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Deposition pattern of interacting droplets
Accepted Manuscript Title: Deposition pattern of interacting droplets Author: Tapan Kumar Pradhan Pradipta Kumar Panigrahi PII: DOI: Reference:
S0927-7757(15)30090-X http://dx.doi.org/doi:10.1016/j.colsurfa.2015.07.013 COLSUA 20025
To appear in:
Colloids and Surfaces A: Physicochem. Eng. Aspects
Received date: Revised date: Accepted date:
8-5-2015 3-7-2015 6-7-2015
Please cite this article as: Tapan Kumar Pradhan, Pradipta Kumar Panigrahi, Deposition pattern of interacting droplets, Colloids and Surfaces A: Physicochemical and Engineering Aspects (2015), http://dx.doi.org/10.1016/j.colsurfa.2015.07.013 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
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*Graphical Abstract (for review)
Single droplet
Weak deposits
Two neighboring dropletsPage 1 of 25
*Highlights (for review)
• Drying pattern of droplets is influenced by droplet interaction. • Non-uniform deposition pattern is observed for two droplets drying adjacent to each other. • Presence of a neighboring droplet influences the evaporation flux on the droplet surface.
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• The convection pattern is asymmetric in two droplets configuration.
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*Manuscript
Tapan Kumar Pradhan, Pradipta Kumar Panigrahi∗
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Deposition pattern of interacting droplets
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Department of Mechanical Engineering, Indian Institute of Technology Kanpur, Kanpur 208016, India
Abstract
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A colloid droplet having pinned contact line forms a ring pattern after drying. The ring pattern of a single droplet shows uniform deposit along the contact line. When two droplets dry adjacent to each other, the deposition pattern
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is influenced by the presence of the neighboring droplet. The deposition pattern at the nearest region of the two droplets shows weak deposit compared to the rest of the region. The drying pattern in two-droplets configuration is
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related to the convection phenomena inside the drying droplet and the influ-
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ence of the neighboring droplet. We have experimentally studied the effect of a neighboring droplet on the convection pattern inside the evaporating droplet using µ-PIV technique to explain the influence of transport phenomena on the drying pattern. COMSOL simulation has also been carried out for understanding the evaporation process. The evaporation rate from the nearest region of the two droplets is lower compared to the rest of the region. Therefore, less number of particles are transported to this region due to low fluid flow causing less deposits in this region. The flow field inside a droplet in the presence of a neighboring droplet shows asymmetric convection pattern unlike single droplet where flow field is symmetric. This convection behavior correlates well with the evaporation flux distribution on the droplet surface and drying pattern. Keywords: Coffe-ring, Droplet, Micro-PIV, Deposition pattern
∗ Corresponding
author Email addresses: [email protected] (Tapan Kumar Pradhan), [email protected] (Pradipta Kumar Panigrahi)
Preprint submitted to Journal of LATEX Templates
July 3, 2015
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1. Introduction Drying of a droplet containing suspended particles forms deposition pattern
on the substrate after drying [1]. The deposition pattern is found in drops of
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aqueous salt solution [2, 3], DNA solution [4, 5], blood [6], suspended nanoparticles [7, 8] etc. Evaporation driven pattern deposition has many practical im-
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plications like two-dimensional crystallization [9], surface coating [10, 11, 12], DNA chip manufacturing [5], biosensing of protein [13], disease diagnosis [6, 14] etc. The famous coffee ring [15] pattern occurs due to the movement of particles
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towards the contact line. Evaporative flux at the contact line of a droplet is more as compared to the top of the droplet [15, 16]. Fluid is convected towards the contact line to replenish the evaporative loss at the contact line [15]. The
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particles get convected along with the fluid and deposited at the edge forming coffee ring pattern [15]. Pattern deposition depends on many factors like particle size [17, 18], droplet size [18], nature of substrate surface [19, 20], particle shapes [21, 22], flow pattern inside droplet [15, 23, 24], presence of surfactant
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and additives [25, 26], substrate temperature [22], droplet composition [27] etc. Flow pattern inside a droplet significantly affects the deposition pattern of
the droplet. Outward flow inside droplet leads to the movement of particles towards the contact line forming ring like deposits [15]. In the presence of
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Marangoni convection, where fluid flows towards the center of the droplet, reverse effect of coffee ring happens and the particles get deposited at the center [23]. Marangoni flow can also be used to form ordered hexagonal and stripe-like nanoparticle patterns [28]. Evaporation condition from the droplet surface affects the flow pattern leading to different deposition pattern [29, 24]. For edge
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enhanced evaporation, fluid flows towards the center forming ring like deposits
and for center enhanced evaporation, fluid flows towards the top of the droplet leading to uniform deposits [24]. Internal flow generated inside the droplet by electrowetting can suppress the coffee ring forming uniform deposits [30]. All the above studies have been carried out in single droplet configuration. 30
However, the hydrodynamics inside an evaporating droplet is significantly af-
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fected by the presence of a neighboring droplet. Carles and Cazabat [31] ob-
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served that a PDMS droplet can be propelled by the presence of a volatile
trans-decaline droplet. Cira et al. [32] study the mobility of two neighboring
droplets of water-PG mixture. They observed both attraction and repulsion between the two droplets depending upon the PG concentration. When two
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drops placed nearer to each other dry simultaneously, they form weak deposits
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at the region of greatest proximity due to lower evaporation at this region [29]. Chen and Evnas [33] reported the formation of arched structure of dried droplet
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when the droplet dries in the presence of another droplet nearer to it. In this paper, we have studied the effect of neighboring droplet on the hydrodynamics inside a droplet of pinned contact line and relate it to the deposition pattern.
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We have experimentally studied the particle convection during drying process of a droplet with and without the presence of a neighboring droplet and the
2. Experimental Methods
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effect of neighboring droplet on the deposition pattern.
DI water with conductivity of 1.05 µS/cm has been used as the working
fluid and the volume of each droplet has been set equal to 0.3 µL. Fluorescent polystyrene particles of 2 µm diameter with concentration of 0.018 % volume fraction have been used as seeding particles. Water containing the seeding par-
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ticles is sonicated for 15 minutes in an ultrasonication bath (Crest Ultrasonics
model-230D) for proper mixing of the seeding particles and to break the agglomerates of particles. Droplets of water containing these seeding particles are placed on a clean microscope glass slide. The glass slide is made of soda lime glass. The glass slide is thoroughly cleaned by sonicating in acetone. The
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roughness of the glass surface is measured by Qualitest surface roughness tester (Model TR100). Surface roughness (Ra ) of the glass surface is equal to 0.1 µm. The droplet with required volume is dispensed on the glass surface using a micro pipette. The droplet forms contact line diameter of approximately 1.8 mm. The contact angle of the droplet is equal to 380 ± 40 . DropSnake plugin in
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Image J [34] is used to measure the contact angle. After drying, the polystyrene
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particles form a deposition pattern. These fluorescent polystyrene particles also act as tracer particle for velocity measurement using particle imaging velocime-
try (PIV). We have studied the flow pattern during the drying process and
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deposition pattern after drying of a single droplet and two droplets.
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Droplet
Glass Substrate
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Objective Lense
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Excitation Dichroic mirror
Laser
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Emission
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Pinhole
PMT
Computer
Figure 1: Experimental arrangement for studying the convection pattern inside evaporating droplets.
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Flow inside the droplet during drying process is studied using micro PIV
technique. Images for the PIV measurements have been captured in confocal
microscope arrangement (Figure 1). The fluorescent particles are illuminated by a laser source of wavelength equal to 488 nm. The emission from the particles is captured by the PMT present in the confocal microscope. The background 70
noise is minimal as a confocal microscope uses pin hole. The separation time between two consecutive images are kept at 1.315 sec. The size of each image
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is equal to 512 ×512 pixels. The images are processed by using DynamicStudio
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V1.45 software to get the velocity vector field information inside the droplet.
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3. Results and discussion
Figure 2 shows the deposition pattern of droplets of fountain pen ink in
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water and 1 µm polystyrene particles in water on a glass surface. Single droplet configuration shows uniform deposit along the contact line after drying which is shown in Figure 2(a) and Figure 2(c). However, when the droplet dries in the
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presence of a neighboring droplet, the deposition pattern is not uniform along the contact line. The deposition at the nearest point of the two droplets is less as compared to the rest of the contact line as shown in Figure 2(b) and Figure
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2(d).
a
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b
Weakest deposition
500 µm
c
500 µm
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Weakest deposition
500 µm
500 µm
Figure 2: Deposition patterns of dried droplet at different conditions: (a) Deposition of a single droplet of ink, (b) Deposition of two interacting droplets of ink having a separation distance of 25 µm, (c) Deposition of a single droplet of water containing 1 µm particles, (d) Deposition of two interacting droplets of water containing 1 µm particles having a separation distance of 95 µm.
The evaporation from the droplet occurs due to the difference in vapor con5
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centration at the surface of the droplet and the ambient air. There are two modes of evaporation from the droplet surface: constant contact angle mode
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and constant contact radius mode [35]. In constant contact angle (CCA) mode,
the contact angle remains constant during the evaporation and the contact ra-
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dius decreases with time [36, 37]. In constant contact radius (CCR) mode, the contact line remains pinned and the contact angle reduces with evaporation
[38, 39]. Evaporation from water droplet placed on glass surface occurs in con-
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stant contact radius (CCR) mode as the contact line remains pinned throughout
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the evaporation. The presence of the particles also enhances the contact line pinning [15, 40]. Evaporation rate from the droplet having low contact angle remains constant throughout the drying process [16, 38]. So the contact angle varies linearly with time [35, 39, 16, 40]. Evaporation from the droplet of pinned
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contact line leads to the outward movement of the particles. The velocity vector field in the single droplet configuration shown in Figure
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3(a) shows symmetric pattern. The flow pattern of a drying droplet in the presence of a neighboring droplet is shown in Figure 3(b). The symmetric flow pattern inside the droplet becomes asymmetric in the presence of a neighboring
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droplet. The flow pattern of two neighboring droplets ( Figure 3(b)) shows that the fluid convection at the nearest region of the two droplets is weaker compared to the rest of the regions.
Similar velocity measurements are taken at 7 horizontal planes with different
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vertical locations from the substrate surface. The 3 D velocity field is recon-
structed [41, 42] from the X and Y components of velocity at 7 horizontal planes using the continuity equation. The reconstructed velocity field in vertical plane (X-Z plane) is shown in Figure 4. Velocity vector for a single droplet without a neighboring droplet is shown in Figure 4(a). It shows that the flow pattern
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is symmetric about Z axis. The flow inside the droplet shows unidirectional behavior towards the contact line unlike a circulating loop incase of Marangoni flow [43, 44] and Rayleigh convection [45]. The vector field in the presence of a neighboring droplet is shown in Figure 4(b), which shows more fluid flow towards the opposite side of the neighboring droplet. 6
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a 500
(µm/s)
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Y (µm)
0.30
0.20
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0.10 0.50
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X (µm)
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b 500
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Y (µm)
(µm/s) 0.30 0.25 0.20
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0.15 0.10 0.50
-500
-500
0
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X (µm)
Figure 3: Experimentally measured velocity vector field inside a drying droplet: (a) without a neighboring droplet and (b) with a neighboring droplet to the right hand side of the droplet.
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The asymmetric flow pattern inside the droplet in the presence of a neighboring droplet can be attributed to the influence of the neighboring droplet on the evaporation from the droplet surface. Two dimensional simulation has been performed to obtain the evaporation flux distribution on the droplet surface 7
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-1000
-500
0
b 400
1000
0.5 µm/s
200 -2000
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Z (µm)
500
X (µm)
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0.5 µm/s
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Z (µm)
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0
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Figure 4: Reconstructed velocity vector field in vertical (X-Z) plane at Y=0: (a) without a neighboring droplet and (b) with a neighboring droplet to the right hand side of the droplet.
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with and without a neighboring droplet. Droplet shape is assumed spherical in shape having contact line diameter of 1.8 mm and contact angle equal to 380 .
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Evaporation from the droplet surface is driven by vapor concentration difference between the surface and the ambient air. In the absence of air convection, transfer of vapor through air occurs by diffusion. The diffusion of water vapor through air can be represented by Laplace equation, ∇2 C = 0. Here, C is the
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water vapor concentration. The vapor concentration at the droplet surface is
taken as the saturation vapor concentration Cs corresponding to the ambient
temperature. The vapor concentration at the far field is taken as ambient value
C∞ . The ambient temperature (T∞ ) is equal to 250 and relative humidity (H) is
equal to 60%. At 250 C the value of saturated vapor concentration Cs is equal to
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2.31 × 10−2 kg/m3 [46]. The ambient vapor concentration, C∞ = HCs is equal to 1.39 × 10−2 kg/m3 . The boundary condition on the non wetting solid surface is taken as zero mass flux surface, ∇C = 0. Evaporative flux from the droplet surface is calculated using Fick’s law, J = −D∇C. Where, D is the coefficient of diffusion of water vapor in air which is taken as 2.52 × 10−5 m2 /s [46]. The
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laplace equation subjected to these boundary conditions is solved using COM-
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SOL Multiphysics V4.3 for both single droplet and two droplets. The simulation
is carried out in a computational domain of 10000 µm × 5000 µm surrounding the droplets. The computational domain is divided into approximately 53000
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triangular grids for both single and two droplets cases. The maximum element
size of the triangular grids is equal to 50 µm and the minimum element size
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is equal to 2 µm. The evaporative flux distribution on the droplet surface is presented in Figure 5.
a
0 -3000
-2500
-2000
-1500
-1000
-500
0
500
1000
1500
2
5.0E-04 kg/m s
2000
2500
3000
X (µm)
b 1000
2
5.0E-04 kg/m s
500
-2500
-2000
-1500
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0 -3000
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Z (µm)
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Z (µm)
1000
-500
0
500
1000
1500
2000
2500
3000
X (µm)
Figure 5: Distribution of evaporative flux from the surface of (a) a single droplet and (b) two droplets adjacent to each other in XZ plane. The evaporative flux distribution is obtained from numerical simulation.
Figure 5(a) shows the evaporative flux distribution on the droplet surface for
the single droplet configuration. It shows higher evaporative flux at the contact
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line compared to the apex of the droplet. The flow of water towards the contact line [15, 24] has been shown in Figure 3(a) and Figure 4(a). The symmetric nature of evaporative flux from the single droplet correlates with the velocity vector field inside the droplet. However, the presence of a neighboring droplet makes the evaporation flux distribution asymmetric as shown in Figure 5(b).
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The evaporative flux at the nearest point of the two droplets shows less evaporation. The presence of neighboring droplet reduces the strength of evaporation
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at this region. Therefore, less fluid is convected to this region (Figure 3(b) and
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Figure 4(b)). Less number of particles are convected to the nearest region of the two droplets leading to weak deposits. However, the flow in the opposite
side of the droplet is higher due to stronger evaporation flux. Therefore, the deposition pattern is stronger in the opposite side. a
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Weak deposits
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300 µm
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Figure 6: Deposition pattern of dried droplet captured by confocal microscope: (a) Pattern formation of single droplet, (b) Pattern formation of a droplet in the presence of a neighboring droplet, (c) Zoomed view of the contact line deposits at the opposite side of the neighboring droplet and (d) Zoomed view of particle deposition of the contact line at the nearest region of the two droplets.
During the drying process, particles get convected to the contact line and
deposit in the contact line region forming a ring like deposits. Figure 6(a) shows the deposition pattern after complete drying of a single droplet. The polystyrene
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particles deposited at the contact line form a ring like pattern. Evaporation flux from the droplet surface is non uniform with higher evaporation from the contact line region compared to the apex of the droplet [15, 16] (Figure 5(a)). Therefore, water moves towards the contact line to replenish the water loss at the contact line and this outward flow of water transfers the particles to the contact line
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forming coffee ring like deposits [15]. The deposition pattern of a single droplet
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remains uniform in the contact line. Figure 3(a) shows that particles convect
uniformly towards the contact line forming almost uniform ring thickness as shown in Figure 6(a). When a droplet dries in the presence of another droplet
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nearer to it, the deposition pattern does not show uniformity along the contact
line. The deposition pattern at the region of higher evaporation shows higher
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deposits. The deposition pattern of two interacting droplets is shown in Figure 6(b). It shows less deposits at the nearest region of the two droplets. Figure
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3(b) shows that the convection towards the contact line at the nearest region of the two droplets is less compared to the rest of the droplet. Hence, less particles 175
are convected towards this region forming weak deposit. The particle deposition
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image at higher magnification near the contact line at the nearest region of two droplets (Figure 6(d)) shows a thin layer of particle deposition. In contrast, the deposition of particles at the contact line region in the opposite side of the
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neighboring droplet at higher magnification (Figure 6(c)) shows a thicker layer of particle deposition. Overall, there is a strong correlation between the drying
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pattern, evaporation flux distribution and velocity vector field in both single and two droplets configuration.
4. Conclusion
The present study focuses on the deposition pattern of a drying droplet in
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the presence of a neighboring droplet. Measurements have been carried out using confocal Micro-PIV technique and numerical simulation has been carried
out using COMSOL multiphysics software. The flow pattern inside the droplet in the presence of another droplet has been correlated to the drying process. Presence of another droplet affects the deposition pattern and weak deposition
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is observed at the nearest region of two droplets. In a single droplet, the evaporative flux from the droplet surface is symmetric in nature. Consequently, the convection flow pattern shows symmetric behavior around the vertical axis leading to almost uniform deposition pattern along the contact line. Incase of
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two interacting droplets, evaporative flux from the surface is asymmetric around the vertical axis to the substrate surface. Evaporation rate from the proximity
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region between the two droplets is lower compared to the rest of the droplet surface. Therefore, there is less convection of particle towards the contact line
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region between the neighboring droplets forming a weak deposit at this region.
The present study demonstrates a strong correlation of drying pattern with the evaporation flux distribution and velocity vector field in both single and two
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droplets configuration.
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the wetting of a low-energy solid surface, J. Phys. Chem. B 102 (1998) 1964–1967. doi:10.1021/jp972552i.
[38] K. S. Birdi, D. T. Vu, A. Winter, A study of the evaporation rates of small
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[39] S. M. Rowan, M. I. Newton, G. McHale, Evaporation of microdroplets and the wetting of solid surfaces, J. Phys. Chem. 99 (1995) 13268–13271.
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drops, Phys. Fluids 16 (2004) 3738–3754. doi:10.1063/1.1772380.
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[45] K. H. Kang, H. C. Lim, H. W. Lee, S. J. Lee, Evaporation-induced saline
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[46] W. M. Haynes, CRC Handbook of Chemistry and Physics, CRC Press,
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Figure(s)
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Droplet
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Dichroic mirror
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S0927-7757(15)30090-X http://dx.doi.org/doi:10.1016/j.colsurfa.2015.07.013 COLSUA 20025
To appear in:
Colloids and Surfaces A: Physicochem. Eng. Aspects
Received date: Revised date: Accepted date:
8-5-2015 3-7-2015 6-7-2015
Please cite this article as: Tapan Kumar Pradhan, Pradipta Kumar Panigrahi, Deposition pattern of interacting droplets, Colloids and Surfaces A: Physicochemical and Engineering Aspects (2015), http://dx.doi.org/10.1016/j.colsurfa.2015.07.013 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
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*Graphical Abstract (for review)
Single droplet
Weak deposits
Two neighboring dropletsPage 1 of 25
*Highlights (for review)
• Drying pattern of droplets is influenced by droplet interaction. • Non-uniform deposition pattern is observed for two droplets drying adjacent to each other. • Presence of a neighboring droplet influences the evaporation flux on the droplet surface.
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• The convection pattern is asymmetric in two droplets configuration.
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*Manuscript
Tapan Kumar Pradhan, Pradipta Kumar Panigrahi∗
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Deposition pattern of interacting droplets
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Department of Mechanical Engineering, Indian Institute of Technology Kanpur, Kanpur 208016, India
Abstract
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A colloid droplet having pinned contact line forms a ring pattern after drying. The ring pattern of a single droplet shows uniform deposit along the contact line. When two droplets dry adjacent to each other, the deposition pattern
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is influenced by the presence of the neighboring droplet. The deposition pattern at the nearest region of the two droplets shows weak deposit compared to the rest of the region. The drying pattern in two-droplets configuration is
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related to the convection phenomena inside the drying droplet and the influ-
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ence of the neighboring droplet. We have experimentally studied the effect of a neighboring droplet on the convection pattern inside the evaporating droplet using µ-PIV technique to explain the influence of transport phenomena on the drying pattern. COMSOL simulation has also been carried out for understanding the evaporation process. The evaporation rate from the nearest region of the two droplets is lower compared to the rest of the region. Therefore, less number of particles are transported to this region due to low fluid flow causing less deposits in this region. The flow field inside a droplet in the presence of a neighboring droplet shows asymmetric convection pattern unlike single droplet where flow field is symmetric. This convection behavior correlates well with the evaporation flux distribution on the droplet surface and drying pattern. Keywords: Coffe-ring, Droplet, Micro-PIV, Deposition pattern
∗ Corresponding
author Email addresses: [email protected] (Tapan Kumar Pradhan), [email protected] (Pradipta Kumar Panigrahi)
Preprint submitted to Journal of LATEX Templates
July 3, 2015
Page 3 of 25
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1. Introduction Drying of a droplet containing suspended particles forms deposition pattern
on the substrate after drying [1]. The deposition pattern is found in drops of
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aqueous salt solution [2, 3], DNA solution [4, 5], blood [6], suspended nanoparticles [7, 8] etc. Evaporation driven pattern deposition has many practical im-
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plications like two-dimensional crystallization [9], surface coating [10, 11, 12], DNA chip manufacturing [5], biosensing of protein [13], disease diagnosis [6, 14] etc. The famous coffee ring [15] pattern occurs due to the movement of particles
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towards the contact line. Evaporative flux at the contact line of a droplet is more as compared to the top of the droplet [15, 16]. Fluid is convected towards the contact line to replenish the evaporative loss at the contact line [15]. The
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particles get convected along with the fluid and deposited at the edge forming coffee ring pattern [15]. Pattern deposition depends on many factors like particle size [17, 18], droplet size [18], nature of substrate surface [19, 20], particle shapes [21, 22], flow pattern inside droplet [15, 23, 24], presence of surfactant
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and additives [25, 26], substrate temperature [22], droplet composition [27] etc. Flow pattern inside a droplet significantly affects the deposition pattern of
the droplet. Outward flow inside droplet leads to the movement of particles towards the contact line forming ring like deposits [15]. In the presence of
20
Marangoni convection, where fluid flows towards the center of the droplet, reverse effect of coffee ring happens and the particles get deposited at the center [23]. Marangoni flow can also be used to form ordered hexagonal and stripe-like nanoparticle patterns [28]. Evaporation condition from the droplet surface affects the flow pattern leading to different deposition pattern [29, 24]. For edge
25
enhanced evaporation, fluid flows towards the center forming ring like deposits
and for center enhanced evaporation, fluid flows towards the top of the droplet leading to uniform deposits [24]. Internal flow generated inside the droplet by electrowetting can suppress the coffee ring forming uniform deposits [30]. All the above studies have been carried out in single droplet configuration. 30
However, the hydrodynamics inside an evaporating droplet is significantly af-
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fected by the presence of a neighboring droplet. Carles and Cazabat [31] ob-
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served that a PDMS droplet can be propelled by the presence of a volatile
trans-decaline droplet. Cira et al. [32] study the mobility of two neighboring
droplets of water-PG mixture. They observed both attraction and repulsion between the two droplets depending upon the PG concentration. When two
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drops placed nearer to each other dry simultaneously, they form weak deposits
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at the region of greatest proximity due to lower evaporation at this region [29]. Chen and Evnas [33] reported the formation of arched structure of dried droplet
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when the droplet dries in the presence of another droplet nearer to it. In this paper, we have studied the effect of neighboring droplet on the hydrodynamics inside a droplet of pinned contact line and relate it to the deposition pattern.
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We have experimentally studied the particle convection during drying process of a droplet with and without the presence of a neighboring droplet and the
2. Experimental Methods
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effect of neighboring droplet on the deposition pattern.
DI water with conductivity of 1.05 µS/cm has been used as the working
fluid and the volume of each droplet has been set equal to 0.3 µL. Fluorescent polystyrene particles of 2 µm diameter with concentration of 0.018 % volume fraction have been used as seeding particles. Water containing the seeding par-
50
ticles is sonicated for 15 minutes in an ultrasonication bath (Crest Ultrasonics
model-230D) for proper mixing of the seeding particles and to break the agglomerates of particles. Droplets of water containing these seeding particles are placed on a clean microscope glass slide. The glass slide is made of soda lime glass. The glass slide is thoroughly cleaned by sonicating in acetone. The
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roughness of the glass surface is measured by Qualitest surface roughness tester (Model TR100). Surface roughness (Ra ) of the glass surface is equal to 0.1 µm. The droplet with required volume is dispensed on the glass surface using a micro pipette. The droplet forms contact line diameter of approximately 1.8 mm. The contact angle of the droplet is equal to 380 ± 40 . DropSnake plugin in
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Image J [34] is used to measure the contact angle. After drying, the polystyrene
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particles form a deposition pattern. These fluorescent polystyrene particles also act as tracer particle for velocity measurement using particle imaging velocime-
try (PIV). We have studied the flow pattern during the drying process and
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deposition pattern after drying of a single droplet and two droplets.
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Excitation Dichroic mirror
Laser
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Pinhole
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Computer
Figure 1: Experimental arrangement for studying the convection pattern inside evaporating droplets.
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Flow inside the droplet during drying process is studied using micro PIV
technique. Images for the PIV measurements have been captured in confocal
microscope arrangement (Figure 1). The fluorescent particles are illuminated by a laser source of wavelength equal to 488 nm. The emission from the particles is captured by the PMT present in the confocal microscope. The background 70
noise is minimal as a confocal microscope uses pin hole. The separation time between two consecutive images are kept at 1.315 sec. The size of each image
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is equal to 512 ×512 pixels. The images are processed by using DynamicStudio
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V1.45 software to get the velocity vector field information inside the droplet.
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3. Results and discussion
Figure 2 shows the deposition pattern of droplets of fountain pen ink in
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water and 1 µm polystyrene particles in water on a glass surface. Single droplet configuration shows uniform deposit along the contact line after drying which is shown in Figure 2(a) and Figure 2(c). However, when the droplet dries in the
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presence of a neighboring droplet, the deposition pattern is not uniform along the contact line. The deposition at the nearest point of the two droplets is less as compared to the rest of the contact line as shown in Figure 2(b) and Figure
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2(d).
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Weakest deposition
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Weakest deposition
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Figure 2: Deposition patterns of dried droplet at different conditions: (a) Deposition of a single droplet of ink, (b) Deposition of two interacting droplets of ink having a separation distance of 25 µm, (c) Deposition of a single droplet of water containing 1 µm particles, (d) Deposition of two interacting droplets of water containing 1 µm particles having a separation distance of 95 µm.
The evaporation from the droplet occurs due to the difference in vapor con5
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centration at the surface of the droplet and the ambient air. There are two modes of evaporation from the droplet surface: constant contact angle mode
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and constant contact radius mode [35]. In constant contact angle (CCA) mode,
the contact angle remains constant during the evaporation and the contact ra-
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dius decreases with time [36, 37]. In constant contact radius (CCR) mode, the contact line remains pinned and the contact angle reduces with evaporation
[38, 39]. Evaporation from water droplet placed on glass surface occurs in con-
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stant contact radius (CCR) mode as the contact line remains pinned throughout
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the evaporation. The presence of the particles also enhances the contact line pinning [15, 40]. Evaporation rate from the droplet having low contact angle remains constant throughout the drying process [16, 38]. So the contact angle varies linearly with time [35, 39, 16, 40]. Evaporation from the droplet of pinned
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contact line leads to the outward movement of the particles. The velocity vector field in the single droplet configuration shown in Figure
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3(a) shows symmetric pattern. The flow pattern of a drying droplet in the presence of a neighboring droplet is shown in Figure 3(b). The symmetric flow pattern inside the droplet becomes asymmetric in the presence of a neighboring
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droplet. The flow pattern of two neighboring droplets ( Figure 3(b)) shows that the fluid convection at the nearest region of the two droplets is weaker compared to the rest of the regions.
Similar velocity measurements are taken at 7 horizontal planes with different
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vertical locations from the substrate surface. The 3 D velocity field is recon-
structed [41, 42] from the X and Y components of velocity at 7 horizontal planes using the continuity equation. The reconstructed velocity field in vertical plane (X-Z plane) is shown in Figure 4. Velocity vector for a single droplet without a neighboring droplet is shown in Figure 4(a). It shows that the flow pattern
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is symmetric about Z axis. The flow inside the droplet shows unidirectional behavior towards the contact line unlike a circulating loop incase of Marangoni flow [43, 44] and Rayleigh convection [45]. The vector field in the presence of a neighboring droplet is shown in Figure 4(b), which shows more fluid flow towards the opposite side of the neighboring droplet. 6
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Figure 3: Experimentally measured velocity vector field inside a drying droplet: (a) without a neighboring droplet and (b) with a neighboring droplet to the right hand side of the droplet.
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The asymmetric flow pattern inside the droplet in the presence of a neighboring droplet can be attributed to the influence of the neighboring droplet on the evaporation from the droplet surface. Two dimensional simulation has been performed to obtain the evaporation flux distribution on the droplet surface 7
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Figure 4: Reconstructed velocity vector field in vertical (X-Z) plane at Y=0: (a) without a neighboring droplet and (b) with a neighboring droplet to the right hand side of the droplet.
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with and without a neighboring droplet. Droplet shape is assumed spherical in shape having contact line diameter of 1.8 mm and contact angle equal to 380 .
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Evaporation from the droplet surface is driven by vapor concentration difference between the surface and the ambient air. In the absence of air convection, transfer of vapor through air occurs by diffusion. The diffusion of water vapor through air can be represented by Laplace equation, ∇2 C = 0. Here, C is the
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water vapor concentration. The vapor concentration at the droplet surface is
taken as the saturation vapor concentration Cs corresponding to the ambient
temperature. The vapor concentration at the far field is taken as ambient value
C∞ . The ambient temperature (T∞ ) is equal to 250 and relative humidity (H) is
equal to 60%. At 250 C the value of saturated vapor concentration Cs is equal to
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2.31 × 10−2 kg/m3 [46]. The ambient vapor concentration, C∞ = HCs is equal to 1.39 × 10−2 kg/m3 . The boundary condition on the non wetting solid surface is taken as zero mass flux surface, ∇C = 0. Evaporative flux from the droplet surface is calculated using Fick’s law, J = −D∇C. Where, D is the coefficient of diffusion of water vapor in air which is taken as 2.52 × 10−5 m2 /s [46]. The
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laplace equation subjected to these boundary conditions is solved using COM-
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SOL Multiphysics V4.3 for both single droplet and two droplets. The simulation
is carried out in a computational domain of 10000 µm × 5000 µm surrounding the droplets. The computational domain is divided into approximately 53000
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triangular grids for both single and two droplets cases. The maximum element
size of the triangular grids is equal to 50 µm and the minimum element size
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is equal to 2 µm. The evaporative flux distribution on the droplet surface is presented in Figure 5.
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Figure 5: Distribution of evaporative flux from the surface of (a) a single droplet and (b) two droplets adjacent to each other in XZ plane. The evaporative flux distribution is obtained from numerical simulation.
Figure 5(a) shows the evaporative flux distribution on the droplet surface for
the single droplet configuration. It shows higher evaporative flux at the contact
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line compared to the apex of the droplet. The flow of water towards the contact line [15, 24] has been shown in Figure 3(a) and Figure 4(a). The symmetric nature of evaporative flux from the single droplet correlates with the velocity vector field inside the droplet. However, the presence of a neighboring droplet makes the evaporation flux distribution asymmetric as shown in Figure 5(b).
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The evaporative flux at the nearest point of the two droplets shows less evaporation. The presence of neighboring droplet reduces the strength of evaporation
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at this region. Therefore, less fluid is convected to this region (Figure 3(b) and
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Figure 4(b)). Less number of particles are convected to the nearest region of the two droplets leading to weak deposits. However, the flow in the opposite
side of the droplet is higher due to stronger evaporation flux. Therefore, the deposition pattern is stronger in the opposite side. a
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Figure 6: Deposition pattern of dried droplet captured by confocal microscope: (a) Pattern formation of single droplet, (b) Pattern formation of a droplet in the presence of a neighboring droplet, (c) Zoomed view of the contact line deposits at the opposite side of the neighboring droplet and (d) Zoomed view of particle deposition of the contact line at the nearest region of the two droplets.
During the drying process, particles get convected to the contact line and
deposit in the contact line region forming a ring like deposits. Figure 6(a) shows the deposition pattern after complete drying of a single droplet. The polystyrene
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particles deposited at the contact line form a ring like pattern. Evaporation flux from the droplet surface is non uniform with higher evaporation from the contact line region compared to the apex of the droplet [15, 16] (Figure 5(a)). Therefore, water moves towards the contact line to replenish the water loss at the contact line and this outward flow of water transfers the particles to the contact line
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forming coffee ring like deposits [15]. The deposition pattern of a single droplet
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remains uniform in the contact line. Figure 3(a) shows that particles convect
uniformly towards the contact line forming almost uniform ring thickness as shown in Figure 6(a). When a droplet dries in the presence of another droplet
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nearer to it, the deposition pattern does not show uniformity along the contact
line. The deposition pattern at the region of higher evaporation shows higher
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deposits. The deposition pattern of two interacting droplets is shown in Figure 6(b). It shows less deposits at the nearest region of the two droplets. Figure
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3(b) shows that the convection towards the contact line at the nearest region of the two droplets is less compared to the rest of the droplet. Hence, less particles 175
are convected towards this region forming weak deposit. The particle deposition
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image at higher magnification near the contact line at the nearest region of two droplets (Figure 6(d)) shows a thin layer of particle deposition. In contrast, the deposition of particles at the contact line region in the opposite side of the
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neighboring droplet at higher magnification (Figure 6(c)) shows a thicker layer of particle deposition. Overall, there is a strong correlation between the drying
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pattern, evaporation flux distribution and velocity vector field in both single and two droplets configuration.
4. Conclusion
The present study focuses on the deposition pattern of a drying droplet in
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the presence of a neighboring droplet. Measurements have been carried out using confocal Micro-PIV technique and numerical simulation has been carried
out using COMSOL multiphysics software. The flow pattern inside the droplet in the presence of another droplet has been correlated to the drying process. Presence of another droplet affects the deposition pattern and weak deposition
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is observed at the nearest region of two droplets. In a single droplet, the evaporative flux from the droplet surface is symmetric in nature. Consequently, the convection flow pattern shows symmetric behavior around the vertical axis leading to almost uniform deposition pattern along the contact line. Incase of
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two interacting droplets, evaporative flux from the surface is asymmetric around the vertical axis to the substrate surface. Evaporation rate from the proximity
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region between the two droplets is lower compared to the rest of the droplet surface. Therefore, there is less convection of particle towards the contact line
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region between the neighboring droplets forming a weak deposit at this region.
The present study demonstrates a strong correlation of drying pattern with the evaporation flux distribution and velocity vector field in both single and two
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droplets configuration.
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Figure(s)
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Figure(s)
Weakest deposition
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Weakest deposition
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500 µm
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20 µm
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