol, which is a highly viscous fluid as compared to water and has very low volatility. Ethanol has been used to induce the Marangoni flow. Also, the changes in glycerol parameters (contact angles, contact radius and volume) after the adsorption of ethanol have been studied to make sure that all the ethanol was only adsorbed and not absorbed.

## Substrate Formation

First of all, the deployment of droplets (of glycerol and water, the fluids which were part of the experiments) required a hydrophobic substrate so that the initial contact angle of the droplets was consistently obtuse (110° ± 3° for water droplet and 100° ± 3° for glycerol droplet). Therefore, Polydimethylsiloxane ((CH3)2SiO) n, a silicone polymer (see ​Fig 4​) was used to make the substrate. It is the most commonly used elastomer in making microfluidic devices.

Polydimethylsiloxane Structure

Polydimethylsiloxane or PDMS has a very low toxicity profile, therefore it harmless to use. It is non-flammable and optically transparent [9] and was easily prepared. Other alternatives of PDMS for making hydrophobic substrate can be Thermoset Polyester (TPE), Polyurethane Methacrylate (PUMA) and Norland Adhesive 81 (NOA81) [10]. The prepared PDMS solution was then coated over glass substrates. Following was the procedure used to prepare the PDMS substrates:

Sylgard 184 is supplied as a pack of 2 liquids (a pre-polymer base and a cross-linking curing agent) which were mixed in the weight ratio of 10:1 respectively. After stirring the solution well, it was placed in a desiccator which was later connected to a vacuum pump. The solution was degassed for approximately 20 minutes to remove the dissolved air from it. Glass substrates were initially cleaned in an ultrasonic cleaner with acetone as the fluid medium for about 10 minutes. They were then coated with the PDMS solution in a spinner. It was run at about 1500 rpm for 1 minute. The substrates with PDMS coated layers were put in a furnace at 90°C for 3-4 hours. The cured substrates were then allowed to cool at room temperature.

## Dye Mixing

All the experiments were conducted at a maintained temperature and humidity. The dye used in the dye-mixing experiments was Rhodamine dye and Food Colour Dye- Kesar (solution of dye powder 0.01% (by wt.) in water). 1.5 µL of the dye solution was suspended on the PDMS substrate with the help of an air displacement micro pipette. The substrate with the suspended dye solution was then left isolated for approximately 30 minutes for the water of the dye to dry. Dye mixing was conducted on two fluids- water and glycerol. Water used was the deionised water and glycerol was anhydrous glycerol. First water was used as the fluid and later glycerol.

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Experimental Setup for Dye-Mixing
Experimental Setup for Dye-Mixing

The images and videos were captured with a DSLR camera (Nikon D7200). Three stages were used for the camera’s movement in the X, Y and Z directions (see​ Fig 5 & 6​). A Navitar lens was attached to the DSLR for getting the optimum depth of field and zoom. One separate stage was used to accommodate the PDMS substrate with movement in all the three mutually perpendicular directions. Syringe pump was used to dispense ethanol and the fluid (both water and glycerol) droplet was dispensed using the micro pipette. A stand with a clamp was used to hold the light source. The light source was white light with variable intensity.

• Without Ethanol: The fluid droplet (once water and then glycerol) of volume 5 μL was dispensed on the dried dye spot on the PDMS substrate using the micro pipette. The initial contact angle was maintained constant by carefully deploying the droplet in case of both the fluids water and glycerol. Dye was allowed to mix with no ethanol in vicinity. White light was casted for imaging as shown in the figure. External disturbances and convection due to air conditioning and other reasons were kept as minimum as possible. In the case of water, images were captured at an interval of 5 seconds for about 3.5 minutes and in case of glycerol, the images were captured at an interval of 10 seconds for about 40 minutes. The time for water-dye mixing was very less as compared to the glycerol-dye mixing because the flow inside the glycerol droplet is very less than that inside water. This is primarily due to the influence of viscosity of the respective fluids.
• With Ethanol: The fluid droplet was dispensed on the PDMS similarly as it was deployed previously. The only difference is that an ethanol droplet of volume 2 μL is deployed beside the fluid droplet using the syringe pump. The distance between the center of the fluid droplet and the center of the ethanol droplet was maintained at 3.5 (± 0.5) mm (see ​Fig 9​). Images were taken as soon as the ethanol droplet was deployed. Ethanol being highly volatile needed constant replenishment. Therefore, as seen in theVideo 1​, ethanol was dispensed using the syringe pump as soon as the previous droplet evaporated. The volume of the ethanol droplet was kept constant throughout the process.
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First and Last Images of Water and Food Color Dye (Kesar) Mixing Trial
First and Last Images of Glycerol and Rhodamine Dye Mixing Trial
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Distance between the glycerol (or water) droplet and the ethanol droplet maintained at 3.5 (±0.5) mm.
A video of the image sequence of one of the Glycerol-Rhodamine dye mixing trials (at 10 fps)

After collecting the images (and videos) in a PC, the images were processed in MATLAB. To quantitatively depict the mixing assay, an algorithm (code 1) along with the colour thresholder application (code 2) within the MATLAB were used to plot the colour intensity change with respect to time within the droplet region. All the images captured were 8-bit RGB images (i.e., there intensity levels had red, green and blue layers, each ranging from 0 to 255). For intensity measurement only the red layer of the image was taken into consideration. The algorithm extracted the intensity values of all the pixels within the droplet and calculated the mean intensity of this droplet. This way, the mean intensity for all the images captured was analysed and the change in the mean intensity relative to the difference between the maximum and the minimum intensity (in case of dye mixing with ethanol), I' was plotted against time ($I\text{'}=\frac{I-{I}_{min}}{{I}_{max}-{I}_{min}}$).​

%Dye_Mixing_Codeclc;clear all;I =['region_image'];I = imread(I); %cropping the imageI = I(1021:2560,309:3380);imshow(I);N=size(I);a=1;for i=1:N(1)    for j=1:N(2)    if I(i,j)>0        K(i,j)=I(i,j);        m(a)=i;        n(a)=j;        a=a+1;    else        M(i,j)=I(i,j);    end    endendimshow(K) index=1;%Processing all the images capturedfor p=4421:4429    if p<1000        Q =['DSC_0' num2str(p) '.jpg'];    else         Q =['DSC_' num2str(p) '.jpg'];    endQ = imread(Q);Q = Q(1021:2560,309:3380,:);%imshow(Q)s=size(m);for i=1:s(2)   A(m(i),n(i))=Q(m(i),n(i));end    imshow(A)   W=size(A);   b=1;   for i=1:W(1);     for  j=1:W(2);       if A(i,j)>0            %Eliminating the white spot created in the imaging           if Q(i,j,1)>253 && Q(i,j,2)>253 && Q(i,j,3)>253               continue;           else                Z(b)=A(i,j);                b=b+1;           end       else           M(b)=A(i,j);       end     end   end   Z=double(Z);   B=size(Z);   Mean(index)=mean(Z);   Mean=double(Mean);   index=index+1;end
MATLAB code for processing images
%Dye_Mixing_Codeclc;clear all;index=1;%Processing all the imagesfor p=4430:4598Q =['DSC_' num2str(p) '.jpg'];Q = imread(Q);%Function created using the color thresholder app in MATLABQ = createMask(Q);%Cropping the imageQ=Q(1000:2670,150:3500);imshow(Q);W=size(Q);b=1;   for i=1:W(1);     for  j=1:W(2);       if Q(i,j)>0           Z(b)=Q(i,j);           b=b+1;       else           continue;       end     end   end   Z=double(Z);   %B=size(Z);   Mean(index)=mean(Z);   %Mean=double(Mean);   index=index+1;end
MATLAB code for processing images using the color thresholder application

Apart from the dye-mixing inside water and glycerol droplets, the effect of ethanol droplet (when placed in the vicinity of the glycerol droplet) on parameters such as contact length, contact angle and the volume of the glycerol droplet was also observed. This objective was achieved by shadowgraphy, i.e., casting light from behind the droplets so as to capture the shadow of the droplet. The experimental setup (see ​Fig 10​) was similar to the previous one, except the light source was shifted to behind the droplet, facing towards the lens and a diffuser was used to diverge the white light.

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Experimental Setup for Shadowgraphy of Glycerol Droplet

A 5 μL glycerol droplet was dispensed on the PDMS substrate using a micro pipette and a 2 μL ethanol droplet was dispensed only once using a syringe pump. The initial contact angle (100° ± 3°) and length were maintained constant. Also, the distance between the ethanol droplet and the glycerol droplet was maintained constant (3.5 ± 0.5 mm). Images were captured at an interval of 5s. The captured images were then analysed using an image processing software ImageJ. Contact length, contact angle and volume graphs were plotted against time. A number of trials were plotted for consistency of the results.

Volume was calculated as follows (can be derived after solving a simple volume integral of a sphere):

$V=\frac{{\mathrm{\pi r}}^{3}\left({\mathrm{cos}}^{3}\mathrm{\theta }-3\mathrm{cos\theta }+2\right)}{3{\mathrm{sin}}^{3}\theta }$;θ=contact angle, r=contact radius

The droplet is assumed to be a spherical cap because the drop height is much smaller than the capillary length ${\left(\frac{\sigma }{\rho g}\right)}^{\frac{1}{2}}$ of glycerol (i.e., 2.23 mm) [11].

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A Shadowgraphy Image of Glycerol droplet on the left and ethanol droplet on the right.

## RESULTS AND DISCUSSION

Intensity vs. Time plot in Water-Dye Mixing
Intensity vs. Time plot in Glycerol-Dye Mixing

It is clear from the above two graphs, that mixing is faster in the presence of ethanol droplet. This shows the presence of much stronger flow due to Marangoni convection inside the droplets. In water, the dye was mixed within a minute (in the presence of ethanol), while in glycerol it took about 20-25 minutes. This is primarily because of the viscosity of the glycerol being higher than that of water.

The graphs below show the behaviour of different parameters of glycerol droplet, after deploying an ethanol droplet beside it at once, in the beginning.

Length (Non-dimensionalised) vs. Time plot for Glycerol.
Volume vs. Time plot for Glycerol.
Contact Angle vs. Time plot for both the left and right side of the glycerol droplet. The ethanol droplet was deployed on the right side.

The graphs clearly depict that in the beginning, when the ethanol droplet is deployed, there is a sudden change in the parameters. The contact length increases (i.e., the droplet spreads) and the contact angle decreases. Soon after the adsorbed ethanol evaporates completely, leaving behind only the glycerol, the parameters try to reset. Consistency of volume (≈ 5 μL) shows that the adsorption of ethanol is not much prominent. The reset of parameters clearly depict that we get pure glycerol droplet after the evaporation of ethanol and hence ethanol was not at all absorbed but only adsorbed. The following image sequence shows the change in parameters of the glycerol droplet after vapour mediated interaction with the ethanol droplet.

Shadowgraphy Image Sequence (at 10 fps)

## CONCLUSION AND RECOMMENDATIONS

The results clearly indicate that a high speed Marangoni convection induced by using a more volatile fluid, can enhance mixing inside droplets. Mixing in biological fluids, which have high viscosity as that of glycerol, can be benefited from this method. The present work was limited to non-biological fluids due to a shortage of time. Repeating the results with biological fluids (such as glucose) can assure the application orientation of this method.

## ACKNOWLEDGEMENTS

First of all, I would like to express my gratitude to Prof. Saptarshi Basu and IAS SRF Programme for giving me this wonderful opportunity to explore a whole new field. Constant support from my guide Omkar Hegde is gratefully acknowledged. This work would not have been possible without his guidance. I would also like to thank all the research scholars and co-interns in the Microfluidics lab for their support which helped me finish this work smoothly.

#### References

• Susmita Dash, Aditya Chandramohan, Justin A. Weibel, Suresh V. Garimella, 2014, Buoyancy-induced on-the-spot mixing in droplets evaporating on nonwetting surfaces, Physical Review E, vol. 90, no. 6

• Maryam Parsa, Souad Harmand, Khellil Sefiane, 2018, Mechanisms of pattern formation from dried sessile drops, Advances in Colloid and Interface Science, vol. 254, pp. 22-47

• Ruth Hernandez-Perez, Z. Hugh Fan, Jose L. Garcia-Cordero, 2016, Evaporation-Driven Bioassays in Suspended Droplets, Analytical Chemistry, vol. 88, no. 14, pp. 7312-7317

• Robert D. Deegan, Olgica Bakajin, Todd F. Dupont, Greb Huber, Sidney R. Nagel, Thomas A. Witten, 1997, Capillary flow as the cause of ring stains from dried liquid drops, Nature, vol. 389, no. 6653, pp. 827-829

• Jung-Hoon Kim, Sang-Byung Park, Jae Hyun Kim, Wang-Cheol Zin, 2011, Polymer Transports Inside Evaporating Water Droplets at Various Substrate Temperatures, The Journal of Physical Chemistry C, vol. 115, no. 31, pp. 15375-15383

• Dileep Mampallil, 2014, Some physics inside drying droplets, Resonance, vol. 19, no. 2, pp. 123-134

• Kwan Hyoung Kang, Hee Chang Lim, Hee Woong Lee, Sang Joon Lee, 2013, Evaporation-induced saline Rayleigh convection inside a colloidal droplet, Physics of Fluids, vol. 25, no. 4, pp. 042001

• Omkar Hegde, Shubhankar Chakraborty, Prasenjit Kabi, Saptarshi Basu, 2018, Vapor mediated control of microscale flow in sessile droplets, Physics of Fluids, vol. 30, no. 12, pp. 122103

• I D Johnston, D K McCluskey, C K L Tan, M C Tracey, 2014, Mechanical characterization of bulk Sylgard 184 for microfluidics and microengineering, Journal of Micromechanics and Microengineering, vol. 24, no. 3, pp. 035017

• Elodie Sollier, Coleman Murray, Pietro Maoddi, Dino Di Carlo, 2011, Rapid prototyping polymers for microfluidic devices and high pressure injections, Lab on a Chip, vol. 11, no. 22, pp. 3752

• Martin E. R. Shanahan, 1995, Simple Theory of "Stick-Slip" Wetting Hysteresis, Langmuir, vol. 11, no. 3, pp. 1041-1043

#### Source

• Fig 4: https://www.elveflow.com/microfluidic-tutorials/microfluidic-reviews-and-tutorials/the-poly-di-methyl-siloxane-pdms-and-microfluidics/
• Fig 7: Images taken using Nikon D7200 at the Microfluidics lab, Mechanical Engineering Department, IISc Bangalore
• Fig 8: Images taken using Nikon D7200 at the Microfluidics lab, Mechanical Engineering Department, IISc Bangalore
• Fig 9: Image taken using Nikon D7200 at the Microfluidics lab, Mechanical Engineering Department, IISc Bangalore
• Video 1: Image sequence captured using Nikon D7200 at the Microfluidics Lab, Mechanical Engineering Department, IISc Bangalore
• Fig 11: Image taken using Nikon D7200 at the Microfluidics lab, Mechanical Engineering Department, IISc Bangalore
• Video 2: Image sequence captured using Nikon D7200 at the Microfluidics lab, Mechanical Engineering Department, IISc Bangalore
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