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Sessile drop evaporation under an electric field
Accepted Manuscript Title: Sessile Drop Evaporation under an Electric Field Authors: H. Almohammadi, A. Amirfazli PII: DOI: Reference:
S0927-7757(18)30625-3 https://doi.org/10.1016/j.colsurfa.2018.07.022 COLSUA 22677
To appear in:
Colloids and Surfaces A: Physicochem. Eng. Aspects
Received date: Revised date: Accepted date:
2-4-2018 10-7-2018 16-7-2018
Please cite this article as: Almohammadi H, Amirfazli A, Sessile Drop Evaporation under an Electric Field, Colloids and Surfaces A: Physicochemical and Engineering Aspects (2018), https://doi.org/10.1016/j.colsurfa.2018.07.022 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.
Sessile Drop Evaporation under an Electric Field
H. Almohammadi, A. Amirfazli*
Corresponding Author: A. Amirfazli: +1-416-736-5901; Email: [email protected]
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Department of Mechanical Engineering, York University, Toronto, ON, M3J 1P3, Canada
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Graphical Abstract
Abstract
In this study, for the first time, the natural (diffusion-limited) evaporation of a sessile drop
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under an electric field was experimentally examined. A sessile drop natural evaporation is affected by the geometry of the drop, e.g. baseline, contact angle, and surface area, which all can be changed in the presence of an electric field. As such, first, the effect of electric field on sessile water droplet geometry was studied, together with how it differs for surfaces with various contact angle and contact angle hysteresis (for both hydrophilic and hydrophobic 1
surfaces). Then, the dynamics (evaporation time and mode) of natural evaporation of sessile droplet under an electric field was studied by measuring the evaporation rate, surface area, contact angle, and baseline of the droplet. It is found that compare to when there is no electric field, the evaporation time of a sessile droplet increases when there is an electric field. This was statistically shown to be significant for drops placed on surfaces with contact angle
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hysteresis lower than 32º. For droplets that evaporate in constant baseline mode initially and
then by evaporation in constant contact angle mode, the presence of the electric field resulted
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in a decrease in the duration of constant baseline mode when the surface had a low contact
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angle hysteresis.
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Keywords: evaporation; sessile drop; electric field; contact angle; diffusion limited
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Introduction
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Sessile drop evaporation has been the subject of many studies due to its numerous applications in surface patterning, inkjet printing, food industry, cosmetics, and biotechnology (e.g. DNA
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mapping)1-4. It is well understood that a sessile droplet evaporates due to different physical
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mechanisms including heat transfer by convection between air and liquid, heat transfer by conduction between liquid and a substrate, and the natural diffusion of the liquid into air5.
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Typically, the latter is considered as a predominant factor when studying natural evaporation of a drop5-7. Thus, the natural (also expressed as diffusion-limited) drop evaporation is controlled by the diffusivity of the vapor in the air, difference in vapor concentration at the
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drop surface and a point far from the drop, and the geometry of the droplet (e.g. baseline, contact angle, and surface area)8. In the literature many studies are dedicated to understand the influence of surface wettability on drop geometry and hence droplet evaporation8-18. It is found that depending on the surface type, a sessile drop evaporates through one of the following three different modes: constant contact angle (CCA) mode where during the evaporation the baseline 2
(BL) decreases but the contact angle (CA) remains constant; constant baseline (CBL) mode in which the contact line of the drop pins to the surface and CA decreases, or a combination of the CCA and CBL modes8,14-16. The presence and the duration of the each mode (in the case of having several modes during the evaporation) depends mainly on contact angle hysteresis (CAH). In the case of high CAH, the evaporation happens mostly in CBL mode; while for a
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small CAH, it is expected to observe CCA as a dominant mode during evaporation19. Depending on the mode of evaporation, theoretical relations are provided in the literature to
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predict the evaporation rate and time for droplet evaporation8-13, 14-18. Such rate is reported to
be independent of the CA when the CA is less than 40°13, 15. However, for CA values higher
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than 40º, an increase in the CA leads to a decrease in the intensity of the evaporative rate, and accordingly an increase in the total evaporation time. For example, the experimental results by
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Sobac et al.13 revealed an increase of 58% in total evaporation time when the CA increased
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from 63° to 135° for a droplet evaporating in CBL mode. It has been shown in the past that when a sessile drop is placed in an electric field (e.g. inside
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a capacitor) the sessile drop starts to elongate along the direction of the electric field20-28. The shape and the stability of sessile drops under electric fields has been analyzed in many works,
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where majority of them provided a model to compute the shape of an axisymmetric drop under a DC electric field20-28. Regarding the effect of the electric field on drop CA, only a few studies
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can be found5,29. The experimental studies summarized in Ref. 5 suggest that with an increase in magnitude of the electric field, depending on the type of surface and liquid, the CA can
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increase or decrease.
Considering the above mentioned points, the question is how the change in the geometry of the droplet brought upon by an electric field may affect the natural evaporation of a sessile drop. This topic is not investigated to date. There are only four related studies where the focus is on heated surface and only one type of the surface was studied30-32. Since the mechanism of the 3
sessile drop evaporation for heated surfaces, where both thermal effects of the solid and air and diffusion play a role, is different from the natural (diffusion-limited) evaporation, the results for a heated surface cannot be expanded to natural evaporation. Thus, it is not clear how an external electric field affects the natural evaporation rate of a droplet. And, how surface
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wettability plays a role in the presence of the external electric field during natural evaporation. Here, in a systematic experimental study, the evaporation of distilled water sessile drops (20
μl) under an electric field (varying from 0 to 11.1 KV/cm) was examined. Drops were placed
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on surfaces with various wettabilities to investigate the roles of CAH and receding/advancing CA on evaporation rate (and mode). To do so, we first studied the effect of electric field on
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sessile droplet geometry for a range of surface wettabilities. We examine the evaporation time
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of a sessile droplet under an electric field. Following this, the results for natural evaporation of
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a sessile drop under an electric field and how it changes with surface wettabilities will be
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presented.
Methods and Materials
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Figure 1 shows the setup used to perform the experiments. The capacitor (i.e. the part where
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drop sits and evaporates; see below) is placed inside a chamber (Figure 1a). The humidity and temperature of the chamber was measured using Fisher-brand Traceable Humidity Meter (Catalog number: 11-661-18). This device reads the temperature and humidity with accuracy
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of ±1ºC and ±2%, respectively. Drop evaporation experiments were done simultaneously in an environmental chamber containing two identical cells (the cells were fabricated for a pervious study [33] where detail can be found). A droplet was placed in each cell, where in one cell an electric field was present, and the other there was no electric field. This procedure helps to
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avoid any error associated with the change in temperature and humidity from test to test when comparing the droplet evaporation with and without electric field. The capacitor is made of two parallel copper discs (diameter of 2.54 cm), see inset in Figure 1a. The upper and lower dicks are identical. The drop (placed using a needle) sits on the target surface which is between the upper and the lower discs (Figure 1b). The target surface has the
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same size as electrodes (diameter of 2.54 cm); the gap between the upper disc and top of the surface is 8.8 mm. An EMCO (E101) high voltage power converter was used to provide the
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high voltage needed between the plates of the capacitor. High voltage power connectors and
wires (Caton Connector Corp., 14 series) were used to connect the power supply (Sorensen, DCS 40-25M37) and the copper discs.
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Drops of distilled water with the volume of 20 μl were used. This size of the droplets
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corresponds to Bond number (𝐵0 = 𝜌𝑔𝑅0 ℎ0 ⁄𝜎, representing the ratio of the gravitational to
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surface forces, where 𝜌 is the liquid density, 𝑔 is the gravitational acceleration, 𝑅0 is the initial
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contact line radius of drop (BL/2), ℎ0 is the initial height of the drop, and 𝜎 is the liquid surface
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tension) of 0.60±0.04 which shows that one can assume the droplet to have a spherical cap shape when there is no electric field. Two cameras (Basler and Photon Focus) were used to
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capture drop images at a frame rate of 0.1 fps. Two light sources (Schot Fostec and ROI) with
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two light diffusers were used to create diffused backlighting to image the drops. The diffused nature of the light and its intensity is not expected to provide any significant heating for the drops.
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The captured images were analyzed using ImageJ and Matlab software. ImageJ was used to measure the contact angle and baseline of the sessile drop; and Matlab was used to measure the volume and surface area of the droplet as follows: firstly a curve was fitted to the outline of the droplet using Inkscape software (see sample in Figure 1c); then the outline was imported to the Matlab; the sessile droplet was assumed to be the sum of several stacked discs with a height of
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one pixel. The volume and surface area of the droplet is calculated by summing the volume and surface area (of sides) of the stacked discs. The errors associated with this procedure was verified by calculating the volume of the droplet by gravimetry and our procedure; the errors was in the range of ±0.5 μl. Four different surfaces, i.e., aluminum, PEMA, PS, and Teflon, were used in this study. Spin
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coating method is used to fabricate PEMA, PS, and Teflon. The solutions that are used for each
surfaces are: PEMA: 1 wt% solution of PMMA (Aldrich MW~120000) in toluene, PS: 1 wt%
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solution of Polystyrene (Aldrich MW ~ 97,400) in toluene, Teflon: Teflon AF (DuPont) diluted with FC-75 (3M) in the ratio of 1:5 (v/v). All of the surfaces are cleaned before coating with
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DI water and acetone. Aluminum is used without any coating but after cleaning. The interested
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reader may refer to Ref. 34 for more surface fabrication details. The receding CA, advancing
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CA, and CAH of the surfaces, measured by sessile drop method, are provided in Figure 1d.
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Note that the reported CA values are a reflection of not only the intrinsic wettability of the substrates, but also the surface roughness and heterogeneity. For instance, the high contact
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angle reported for aluminum is reflective of it being a technical grade sample, i.e somewhat rough and heterogeneous. For each surface, at least three experiments were performed at
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similar temperature (21.4±0.6 ºC) and relative humidity (2.50±0.9 %) conditions.
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To observe the highest effect by the electric field on the geometry and subsequently the evaporation of a sessile droplet, we set the magnitudes of the electric field to just below the maximum for each surface. A higher value than the maximum electric field results in spark or
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bursting of the drop. The magnitude of the electric field was 11.1 KV/cm for aluminum and PEMA; and it was 10.3 KV/cm and 7.5 KV/cm for PS and Teflon surfaces, respectively. These values are ~0.2 KV/cm lower than the maximum electric field for each surface. The main reason for having lower electric field values for surfaces with higher wettability, is the higher
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height of the droplet for a given droplet volume. The droplet with a higher height bursts at lower magnitude of the electric field. Note that the electric potential corresponding to above mentioned electric field magnitudes are: aluminum (9.8 KV), PEMA (9.8 KV), PS (9.1 KV), Teflon (6.6 KV). Although, through this paper, we use the electric field values but it should be noted that the electric field is only
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uniform when there is no droplet between the electrodes; the presence of the droplet between
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electrodes distorts the uniformity of the electric field.
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Figure 1. (a) Overhead view of the experimental setup for drop evaporation; the capacitor is shown in inset. (b) Schematic view of the capacitor. (c) The sessile water droplet (20 μl) is
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placed over PEMA when there is no electric field. The yellow curve shows the fitted outline to calculate the volume and surface area of the droplet. (d) The wettability of the surfaces that are
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used in this study; the numbers above each bar shows the value of the CA. The errors for the
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reported CA in (d) are in the range of ±1º.
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Results and Discussion Effect of electric field on the sessile drop geometry. Figure 2 shows the effect of an external electric field on the geometry of a sessile droplet that is placed over surfaces with various wettabilities. Note that the first row in Figure 2 shows the droplets before activating the electric field, while second row is captured once the electric field is reached to the given magnitude.
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The time gap between the first and the second row is 1.50±0.08 min as one needs to ramp up the electric field to the desired magnitude (this period is considered to have a negligible effect
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on the comparative plots for evaporation given the totality of the experiment period and the
experimental uncertainties, e.g. see error bars in Fig. 3). The overlapped view of the first and
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the second row is presented in the third row. Following this, in Figure 2e, the percentage change
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of the parameters that affect the drop natural evaporation i.e. baseline, CA, and surface area
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when the electric field is provided.
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As it is clear in Figure 2, an external electric field elongates the sessile drop along the direction of the field. This can be understood by examining the augmented Younge-Laplace equation
at the apex as follows: 2
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σ ( r ) = ∆P0 + ∆Pe
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(Eq. 1), that relates the shape of the droplet to the pressure difference across the drop interface,
(1)
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where r is the radius of the curvature at apex, ∆P0 and ∆Pe represent the pressure difference across the drop interface due to the surface tension and electric field stress, respectively. Note that in Eq. (1), we considered the sessile droplet to be axis-symmetric and the gravity is
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neglected as Bond number for the studied droplet is 0.60±0.04 (see previous section). Physically Eq. (1) describes that to keep the mechanical equilibrium, the left hand side of the Eq. (1) needs to be increased by ∆Pe in the presence of the electric field. Thus, assuming negligible change in surface tension, the radius of the curvature (i.e. the term r in Eq. 1) should be decreased, which manifests itself as an elongation of the sessile droplet in the direction of 9
the electric field. Such elongation depending on the surface wettability may result in different form of the changes seen in the droplet geometry. For the aluminum and PS, the electric field decreases the CA while drop’s contact line is pinned to the surface. Pining of the drop’s contact line can be related to the high value of the CAH for
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these surfaces; the deformation of the drop by electric field force is not sufficiently large to decrease the initial contact angle of the droplet to below the receding CA. As such, the contact
line cannot recede and remains pinned, and only the contact angle decreases. On the other hand,
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for the PEMA and Teflon, both the baseline and CA of the of the droplet decrease in the presence of the electric field. The low value of the CAH, which results in a small difference
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between the initial contact angle (as placed droplet) and receding contact angle, is the reason
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for the receding of the contact line. For all surfaces, the presence of the electric field, resulted
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in an increase in the surface area of the drop which is due to the elongation of the droplet along
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the direction of the electric field. Such increase is higher for droplet on Teflon and PEMA compared to that of PS and aluminum. Thus, it can be understood that when there is receding
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for the droplet in the presence of the electric field, which happens for surfaces with small CAH,
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the surface area increases significantly by the electric field. To sum up, it seems that CAH plays a main role in the trend of the changes in the geometry of
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the droplet under the electric field. When the CAH is small, the presence of the electric field results in a decrease in baseline and CA. While for a high value of CAH, the contact line remains pinned and contact angle decreases. For all cases, surface area increases in the presence
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of electric field. Such issues (especially the trend of the change in CA) has not been clear in the literature5; some works reported that the presence of the electric field increases the contact angle, and other stated the opposite.
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Figure 2. The geometry of the sessile water droplet that is placed over (a) aluminum, (b) PEMA, (c) PS, and (d) Teflon surfaces. The magnitude of the baseline (BL, in mm), contact
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angle (CA, in º), and surface area (SA, in mm2) are reported below each image. The first row shows the droplet (19.25±0.48 μl) when there is no electric field, and the second row shows
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the droplet (18.76±0.52 μl) in the presence of electric field. In each column, third row shows the overlapped view of the first and the second rows. (e) Shows the percentage change in baseline, CA, and surface area of a droplet over aluminum, PEMA, PS, and Teflon in the
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presence of the electric field. For instance, the surface area increases by ((SAE-SA0)/SA0)=12%
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when the electric field is applied for a droplet that is placed over Teflon.
Effect of electric field on drop evaporation. Figures 3a to 3d show the process of the drop evaporation with and without an external electric field for drops placed on aluminum, PEMA, PS, and Teflon, respectively. The evaporation time for water droplet (20 μl) is given in Figure 3e.
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Looking at Figure 3e, the duration of the evaporation from high to low when there is no electric field is for drops on: PEMA, Teflon, PS, and aluminum. However, considering the error bars, it is clear that the surface wettability does not affect the evaporation time in a dramatic manner. To comprehend the reason for this behavior, detailed time evolution of the volume, surface area, baseline, and CA of droplets during the evaporation process for all of the surfaces is given
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in Figure 4. When there is no electric field, for all surfaces, evaporation is first in the CBL
mode and then as time progresses it falls in the CCA mode. However, the duration of the CBL
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mode is different from one surface to another. Such duration, from high to low is for drops on: aluminum, PS, PEMA, and Teflon. Thus, it can be seen that surfaces with high CAH have a
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higher duration of the CBL mode. This happens as the drop needs more time to change its
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contact angle from initial contact angle (for as placed droplet) to the value that results in receding of the contact line (i.e. receding CA). In the literature, it is reported that the
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evaporation time is lower in CBL mode compared to that of CCA17-18. However, evaporation time is a function of not only the mode of the evaporation, but also the magnitude of CA, the
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length of baseline, and surface area13. From Figure 4, for surfaces with lower wettability from one hand, the increase in contact angle, and decrease in baseline, should reduce the rate of
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evaporation, but on the other hand, the surface area increases which favors an increase in evaporation rate13. It is worth to note that in the case of high contact angle values, the free space
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around the triple line is small. Therefore, the concentration of water increases near the triple line and air circulation near the contact line is hindered. This results in low vapor diffusion into
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surrounding atmosphere and consequently a decrease in the evaporation mass flux13. The vapor diffusion into surrounding air also can be limited by small length of the contact line (or base line which is the indication for contact line length) for the droplet. Thus, using surfaces with lower wettabilities, from CA and baseline prospective, the evaporation is hindered, but from surface area point of view, the evaporation rate is enhanced. 12
From Figure 3e, it can be understood that the total evaporation time, which is a function of all
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of the above mentioned parameters, is not affected significantly by the surface wettability.
Figure 3. The evaporation of sessile water droplets placed on (a) aluminum, (b) PEMA, (c) PS, and (d) Teflon surfaces at different time. (e) Shows the evaporation time of sessile droplets
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(20 μl) over surfaces with various wettabilities with and without electric field. Error bars represent one standard deviation. The numbers printed inside each bar shows the exact
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evaporation time.
When there is an electric field, the evaporation time shows higher values (see Figure 3e). However, considering the error bars, the question is whether there is a difference between the total evaporation time for drops with and without an electric field. To answer this, as explained earlier, the drop evaporation experiments were done simultaneously in an environmental 13
chamber for two drops, one under an electric field and another in normal condition (no electric field). We used a statistical method i.e. ‘one way ANOVA with blocking’ to evaluate our data. This method ignores the errors associated with the fluctuation of the temperature and humidity from one experiment to another; and, focuses only on the electric field effect. We used the above method in MINITAB software and found the following P-values for drops on each of
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the surfaces: Aluminum (P=0.144), PEMA (P=0.025), PS (P=0.037), and Teflon (P=0.045). These P values indicate that the drop evaporation time is higher in the presence of electric field
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using PEMA, PS, and Teflon surfaces. But, for the aluminum the data does not indicate a significant change is evaporation time when an electric field is present.
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As it is clear from Figure 4, using of the electric field does not affect significantly the trend of
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the change of the volume over the time for the sessile drop evaporation. For all of the surfaces,
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volume of the drop changes linearly versus time for the period when the droplet evaporates in
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CBL mode (see initial time of droplet evaporation in Figure 4). The slope of linear function fitted (a) to the data is calculated in Figure 4 (see a values). Considering 95% confidence limit,
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a values with or without an electric field are the same. The reported a values in Figure 4 have ±7.3% deviation from the prediction of the Hu et al.15 that is typically used in the literature to
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estimate the rate of natural drop evaporation in CBL mode (see equation 19 in Ref. 15).
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For the times following the CBL mode, the drop evaporates in the CCA and it is observed that the volume changes in a nonlinear form in this period (see shaded area in Figure 4). As it is well predicted by Erbil et al.9, plotting the data as a function of drop volume to the power of
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2/3, versus time (see insets in Figure 4a to 4d where the change of the volume over the time for CCA is plotted), linear behavior can be observed. The change of the volume over time is calculated for all surfaces with and without electric field (see b values in Figure 4). For aluminum and PS, the change of the volume over time (or b value) is the same with and without an electric field. However, for Teflon and PEMA, when there is an electric field, b values are 14
0.1 lower compared to that of when there is no electric field i.e. reported values in Figures 4b and 4d. We also compared the rate of droplet evaporation from our data when there is no electric field (b values in Figure 4) and the most referred relations in the literature for natural drop evaporation (i.e. by Picknett and Bexon8, Rowan et al.12, and Bourges-Monnier and Shanahan10). It was found that the prediction of Bourges-Monnier and Shanahan10 has the
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closest estimation to our fitted values (with ±5.5% deviation), see b values in insets in Figures
4a to 4d. The deviation of our results from Picknett and Bexon8 and Rowan et al.12 perditions
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are ±32% and ±54%, respectively.
The presence of the electric field does not affect the modes of the evaporation for aluminum
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and PS. However, for PEMA and Teflon (which have small CAH), it decreases the duration of
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the CBL. This can be understood by the fact that electric field decreases the initial contact angle
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of the droplet to values very close to the receding contact angle. Thus, by a small decrease in
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the volume of the drop, the CA reaches the receding CA, and hence contact line recedes. This observation in practice results in lower baseline for the droplet in the presence of the electric
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field (see Figure 4) for the PEMA and Teflon surfaces which can be the reason for the higher evaporation time. For PS, decrease in the baseline of the drop which results in the higher
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evaporation time is very slight.
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To capture the effect of the electric field on the contact angle during the evaporation, we compared the contact angle of droplets for cases with and without electric field in Figure 5 (note during evaporation, the receding contact angle is generally observed). As it is clear during
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CBL mode, the presence of the electric field results in a lower CA (see also Figures 4m to 4p). However, in CCA modes, the CA is the same for the systems with and without electric field.
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Figure 4. Experimental results of drop evaporation over aluminum, PEMA, PS, and Teflon
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surfaces with (red symbols) and without (blue symbols) an external electric field. Error bars represent one standard deviation. In all of the plots, the electric field is activated at 5.5 min. In (a) to (d), a and b are the slope of linear function fitted to the data of drop evaporation when
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there is no electric field (i.e. blue symbols) at CBL and CCA modes, respectively. The magnitude of a and b are the same for with and without electric field, except for PEMA and
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Teflon for which the b value is -0.07. Note that the vertical and horizontal units of the insets in
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plots (a) to (d) are 1 mm3 and 10 min, respectively.
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Figure 5. Contact angle of the droplet during evaporation over aluminum, PEMA, PS, and
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Teflon surfaces with and without electric field.
Conclusion
In summary, we studied the natural evaporation of a sessile drop under an electric field. The
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effect of the electric field on sessile water droplet geometry (contact angle, baseline, and
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surface area) was examined for various surface wettabilities. The dynamics of diffusion-limited
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evaporation of sessile droplet under an electric field was studied. It is found that an electric
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field decrease the rate (or increase the time) of evaporation except for a surface with very large
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CAH. This is explained by our observations for surfaces with low CAH in which the presence of the electric field decreases/increases the duration of the of CBL/CCA modes during
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evaporation. It is also found that the electric field does not affect the trend of the change of drop’s volume over a time for surfaces with large CAH (larger than 32 deg.); but, the rate of
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the change in volume of the drop is lower in the presence of the electric field for surfaces with small CAH.
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Acknowledgment The Funding by the European Space agency under MAP program is acknowledged. We also would like to thank Craig Burkett who pointed us toward the statistical approach used in this study.
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24. S. N. Reznik, A. L. Yarin, A. Theron, and E. Zussman, J. Fluid Mech. 516, 349 (2004). 25. C. Roero, Contact Angle, Wettability and Adhesion, 4, 165 (2006). 26. A. Bateni, A. Amirfazli, and A.W. Neumann, Colloids Surf., A 289, 25 (2006). 27. J. M. Roux, J. L. Achard, and Y. Fouillet, J. Electrostatics 66, 283 (2008). 28. J. M. Roux and J. L. Achard, J. Electrostatics 67, 789 (2009). 29. A. Bateni, S. Laughton, H. Tavana, S. S. Susnar, A. Amirfazli, and A.W.Neumann, J. Colloid Interface Sci. 283, 215-222 (2005). 30. K. Takano, I. Tanasawa, and S. Nishio, Int. J. Heat Mass Transfer 37, 65 (1994). 31. K. Takano, I. Tanasawa, and S. Nishio, J. Enhanc. Heat Transfer 3, 73 (1996). 32. M. J. Gibbons, C. M. Howe, P. Di Marco, and A. J. Robinson, In J. of Phys.: Conf. Series 745, 032066 (2016). 33. A. Bateni, A. Ababneh, J. A. W. Elliott, A. Neumann, and A. Amirfazli, Adv. Space Res. 36, 64–69 (2005). 34. H. Chen, T. Tang, and A. Amirfazli, Colloids Surf., A 408, 17 (2012).
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S0927-7757(18)30625-3 https://doi.org/10.1016/j.colsurfa.2018.07.022 COLSUA 22677
To appear in:
Colloids and Surfaces A: Physicochem. Eng. Aspects
Received date: Revised date: Accepted date:
2-4-2018 10-7-2018 16-7-2018
Please cite this article as: Almohammadi H, Amirfazli A, Sessile Drop Evaporation under an Electric Field, Colloids and Surfaces A: Physicochemical and Engineering Aspects (2018), https://doi.org/10.1016/j.colsurfa.2018.07.022 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.
Sessile Drop Evaporation under an Electric Field
H. Almohammadi, A. Amirfazli*
Corresponding Author: A. Amirfazli: +1-416-736-5901; Email: [email protected]
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*
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Department of Mechanical Engineering, York University, Toronto, ON, M3J 1P3, Canada
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Graphical Abstract
Abstract
In this study, for the first time, the natural (diffusion-limited) evaporation of a sessile drop
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under an electric field was experimentally examined. A sessile drop natural evaporation is affected by the geometry of the drop, e.g. baseline, contact angle, and surface area, which all can be changed in the presence of an electric field. As such, first, the effect of electric field on sessile water droplet geometry was studied, together with how it differs for surfaces with various contact angle and contact angle hysteresis (for both hydrophilic and hydrophobic 1
surfaces). Then, the dynamics (evaporation time and mode) of natural evaporation of sessile droplet under an electric field was studied by measuring the evaporation rate, surface area, contact angle, and baseline of the droplet. It is found that compare to when there is no electric field, the evaporation time of a sessile droplet increases when there is an electric field. This was statistically shown to be significant for drops placed on surfaces with contact angle
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hysteresis lower than 32º. For droplets that evaporate in constant baseline mode initially and
then by evaporation in constant contact angle mode, the presence of the electric field resulted
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in a decrease in the duration of constant baseline mode when the surface had a low contact
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angle hysteresis.
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Keywords: evaporation; sessile drop; electric field; contact angle; diffusion limited
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Introduction
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Sessile drop evaporation has been the subject of many studies due to its numerous applications in surface patterning, inkjet printing, food industry, cosmetics, and biotechnology (e.g. DNA
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mapping)1-4. It is well understood that a sessile droplet evaporates due to different physical
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mechanisms including heat transfer by convection between air and liquid, heat transfer by conduction between liquid and a substrate, and the natural diffusion of the liquid into air5.
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Typically, the latter is considered as a predominant factor when studying natural evaporation of a drop5-7. Thus, the natural (also expressed as diffusion-limited) drop evaporation is controlled by the diffusivity of the vapor in the air, difference in vapor concentration at the
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drop surface and a point far from the drop, and the geometry of the droplet (e.g. baseline, contact angle, and surface area)8. In the literature many studies are dedicated to understand the influence of surface wettability on drop geometry and hence droplet evaporation8-18. It is found that depending on the surface type, a sessile drop evaporates through one of the following three different modes: constant contact angle (CCA) mode where during the evaporation the baseline 2
(BL) decreases but the contact angle (CA) remains constant; constant baseline (CBL) mode in which the contact line of the drop pins to the surface and CA decreases, or a combination of the CCA and CBL modes8,14-16. The presence and the duration of the each mode (in the case of having several modes during the evaporation) depends mainly on contact angle hysteresis (CAH). In the case of high CAH, the evaporation happens mostly in CBL mode; while for a
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small CAH, it is expected to observe CCA as a dominant mode during evaporation19. Depending on the mode of evaporation, theoretical relations are provided in the literature to
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predict the evaporation rate and time for droplet evaporation8-13, 14-18. Such rate is reported to
be independent of the CA when the CA is less than 40°13, 15. However, for CA values higher
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than 40º, an increase in the CA leads to a decrease in the intensity of the evaporative rate, and accordingly an increase in the total evaporation time. For example, the experimental results by
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Sobac et al.13 revealed an increase of 58% in total evaporation time when the CA increased
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from 63° to 135° for a droplet evaporating in CBL mode. It has been shown in the past that when a sessile drop is placed in an electric field (e.g. inside
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a capacitor) the sessile drop starts to elongate along the direction of the electric field20-28. The shape and the stability of sessile drops under electric fields has been analyzed in many works,
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where majority of them provided a model to compute the shape of an axisymmetric drop under a DC electric field20-28. Regarding the effect of the electric field on drop CA, only a few studies
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can be found5,29. The experimental studies summarized in Ref. 5 suggest that with an increase in magnitude of the electric field, depending on the type of surface and liquid, the CA can
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increase or decrease.
Considering the above mentioned points, the question is how the change in the geometry of the droplet brought upon by an electric field may affect the natural evaporation of a sessile drop. This topic is not investigated to date. There are only four related studies where the focus is on heated surface and only one type of the surface was studied30-32. Since the mechanism of the 3
sessile drop evaporation for heated surfaces, where both thermal effects of the solid and air and diffusion play a role, is different from the natural (diffusion-limited) evaporation, the results for a heated surface cannot be expanded to natural evaporation. Thus, it is not clear how an external electric field affects the natural evaporation rate of a droplet. And, how surface
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wettability plays a role in the presence of the external electric field during natural evaporation. Here, in a systematic experimental study, the evaporation of distilled water sessile drops (20
μl) under an electric field (varying from 0 to 11.1 KV/cm) was examined. Drops were placed
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on surfaces with various wettabilities to investigate the roles of CAH and receding/advancing CA on evaporation rate (and mode). To do so, we first studied the effect of electric field on
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sessile droplet geometry for a range of surface wettabilities. We examine the evaporation time
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of a sessile droplet under an electric field. Following this, the results for natural evaporation of
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a sessile drop under an electric field and how it changes with surface wettabilities will be
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presented.
Methods and Materials
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Figure 1 shows the setup used to perform the experiments. The capacitor (i.e. the part where
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drop sits and evaporates; see below) is placed inside a chamber (Figure 1a). The humidity and temperature of the chamber was measured using Fisher-brand Traceable Humidity Meter (Catalog number: 11-661-18). This device reads the temperature and humidity with accuracy
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of ±1ºC and ±2%, respectively. Drop evaporation experiments were done simultaneously in an environmental chamber containing two identical cells (the cells were fabricated for a pervious study [33] where detail can be found). A droplet was placed in each cell, where in one cell an electric field was present, and the other there was no electric field. This procedure helps to
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avoid any error associated with the change in temperature and humidity from test to test when comparing the droplet evaporation with and without electric field. The capacitor is made of two parallel copper discs (diameter of 2.54 cm), see inset in Figure 1a. The upper and lower dicks are identical. The drop (placed using a needle) sits on the target surface which is between the upper and the lower discs (Figure 1b). The target surface has the
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same size as electrodes (diameter of 2.54 cm); the gap between the upper disc and top of the surface is 8.8 mm. An EMCO (E101) high voltage power converter was used to provide the
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high voltage needed between the plates of the capacitor. High voltage power connectors and
wires (Caton Connector Corp., 14 series) were used to connect the power supply (Sorensen, DCS 40-25M37) and the copper discs.
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Drops of distilled water with the volume of 20 μl were used. This size of the droplets
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corresponds to Bond number (𝐵0 = 𝜌𝑔𝑅0 ℎ0 ⁄𝜎, representing the ratio of the gravitational to
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surface forces, where 𝜌 is the liquid density, 𝑔 is the gravitational acceleration, 𝑅0 is the initial
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contact line radius of drop (BL/2), ℎ0 is the initial height of the drop, and 𝜎 is the liquid surface
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tension) of 0.60±0.04 which shows that one can assume the droplet to have a spherical cap shape when there is no electric field. Two cameras (Basler and Photon Focus) were used to
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capture drop images at a frame rate of 0.1 fps. Two light sources (Schot Fostec and ROI) with
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two light diffusers were used to create diffused backlighting to image the drops. The diffused nature of the light and its intensity is not expected to provide any significant heating for the drops.
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The captured images were analyzed using ImageJ and Matlab software. ImageJ was used to measure the contact angle and baseline of the sessile drop; and Matlab was used to measure the volume and surface area of the droplet as follows: firstly a curve was fitted to the outline of the droplet using Inkscape software (see sample in Figure 1c); then the outline was imported to the Matlab; the sessile droplet was assumed to be the sum of several stacked discs with a height of
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one pixel. The volume and surface area of the droplet is calculated by summing the volume and surface area (of sides) of the stacked discs. The errors associated with this procedure was verified by calculating the volume of the droplet by gravimetry and our procedure; the errors was in the range of ±0.5 μl. Four different surfaces, i.e., aluminum, PEMA, PS, and Teflon, were used in this study. Spin
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coating method is used to fabricate PEMA, PS, and Teflon. The solutions that are used for each
surfaces are: PEMA: 1 wt% solution of PMMA (Aldrich MW~120000) in toluene, PS: 1 wt%
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solution of Polystyrene (Aldrich MW ~ 97,400) in toluene, Teflon: Teflon AF (DuPont) diluted with FC-75 (3M) in the ratio of 1:5 (v/v). All of the surfaces are cleaned before coating with
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DI water and acetone. Aluminum is used without any coating but after cleaning. The interested
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reader may refer to Ref. 34 for more surface fabrication details. The receding CA, advancing
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CA, and CAH of the surfaces, measured by sessile drop method, are provided in Figure 1d.
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Note that the reported CA values are a reflection of not only the intrinsic wettability of the substrates, but also the surface roughness and heterogeneity. For instance, the high contact
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angle reported for aluminum is reflective of it being a technical grade sample, i.e somewhat rough and heterogeneous. For each surface, at least three experiments were performed at
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similar temperature (21.4±0.6 ºC) and relative humidity (2.50±0.9 %) conditions.
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To observe the highest effect by the electric field on the geometry and subsequently the evaporation of a sessile droplet, we set the magnitudes of the electric field to just below the maximum for each surface. A higher value than the maximum electric field results in spark or
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bursting of the drop. The magnitude of the electric field was 11.1 KV/cm for aluminum and PEMA; and it was 10.3 KV/cm and 7.5 KV/cm for PS and Teflon surfaces, respectively. These values are ~0.2 KV/cm lower than the maximum electric field for each surface. The main reason for having lower electric field values for surfaces with higher wettability, is the higher
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height of the droplet for a given droplet volume. The droplet with a higher height bursts at lower magnitude of the electric field. Note that the electric potential corresponding to above mentioned electric field magnitudes are: aluminum (9.8 KV), PEMA (9.8 KV), PS (9.1 KV), Teflon (6.6 KV). Although, through this paper, we use the electric field values but it should be noted that the electric field is only
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uniform when there is no droplet between the electrodes; the presence of the droplet between
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electrodes distorts the uniformity of the electric field.
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Figure 1. (a) Overhead view of the experimental setup for drop evaporation; the capacitor is shown in inset. (b) Schematic view of the capacitor. (c) The sessile water droplet (20 μl) is
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placed over PEMA when there is no electric field. The yellow curve shows the fitted outline to calculate the volume and surface area of the droplet. (d) The wettability of the surfaces that are
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used in this study; the numbers above each bar shows the value of the CA. The errors for the
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reported CA in (d) are in the range of ±1º.
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Results and Discussion Effect of electric field on the sessile drop geometry. Figure 2 shows the effect of an external electric field on the geometry of a sessile droplet that is placed over surfaces with various wettabilities. Note that the first row in Figure 2 shows the droplets before activating the electric field, while second row is captured once the electric field is reached to the given magnitude.
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The time gap between the first and the second row is 1.50±0.08 min as one needs to ramp up the electric field to the desired magnitude (this period is considered to have a negligible effect
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on the comparative plots for evaporation given the totality of the experiment period and the
experimental uncertainties, e.g. see error bars in Fig. 3). The overlapped view of the first and
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the second row is presented in the third row. Following this, in Figure 2e, the percentage change
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of the parameters that affect the drop natural evaporation i.e. baseline, CA, and surface area
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when the electric field is provided.
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As it is clear in Figure 2, an external electric field elongates the sessile drop along the direction of the field. This can be understood by examining the augmented Younge-Laplace equation
at the apex as follows: 2
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σ ( r ) = ∆P0 + ∆Pe
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(Eq. 1), that relates the shape of the droplet to the pressure difference across the drop interface,
(1)
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where r is the radius of the curvature at apex, ∆P0 and ∆Pe represent the pressure difference across the drop interface due to the surface tension and electric field stress, respectively. Note that in Eq. (1), we considered the sessile droplet to be axis-symmetric and the gravity is
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neglected as Bond number for the studied droplet is 0.60±0.04 (see previous section). Physically Eq. (1) describes that to keep the mechanical equilibrium, the left hand side of the Eq. (1) needs to be increased by ∆Pe in the presence of the electric field. Thus, assuming negligible change in surface tension, the radius of the curvature (i.e. the term r in Eq. 1) should be decreased, which manifests itself as an elongation of the sessile droplet in the direction of 9
the electric field. Such elongation depending on the surface wettability may result in different form of the changes seen in the droplet geometry. For the aluminum and PS, the electric field decreases the CA while drop’s contact line is pinned to the surface. Pining of the drop’s contact line can be related to the high value of the CAH for
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these surfaces; the deformation of the drop by electric field force is not sufficiently large to decrease the initial contact angle of the droplet to below the receding CA. As such, the contact
line cannot recede and remains pinned, and only the contact angle decreases. On the other hand,
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for the PEMA and Teflon, both the baseline and CA of the of the droplet decrease in the presence of the electric field. The low value of the CAH, which results in a small difference
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between the initial contact angle (as placed droplet) and receding contact angle, is the reason
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for the receding of the contact line. For all surfaces, the presence of the electric field, resulted
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in an increase in the surface area of the drop which is due to the elongation of the droplet along
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the direction of the electric field. Such increase is higher for droplet on Teflon and PEMA compared to that of PS and aluminum. Thus, it can be understood that when there is receding
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for the droplet in the presence of the electric field, which happens for surfaces with small CAH,
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the surface area increases significantly by the electric field. To sum up, it seems that CAH plays a main role in the trend of the changes in the geometry of
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the droplet under the electric field. When the CAH is small, the presence of the electric field results in a decrease in baseline and CA. While for a high value of CAH, the contact line remains pinned and contact angle decreases. For all cases, surface area increases in the presence
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of electric field. Such issues (especially the trend of the change in CA) has not been clear in the literature5; some works reported that the presence of the electric field increases the contact angle, and other stated the opposite.
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Figure 2. The geometry of the sessile water droplet that is placed over (a) aluminum, (b) PEMA, (c) PS, and (d) Teflon surfaces. The magnitude of the baseline (BL, in mm), contact
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angle (CA, in º), and surface area (SA, in mm2) are reported below each image. The first row shows the droplet (19.25±0.48 μl) when there is no electric field, and the second row shows
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the droplet (18.76±0.52 μl) in the presence of electric field. In each column, third row shows the overlapped view of the first and the second rows. (e) Shows the percentage change in baseline, CA, and surface area of a droplet over aluminum, PEMA, PS, and Teflon in the
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presence of the electric field. For instance, the surface area increases by ((SAE-SA0)/SA0)=12%
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when the electric field is applied for a droplet that is placed over Teflon.
Effect of electric field on drop evaporation. Figures 3a to 3d show the process of the drop evaporation with and without an external electric field for drops placed on aluminum, PEMA, PS, and Teflon, respectively. The evaporation time for water droplet (20 μl) is given in Figure 3e.
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Looking at Figure 3e, the duration of the evaporation from high to low when there is no electric field is for drops on: PEMA, Teflon, PS, and aluminum. However, considering the error bars, it is clear that the surface wettability does not affect the evaporation time in a dramatic manner. To comprehend the reason for this behavior, detailed time evolution of the volume, surface area, baseline, and CA of droplets during the evaporation process for all of the surfaces is given
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in Figure 4. When there is no electric field, for all surfaces, evaporation is first in the CBL
mode and then as time progresses it falls in the CCA mode. However, the duration of the CBL
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mode is different from one surface to another. Such duration, from high to low is for drops on: aluminum, PS, PEMA, and Teflon. Thus, it can be seen that surfaces with high CAH have a
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higher duration of the CBL mode. This happens as the drop needs more time to change its
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contact angle from initial contact angle (for as placed droplet) to the value that results in receding of the contact line (i.e. receding CA). In the literature, it is reported that the
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evaporation time is lower in CBL mode compared to that of CCA17-18. However, evaporation time is a function of not only the mode of the evaporation, but also the magnitude of CA, the
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length of baseline, and surface area13. From Figure 4, for surfaces with lower wettability from one hand, the increase in contact angle, and decrease in baseline, should reduce the rate of
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evaporation, but on the other hand, the surface area increases which favors an increase in evaporation rate13. It is worth to note that in the case of high contact angle values, the free space
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around the triple line is small. Therefore, the concentration of water increases near the triple line and air circulation near the contact line is hindered. This results in low vapor diffusion into
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surrounding atmosphere and consequently a decrease in the evaporation mass flux13. The vapor diffusion into surrounding air also can be limited by small length of the contact line (or base line which is the indication for contact line length) for the droplet. Thus, using surfaces with lower wettabilities, from CA and baseline prospective, the evaporation is hindered, but from surface area point of view, the evaporation rate is enhanced. 12
From Figure 3e, it can be understood that the total evaporation time, which is a function of all
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of the above mentioned parameters, is not affected significantly by the surface wettability.
Figure 3. The evaporation of sessile water droplets placed on (a) aluminum, (b) PEMA, (c) PS, and (d) Teflon surfaces at different time. (e) Shows the evaporation time of sessile droplets
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(20 μl) over surfaces with various wettabilities with and without electric field. Error bars represent one standard deviation. The numbers printed inside each bar shows the exact
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evaporation time.
When there is an electric field, the evaporation time shows higher values (see Figure 3e). However, considering the error bars, the question is whether there is a difference between the total evaporation time for drops with and without an electric field. To answer this, as explained earlier, the drop evaporation experiments were done simultaneously in an environmental 13
chamber for two drops, one under an electric field and another in normal condition (no electric field). We used a statistical method i.e. ‘one way ANOVA with blocking’ to evaluate our data. This method ignores the errors associated with the fluctuation of the temperature and humidity from one experiment to another; and, focuses only on the electric field effect. We used the above method in MINITAB software and found the following P-values for drops on each of
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the surfaces: Aluminum (P=0.144), PEMA (P=0.025), PS (P=0.037), and Teflon (P=0.045). These P values indicate that the drop evaporation time is higher in the presence of electric field
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using PEMA, PS, and Teflon surfaces. But, for the aluminum the data does not indicate a significant change is evaporation time when an electric field is present.
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As it is clear from Figure 4, using of the electric field does not affect significantly the trend of
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the change of the volume over the time for the sessile drop evaporation. For all of the surfaces,
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volume of the drop changes linearly versus time for the period when the droplet evaporates in
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CBL mode (see initial time of droplet evaporation in Figure 4). The slope of linear function fitted (a) to the data is calculated in Figure 4 (see a values). Considering 95% confidence limit,
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a values with or without an electric field are the same. The reported a values in Figure 4 have ±7.3% deviation from the prediction of the Hu et al.15 that is typically used in the literature to
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estimate the rate of natural drop evaporation in CBL mode (see equation 19 in Ref. 15).
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For the times following the CBL mode, the drop evaporates in the CCA and it is observed that the volume changes in a nonlinear form in this period (see shaded area in Figure 4). As it is well predicted by Erbil et al.9, plotting the data as a function of drop volume to the power of
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2/3, versus time (see insets in Figure 4a to 4d where the change of the volume over the time for CCA is plotted), linear behavior can be observed. The change of the volume over time is calculated for all surfaces with and without electric field (see b values in Figure 4). For aluminum and PS, the change of the volume over time (or b value) is the same with and without an electric field. However, for Teflon and PEMA, when there is an electric field, b values are 14
0.1 lower compared to that of when there is no electric field i.e. reported values in Figures 4b and 4d. We also compared the rate of droplet evaporation from our data when there is no electric field (b values in Figure 4) and the most referred relations in the literature for natural drop evaporation (i.e. by Picknett and Bexon8, Rowan et al.12, and Bourges-Monnier and Shanahan10). It was found that the prediction of Bourges-Monnier and Shanahan10 has the
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closest estimation to our fitted values (with ±5.5% deviation), see b values in insets in Figures
4a to 4d. The deviation of our results from Picknett and Bexon8 and Rowan et al.12 perditions
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are ±32% and ±54%, respectively.
The presence of the electric field does not affect the modes of the evaporation for aluminum
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and PS. However, for PEMA and Teflon (which have small CAH), it decreases the duration of
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the CBL. This can be understood by the fact that electric field decreases the initial contact angle
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of the droplet to values very close to the receding contact angle. Thus, by a small decrease in
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the volume of the drop, the CA reaches the receding CA, and hence contact line recedes. This observation in practice results in lower baseline for the droplet in the presence of the electric
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field (see Figure 4) for the PEMA and Teflon surfaces which can be the reason for the higher evaporation time. For PS, decrease in the baseline of the drop which results in the higher
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evaporation time is very slight.
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To capture the effect of the electric field on the contact angle during the evaporation, we compared the contact angle of droplets for cases with and without electric field in Figure 5 (note during evaporation, the receding contact angle is generally observed). As it is clear during
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CBL mode, the presence of the electric field results in a lower CA (see also Figures 4m to 4p). However, in CCA modes, the CA is the same for the systems with and without electric field.
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Figure 4. Experimental results of drop evaporation over aluminum, PEMA, PS, and Teflon
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surfaces with (red symbols) and without (blue symbols) an external electric field. Error bars represent one standard deviation. In all of the plots, the electric field is activated at 5.5 min. In (a) to (d), a and b are the slope of linear function fitted to the data of drop evaporation when
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there is no electric field (i.e. blue symbols) at CBL and CCA modes, respectively. The magnitude of a and b are the same for with and without electric field, except for PEMA and
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Teflon for which the b value is -0.07. Note that the vertical and horizontal units of the insets in
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plots (a) to (d) are 1 mm3 and 10 min, respectively.
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Figure 5. Contact angle of the droplet during evaporation over aluminum, PEMA, PS, and
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Teflon surfaces with and without electric field.
Conclusion
In summary, we studied the natural evaporation of a sessile drop under an electric field. The
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effect of the electric field on sessile water droplet geometry (contact angle, baseline, and
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surface area) was examined for various surface wettabilities. The dynamics of diffusion-limited
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evaporation of sessile droplet under an electric field was studied. It is found that an electric
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field decrease the rate (or increase the time) of evaporation except for a surface with very large
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CAH. This is explained by our observations for surfaces with low CAH in which the presence of the electric field decreases/increases the duration of the of CBL/CCA modes during
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evaporation. It is also found that the electric field does not affect the trend of the change of drop’s volume over a time for surfaces with large CAH (larger than 32 deg.); but, the rate of
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the change in volume of the drop is lower in the presence of the electric field for surfaces with small CAH.
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Acknowledgment The Funding by the European Space agency under MAP program is acknowledged. We also would like to thank Craig Burkett who pointed us toward the statistical approach used in this study.
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