Water vapor uptake into hygroscopic lithium bromide desiccant droplets: mechanisms of droplet growth and spreading

Zhenying Wang ab, Daniel Orejon *ab, Khellil Sefiane c and Yasuyuki Takata *ab
aInternational Institute for Carbon-Neutral Energy Research (WPI-I2CNER), Kyushu University, Fukuoka 819-0395, Japan
bDepartment of Mechanical Engineering, Thermofluid Physics Laboratory, Kyushu University, Fukuoka 819-0395, Japan. E-mail: orejon.daniel@heat.mech.kyushu-u.ac.jp; takata@mech.kyushu-u.ac.jp
cSchool of Engineering, Institute for Multiscale Thermofluids, University of Edinburgh, King's Buildings, Mayfield Road, Edinburgh EH9 3JL, UK

Received 16th July 2018 , Accepted 9th October 2018

First published on 10th October 2018


The study of vapor absorption into liquid desiccant droplets is of general relevance to a better understanding and description of vapor absorption phenomena occurring at the macroscale as well as for practical optimization of dehumidification and refrigeration processes. Hence, in the present work, we provide the first systematic experimental study on the fundamentals of vapor absorption into liquid desiccant at the droplet scale, which initiates a novel avenue for the research of hygroscopic droplet growth. More specifically we address the behavior of lithium bromide–water droplets on hydrophobic PTFE and hydrophilic glass substrates under controlled ambient conditions. Driven by the vapor pressure difference between the ambient air and the droplet interface, desiccant droplets absorb water vapor and increase in volume. To provide further insights on the vapor absorption process, the evolution of the droplet profile is recorded using optical imaging and relevant profile characteristics are extracted. Results show that, even though the final expansion ratio of droplet volume is only a function of relative humidity, the dynamics of contact line and the absorption rate are found to differ greatly when comparing data with varying substrate wettability. Droplets on hydrophilic substrates show higher absorption kinetics and reach equilibrium with the ambient much faster than those on hydrophobic substrates. This is attributed to the absorption process being controlled by solute diffusion on the droplet side and to the shorter characteristic length for the solute diffusion on hydrophilic substrates. Moreover, the apparent droplet spreading process on hydrophilic substrates when compared to hydrophobic ones is explained based on a force balance analysis near the triple contact line, by the change of liquid–vapor surface tension due to the increase in water concentration, and assuming a development of a precursor film.


1. Introduction

Droplet evaporation is a widely observed phenomenon in nature, and has been applied in several industrial and biological fields from ink-jet printing1 and thin film coating,2,3 to DNA stretching and disease diagnosis.4 In recent years, an increasing number of investigations have been carried out on the effect of ambient pressure,5,6 ambient temperature and humidity,7,8 as well as substrate wettability,9,10 thermal conductivity and temperature11,12 on the drop evaporation process. Depending on the surface wettability and surface structure, droplets evaporate in different modes. The widely accepted evaporation mechanisms, depending on the dynamics of the triple contact line (TCL), are the constant contact angle (CCA) mode, the constant contact radius (CCR) mode, and the CCR–CCA mixed mode.13,14 Typically, the CCA mode happens on smooth hydrophobic substrates where the droplet contact line recedes while the contact angle remains constant to account for the liquid evaporated. On a hydrophilic and/or on a rougher substrate where the surface hysteresis is high though, the triple contact line tends to be pinned while the contact angle decreases with time, namely, the CCR mode. In addition, during evaporation of nanofluid droplets15,16 or pure fluid droplets on structured surfaces,17 a stick-slip evaporative behavior has also been reported. As a consequence of the different evaporation behavior, the lifetime of a droplet is found to differ.9,18,19 The evolution, and in particular, the lifetimes, of droplets evaporating in a variety of different modes of evaporation have been studied by Stauber et al.20,21 and Schofield et al.22 using the diffusion-limited evaporation model (see, for example, Popov18 and Saada et al.23).

On the other hand, liquid desiccants are a special type of aqueous salt solution, which have excellent hygroscopic properties. Due to the hygroscopic nature of liquid desiccants, they are widely applied in all kinds of dehumidification systems,24 absorption heat pumps,25,26 and absorption heat transformers.27 Most commonly used ionic liquid desiccant salts include lithium bromide (LiBr), lithium chloride (LiCl) and calcium chloride (CaCl2).28 These salts have strong affinity and adhesion to the water molecules, and after dissolving in water, they reduce greatly the partial vapor pressure of the solution at the liquid–air interface. In the case of droplet evaporation, the vapor diffusion is driven by the vapor pressure difference between the saturated droplet interface and the unsaturated air bulk.29 Nonetheless, when it comes to liquid desiccant droplets, the vapor pressure at the droplet interface becomes lower than the partial vapor pressure of the ambient air. Therefore, the direction of vapor diffusion converses, and water vapor diffuses spontaneously from the air side to the droplet side.

The coupled heat and mass transfer between humid air and liquid desiccant is fundamental and of significant importance to all kinds of dehumidification applications. Up to now, most of the research carried out on liquid desiccants addresses: the performance of dehumidifiers with different flow patterns,30,31 different type of inner packing,32,33 presence or absence of inner heat sources,34,35 and different desiccant solutions or ambient conditions,36,37 at the macro-scale or at the system scale. Some theoretical models38 have also been mathematically developed and experimentally verified, which are capable of predicting to some extent the heat and mass transfer process within the dehumidifier as a whole system. Despite of the above mentioned studies, the performance of liquid desiccant droplets within a dehumidifier has been rarely reported. At the inlet of the dehumidifier, desiccant droplets are formed at the liquid distributor before impinging onto the inner packing.39 Upon impingement, discrete drops varying in size and shape appear at the top of the packing and flow down in a dropwise or filmwise fashion depending on the surface wettability. In industrial applications, the inner fillers vary from light polymers, non-corrosive ceramics, to high-strength metals,40 which provide different surface wettability, and therefore the flow regime of the desiccant solution inside also differs. A further investigation on vapor absorption into individual liquid desiccant droplets will shed light on the absorption process especially at the initial stage of dehumidification where discrete droplets in contact with the substrate are present. Further understanding on the dynamics of droplet growth during vapor absorption on different substrates will also help providing new insights on the mechanisms of filmwise or dropwise formation and its relation with surface properties, so that one can provide a more accurate prediction of the vapor uptake happening inside different desiccant dehumidification devices.

Hence, in this study, we investigate the vapor absorption mechanisms of LiBr–H2O droplets on surfaces with different wettability at certain controlled ambient conditions. Experiments are carried out with 54 wt% aqueous lithium bromide–water (LiBr–H2O) droplets on hydrophobic polytetrafluoroethylene (PTFE) and on hydrophilic glass substrates, which are commonly used as inner packing in dehumidification systems at laboratory and at industrial scales. The dynamics of triple contact line (TCL) and the evolution of droplet volume are compared, indicating the strong effect of surface wettability on the vapor absorption process into droplets. By looking into the solute diffusion process on the droplet side we demonstrate the different kinetics of absorption and droplet growth function of surface wettability. Moreover, several plausible explanations are provided to account for the apparent droplet spreading phenomenon observed on hydrophilic glass substrates when compared to hydrophobic PTFE one.

2. Experimental setup

Experiments are carried out within an insulated environmentally controlled chamber (800L, PR-3KT from ESPEC Corp., Japan), capable of providing constant temperature, Tamb, and relative humidity, RH (Tamb = −20 to 100 °C and RH = 20–98%) environments. In this study, experiments are carried out at six representative ambient conditions with Tamb = 25 °C and 45 °C, and RH = 30%, 60%, and 90%. During experimental observations, the environmental condition within the chamber is monitored both by the chamber panel and by an electronic hygrothermograph (testo 610 from testo AG (Germany), Tamb = −10 to 80 °C and RH = 20–100%). Schematic of the experimental setup is shown in Fig. 1, which includes: environmental chamber, CCD camera and lens, LED back light, stainless steel laboratory jack, droplet dosing system and data acquisition system. The high-definition CCD camera (Sentech STC-MC152USB with a RICOH lens and 25 mm spacing ring) along with a LED backlight are used to image the droplet profile at 4.8 frames per second. The real-time video of the droplet profile is thereafter processed with the software ImageJ® and MATLAB®. Then, the evolutions of droplet volume, V (μL), contact radius, R (mm), and contact angle, θ (deg), along with time, t (s), are extracted by assuming the shape of the droplet as spherical cap geometry.
image file: c8cp04504f-f1.tif
Fig. 1 Overview of the experimental setup. (a) Experimental part: environmental chamber, CCD camera, back light, stainless steel vertical platform, X–Y platform, droplet dosing system; (b) data acquisition system with Image J® and Matlab®; (c) experimental conditions shown on the psychrometric chart.

54.0 wt% lithium bromide (LiBr) solution and deionized water from Sigma-Aldrich are used as testing fluids for the experimental observations. Typically, a sessile droplet whose largest dimension is smaller than the capillary length will adopt spherical cap shape. For pure water in air, the capillary length is estimated as 2.6–2.7 mm (calculated according to the definition of capillary length, image file: c8cp04504f-t1.tif,41 where λ is the capillary length in meters, γlg is the liquid–air surface tension in N m−1, ρ is the liquid density in kg m−3, g is the gravitational acceleration in m2 s−1). On the other hand, for 54 wt% LiBr–H2O solution in air, the capillary length is ca. 2.42 mm. In our study, the contact radius of both water droplets and LiBr–H2O droplets did not exceed the capillary length throughout the vapor absorption process, therefore, the gravity effect on the droplet shape can be neglected and the assumption of treating the droplet as spherical cap is reasonable. We note here that some vapor absorption onto the droplet might happen during droplet deposition.

Table 1 includes the properties of 54.0 wt% LiBr–H2O solution and those of pure water. LiBr–H2O solution has higher viscosity and greater liquid-gas surface tension, which contributes to the higher equilibrium contact angle of LiBr–H2O droplets on the same substrates when compared to pure water droplets. Moreover, the boiling point of 54 wt% LiBr–H2O solution at 1 atmosphere is ca. 40 °C higher than that of pure water, which suggests the apparent lower vapor pressure at the solution surface.

Table 1 Properties of 54 wt% LiBr solution and distilled water as specific heat capacity cp (kJ kg−1 K−1); density ρ (kg m−3); liquid-gas surface tension γlg (mN m−1); viscosity ν (mPa s); thermal conductivity k (W m−1 K−1); boiling temperature Tboiling (°C). Properties shown were obtained at 20 °C and at 1 atm
Liquid type c p (kJ kg−1 K−1) ρ (kg m−3) γ lg (mN m−1) ν (mPa s) k (W m−1 K−1) T boiling (°C)
54 wt% LiBr solution 1.98 1600 91.54 4.751 0.4286 140
Distilled water 4.18 998 72.75 1.005 0.5984 100


Two types of substrates are chosen for the experiments; hydrophobic polytetrafluoroethylene (PTFE) and hydrophilic glass. Table 2 lists the main properties of the two substrates, where the surface roughness, Sq, is assessed with a 3D optical laser scanning microscope (Olympus LEXT OLS4000, Japan), and the droplet equilibrium contact angle for deionized water, θ0, is measured using a custom-built contact angle analyzer at laboratory ambient conditions, i.e., Tamb = 20 °C and 55% RH.

Table 2 Properties of glass and PTFE substrates as density ρ (kg m−3); specific heat capacity cp (J kg−1 K−1); thermal conductivity k (W m−1 K−1); thermal diffusivity α (m2 s−1), α = k/ρcp; surface roughness Sq (μm); and equilibrium contact angle for a 3 μL water droplet, θ0,W (°), and for a 3 μL LiBr droplet, θ0,S (°), at 20 °C and 1 atm
Material ρ (kg m−3) c p (kJ kg−1 K−1) k (W m−1 K−1) α (m2 s−1) S q (μm) Equilibrium θ0,W (°) Equilibrium θ0,S (°)
PTFE 2200 1.05 0.25 0.52 0.516 98 ± 3 108 ± 3
Glass 2400 0.84 0.75 2.15 0.012 70 ± 3 75 ± 3


Before experiments, substrates are cleaned by immersing each sample in an ultrasonic bath with ethanol for 15 minutes. After that, the sample is taken out and rinsed with large amount of deionized water. Then, substrates are further dried with filtered compressed air to remove any possible remaining dust or contaminants. After drying, the substrate is placed inside the chamber for sufficiently long time for the substrate to reach equilibrium temperature with the environment. Then, a droplet of 4 ± 0.5 μL is deposited within the environmental chamber on the chosen substrate. We note here that dosing system and substrate are inside the chamber for sufficient time to ensure that both fluid and substrate are at Tamb. Before droplet deposition, CCD acquisition is started and the evolution of the droplet profile is then recorded in time.

3. Experimental results

3.1. Droplet TCL dynamics on hydrophilic glass substrates

Representative evolution curves of contact angle, θ, and normalized contact radius, R/R0, of LiBr–H2O droplets on a hydrophilic glass substrate for the six different ambient conditions are plotted in Fig. 2. The initial contact angle for LiBr–H2O droplets on a glass substrate is ca. 75° ± 3°, about 5° larger than that of pure water droplets due to the higher liquid-air surface tension (see Table 1). Depending on the ambient condition, droplets on hydrophilic glass substrates show different degree of spreading. We note here that the slow spreading evolution reported here differs from early regimes of spreading where the droplet establishes the spherical cap in the first few seconds after deposition. Further discussion on the spreading mechanisms is included within Section 4.2. At 30% RH (Fig. 2(a)), θ decreases from 75° to about 52°, while the contact radius increases to 1.24 times of its initial value. At 60% RH (Fig. 2(b)) and at 90% RH (Fig. 2(c)), qualitatively, the decrease in contact angle follows the same trend to that reported for 30% RH, where there is an initial decrease and then flattens. Quantitatively, at high humidity of 90% RH, the contact angle decreases to about 40° while the contact radius increases to ca. 2 times due to greater drop spreading coupled with greater amount of water vapor absorbed. The quantitative behavior at intermediate humidity of 60% RH (Fig. 2(b)) is found to lie between low and high relative humidity cases where the contact angle decreases to a value between 40° and 50° and the contact radius increases to a value of ca. 1.4 times the initial one. Ambient temperature Tamb is found to influence the rate of droplet spreading during the initial stage of vapor absorption, where the droplet contact angle and contact radius vary more rapidly at 45 °C than at 25 °C.
image file: c8cp04504f-f2.tif
Fig. 2 Evolution of (up-triangles) contact angle, θ (°), and (diamonds) normalized contact radius, R/R0, of LiBr–H2O droplets, versus time (s) for (a) 30% RH, (b) 60% RH, and (c) 90% RH, at (open symbols) Tamb = 25 °C and (close symbols) Tamb = 45 °C on hydrophilic glass substrates. (d) Initial (t = 0 s) and final (t = 6000 s) snapshots of a LiBr–H2O droplet on a hydrophilic glass substrate at 45 °C and 90% RH.

To exemplify the droplet profile change during vapor absorption, Fig. 2(d) shows snapshots of a LiBr–H2O droplet on a hydrophilic glass substrate at 45 °C and 90% RH at the initial (t = 0 s) and at the final (t = 6000 s) stage of absorption. Due to water uptake, an expansion of droplet volume is observed. In addition, due to both droplet expansion and contact angle decrease, the triple contact line (TCL) advances greatly throughout the absorption process, i.e., radius increases to approximately 1.2, 1.4 and 2.0 times its initial value at 30%, 60% and 90% RH, respectively.

3.2. Droplet TCL dynamics on hydrophobic PTFE substrates

Representative evolution curves of contact angle, θ, and normalized contact radius, R/R0, of LiBr–H2O droplets on a hydrophobic PTFE substrate for the six different ambient conditions are shown in Fig. 3. The initial contact angle of a LiBr–H2O droplet on the hydrophobic PTFE substrate is ca. 108° ± 3° for all the experimental conditions, about 10° higher than that of pure water droplets on the same PTFE substrate studied. At 30% RH (Fig. 3(a)) the contact angle of a LiBr–H2O droplet decreases from 108° to 93° ± 4°, while the contact radius increases to ca. 1.2 times its initial value and reaches equilibrium after ca. 700 seconds. At 60% RH (Fig. 3(b)) the droplet contact radius increases to 1.3 times its initial value, while the droplet contact angle decreases from 108° to 93°. At 90% RH (Fig. 3(c)) the droplet grows even larger as the final R/R0 reaches ca. 1.6, while the contact angle decreases from 107° to 90°. Spreading behavior reported here also differs from early regime of spreading where the droplet establishes the spherical cap, which is further discussed within Section 4.2. For the same ambient humidity, the increase in contact radius and the decrease in contact angle are actually more marked at high ambient temperatures (Tamb = 45 °C) than at low ambient temperatures (Tamb = 25 °C).
image file: c8cp04504f-f3.tif
Fig. 3 Evolution of (up-triangles) contact angle, θ, and (diamonds) normalized contact radius, R/R0, of LiBr–H2O droplets, versus time (s) for (a) 30% RH, (b) 60% RH, and (c) 90% RH, at (open symbols) Tamb = 25 °C and (close symbols) Tamb = 45 °C on a hydrophobic PTFE substrate. (d) Initial (t = 0 s) and final (t = 6000 s) snapshots of a LiBr–H2O droplet on a PTFE substrate at 45 °C and 90% RH.

Moreover, on a PTFE substrate we report the sudden decrease in the contact angle accompanied with the increase in the contact radius in an advancing stick-slip fashion, which is marked with black arrows in Fig. 3(b) and (c). We henceforth refer to such behavior as advancing stick-slip. For a LiBr–H2O droplet sitting on a hydrophobic PTFE substrate, the TCL remains pinned or slightly increases while the contact angle increases to account for the increase in volume due to vapor absorption (Fig. 3(b) and (c)). Heterogeneities on the PTFE solid surface may induce the observed additional pinning barrier, which must be overcome before the TCL slips or jumps forward.15,16 Typically, as the contact angle deviates from the equilibrium one, the droplet gains certain excess of free energy and when such excess of free energy overcomes the pinning barrier exerted by the solid surface the jump of the TCL ensues.16 The advancing slip or jump of the TCL observed is characterized by the sudden decrease in the contact angle and the associated increase in the contact radius. Advancing stick-slip reported here differs from receding stick-slip behavior reported earlier during nanofluid droplet evaporation15,16 or pure fluid droplets evaporating on structured surfaces.17 In the case of receding stick-slip, the contact angle decreases to account for the loss of volume due to evaporation while the TCL remains pinned to the substrate.15,16 Then, as the droplet evaporates, the excess of free energy increases and when the excess of free energy becomes greater than the pinning barrier the jump of the TCL ensues.16 During receding stick-slip the jump of the TCL is characterized by the sudden increase in the contact angle and the associated decrease in contact radius, opposite to the decrease in contact angle and increase in droplet radius here reported during advancing stick-slip. In addition, the advancing stick-slip appears to be more frequent and marked at high humidity conditions; especially at 90% RH (Fig. 3(c)), due to the more rapid droplet expansion when compared to 30% RH (Fig. 3(a)) and to 60% RH (Fig. 3(b)). To illustrate the vapor absorption behavior, Fig. 3(d) shows snapshots of a LiBr–H2O droplet on a hydrophobic PTFE substrate at 45 °C and 90% RH at initial droplet deposition (t = 0 s) and at later stage of absorption (t = 6000 s).

It is then evident that hygroscopic LiBr–H2O droplets behave differently depending on the wettability of the surface. The characteristic behavior of absorption for LiBr–H2O droplets on a hydrophobic PTFE substrate is then characterized by smaller TCL spreading when compared to that observed on hydrophilic glass. On a PTFE substrate the increase of both droplet contact radius and droplet height are solely due to vapor absorption, whereas for LiBr–H2O droplets on a hydrophilic glass, the coupling mechanisms of both droplet spreading and vapor absorption govern the advancing behavior of the TCL and its dynamics. We also note here that the dynamics of the TCL during vapor absorption into liquid desiccant droplets differ from those of droplet evaporation, dropwise condensation, droplet growth during freezing and/or from the simultaneous monotonic increase in contact angle and decrease in contact radius due to the water adsorption–absorption and/or condensation during organic solvent evaporation.42–45

3.3. Evolution of droplet volume during vapor absorption

During vapor absorption, the droplet volume increases in different trends depending on the ambient condition. Fig. 4 presents evolution of the normalized droplet volume along with time on hydrophilic glass (Fig. 4(a)) and on hydrophobic PTFE substrates (Fig. 4(b)). At low ambient humidity of 30% RH, the droplet volume increases ca. 10% reaching equilibrium with the ambient after several hundred seconds. At 60% RH, droplet expansion is more evident, and it also takes longer for the droplets to reach equilibrium with the ambient, ca. 1000–2000 seconds. At high humidity of 90% RH, droplets grow following a saturating trend throughout the complete duration of the experimental observations ca. 2 hours. When comparing the final values of the droplet volume in Fig. 4, it shows that the final expansion ratio of droplet volume, Vf/V0, is only related to the relative humidity: Vf/V0 (30% RH) ≈ 1.07, Vf/V0 (60% RH) ≈ 1.5 and Vf/V0 (90% RH) ≈ 2.7–3.3 regardless of surface wettability and ambient temperature. We note here that although surface wettability does not have an impact on the final droplet volume, there are differences on the absorption kinetics, which will be discussed in the next section (Section 4).
image file: c8cp04504f-f4.tif
Fig. 4 Evolution of normalized droplet volume, V/V0, versus time, t (s), for LiBr–H2O droplets on (a) glass substrate and (b) PTFE substrate at (close symbols) Tamb = 25 °C and (open symbols) Tamb = 45 °C for (squares) 30%, (up-triangles) 60% and (diamonds) 90% RH. (Blue dashed line) time at which the droplet reaches V/V0 = 1.5 at 60% RH and (red dashed line) time at which the droplet reaches V/V0 = 2.5 at 90% RH, on a glass and on a PTFE substrate.

As marked with red and blue dashed lines in Fig. 4, for the same ambient condition of 45 °C and 90% RH, on a hydrophobic PTFE substrate it takes 4000 seconds for the LiBr–H2O droplet to expand to 2.5 times of its initial volume, while on a hydrophilic glass substrate it takes ca. 2550 seconds. At 45 °C and 60% RH, on a hydrophobic PTFE substrate it takes 1650 seconds for the droplets to expand to 1.5 times of its initial volume, while on a hydrophilic glass substrate it takes about half of it, i.e., ca. 900 seconds. To provide further quantification and comparison on the amount of water uptake during the absorption process, Table 3 presents the normalized droplet volume at different instants of time with t = 0 s as the droplet deposition. On one hand, at low relative humidity 30% RH the droplet volume remains constant during the absorption times reported in Table 3. On the other hand, when looking into medium and high relative humidity conditions, i.e., 60% RH and 90% RH, the droplet volume increases faster on hydrophilic glass when compared to hydrophobic PTFE. We note here that in the case of high relative humidity 90% RH, the droplet volume continuously increases for the experimental times reported.

Table 3 Normalized droplet volume, V/V0, at 25 °C and 30%, 60% and 90% RH on both hydrophilic glass and hydrophobic PTFE substrates at t = 500, 1000, 2000, 3000 and 4000 seconds with t = 0 seconds as the droplet deposition instant
Normalized droplet volume, V/V0, at 25 °C 500 s 1000 s 2000 s 3000 s 4000 s
Glass PTFE Glass PTFE Glass PTFE Glass PTFE Glass PTFE
30% RH 1.06 1.09 1.09 1.09 1.10 1.11 1.11 1.11
60% RH 1.32 1.33 1.55 1.48 1.60 1.57 1.61 1.63
90% RH 1.49 1.46 1.82 1.75 2.33 2.16 2.73 2.39 2.89 2.52


To demonstrate the amount of water absorbed during droplet expansion depending on Tamb and RH, Fig. 5 includes the psychometric chart representing the humidity ratio (kg water/kg dry air) versus Tamb and RH. The properties of LiBr–H2O solution and humid air in the chart are calculated with embedded functions in EES® (Engineering Equation Solver) software. Black solid lines in Fig. 5 show the condition (Tamb and humidity ratio) of ambient air at different RH, while blue dashed lines represent the condition (Tamb and humidity ratio) of the equivalent humid air layer at the surface of LiBr–H2O solution with different concentrations. It can be seen that the iso-concentration curves of LiBr–H2O solution and the iso-relative humidity curves of ambient air are in parallel or overlap with each other, which indicates that the humid air at a certain relative humidity is in equilibrium with the solution for a certain salt concentration. When the ambient relative humidity keeps constant, the desiccant droplet will keep absorbing water vapor until it reaches equilibrium with the ambient.


image file: c8cp04504f-f5.tif
Fig. 5 Psychrometric chart showing the condition of the humid air (solid line) at different relative humidity, and the condition of equivalent humid air layer at the surface of LiBr–H2O solution (blue dashed line) at different concentrations. Red solid arrows present the concentration variation of LiBr–H2O solution during vapor absorption.

The red points in Fig. 5 represent the initial and final conditions (Sinitial,25°C, Sfinal,25°C, Sinitial,45°C, Sfinal,45°C) of the LiBr–H2O droplets at 25 °C, 45 °C, and 90% RH. During vapor absorption, the liquid desiccant salts stay within the droplet in the form of ions, and therefore, the solution concentration of LiBr, x, should follow the solute conservation equation shown in eqn (1):

 
ρinitialVinitialxinitial = ρfinalVfinalxfinal(1)
For droplets at 25 °C and 45 °C, the expansion ratio of droplet volume is therefore derived as:
 
image file: c8cp04504f-t2.tif(2)
Taking 90% RH as an example, the ρinitial/ρfinal is 1.430 at 25 °C, and 1.433 at 45 °C according to our calculation based on the correlation provided in ref. 46. And since the ratio of droplet concentration xinitial/xfinal is also the same for 25 °C and for 45 °C, the same final expansion ratio of droplet volume Vfinal/Vinitial regardless of the ambient temperature and surface wettability is then demonstrated.

4. Analysis and discussion

4.1. Effect of surface wettability on the absorption kinetics

From the evolution of droplet volume, it is also worth noticing that the surface wettability has a strong effect on the kinetics of vapor absorption and on the dynamics of the TCL, which in turn dictates the mechanisms of droplet growth. Further quantification of the results presented in Section 3 is included in Table 4, which shows the normalized vapor absorption rates for the first 100 seconds after the droplet deposition. Droplets on hydrophilic glass substrates show higher vapor absorption rates than those on hydrophobic PTFE. In addition, the expected greater initial absorption rates at high ambient temperature (Tamb = 45 °C) when compared to low ambient temperature (Tamb = 25 °C) are also highlighted.
Table 4 Normalized initial vapor absorption rate, d(V/V0)/dt, during the first 100 seconds for: 25 °C–60% RH, 25 °C–90% RH, 45 °C–60% RH, and 45 °C–90% RH, on hydrophilic glass and hydrophobic PTFE substrates
Normalized absorption rate d(V/V0)/dt (s−1) 25 °C–60% RH 25 °C–90% RH 45 °C–60% RH 45 °C–90% RH
Hydrophilic glass 0.00102 0.00103 0.00137 0.00132
Hydrophobic PTFE 0.00098 0.00089 0.00133 0.00124


Droplet growth due to vapor uptake into liquid desiccant droplets reported in this study is driven by the vapor pressure difference between the humid air and the droplet surface. The vapor absorption from the humid air into the LiBr–H2O droplet can be divided into three steps: the water vapor diffusion on the air side, the vapor to water phase-change transition at the air–liquid interface, and the diffusion of water molecules from the droplet interface toward the droplet bulk (or the solute (Li+, Br) diffusion from the bulk of the droplet towards the droplet interface). Fig. 6 shows one-dimensional evolution of ambient air and liquid desiccant solution during the vapor absorption process, where the thickness of the liquid layer for the diffusion of the solute equals the droplet characteristic length (h*), and the air layer is assumed to be infinite since the chamber is large enough compared to the size of the droplets. At the very initial stage, right after the droplet deposition (t = 0 seconds), we assume that there is no mass diffusion between the humid air and the aqueous solution, and an apparent vapor pressure difference between the ambient air and the liquid surface is present. Then, driven by the pressure difference, water vapor gradually diffuses from the air side to the liquid–air interface, and gets absorbed. Due to vapor absorption, the concentration of solute (Li+ and Br ions) near the liquid–air interface decreases. Then, Li+ and Br ions diffuse from the high concentration side at the droplet bulk to the low concentration side at the liquid interface following the concentration gradient. As the absorption process continues and as a consequence of the increase in water concentration within the droplet, the vapor pressure difference between the liquid surface and the ambient air decreases. At the same time, the concentration gradient of LiBr solute within the aqueous solution also decreases until equilibrium is attained. The local change in concentration at the liquid–air interface and in the droplet profile due to vapor absorption reported here, differs from the concentration change due to preferential evaporation of one component during evaporation of binary mixtures.43,47–49


image file: c8cp04504f-f6.tif
Fig. 6 Schematic of water vapor concentration in the air side and the concentration of liquid water in the bulk of the droplet (a) at initial stage right after droplet deposition, t = 0 s, (b) during vapor absorption, and (c) at equilibrium, t = ∞.

Since vapor absorption is a surface area related problem, it is noteworthy providing a comparison between the spherical cap surface area of liquid desiccant droplets on hydrophilic versus hydrophobic substrates. For droplets on hydrophilic glass substrate, the interfacial area for mass transfer is ca. 9.02–10.65 mm2, while for droplets on hydrophobic PTFE, the interfacial area is ca. 9.04–10.68 mm2. Since there is no large difference in the effective droplet areas for vapor absorption, the absorption rate must be governed by the mass diffusion process on the air side and/or on the liquid side. Typically, the mass diffusion rate in the liquid phase is 103–104 times of that in the gas phase (Dwater/air/DLiBr/LiBr–H2O ∼ 10−5/10−9 ∼ 104).50 Therefore, we can assume that the vapor absorption process is limited by the solute diffusion on the liquid side.

The solute diffusion process within the LiBr–H2O droplet can be further evaluated by the characteristic time, τ, presented as eqn (3),

 
τ = L2/D(3)
where L is the characteristic length for mass diffusion, which we assume as the characteristic length of the droplet, h*, and D is the mass diffusion rate (m2 s−1).

According to eqn (3), the characteristic time for the solute diffusion on the liquid side is calculated as ca. 103 seconds, where the characteristic length of the droplet, L, is estimated as 1 mm, and the water diffusion rate, Ds, is 10−9 m2 s−1.51,52 It shows that the characteristic time for solute diffusion is in the same order of magnitude to that of the vapor absorption period reported in the experiments (500–8000 seconds). Hence, solute concentration gradient within the LiBr–H2O droplet is the dominant mechanism governing vapor absorption onto liquid desiccant droplets and cannot be neglected.

Considering the solute diffusion process within the droplet governed by Fick's law, the characteristic length for solute diffusion is the shortest path for the diffusing molecules of water to reach the solid surface or to “meet” each other, and for the Li+ and Br molecules to reach the liquid–air interface. While the solid surface can be treated as an impermeable boundary with zero mass flux, the liquid–air interface must be treated as a moving boundary condition governed by the change in droplet volume due to water vapor absorption. On hydrophilic glass substrates where the droplet contact angle is less than 90°, the characteristic length for solute diffusion required for the theoretical description of this process is the droplet height h* = hdrop as shown in Fig. 7(a). Whereas on hydrophobic PTFE substrates where the droplet contact angle is larger than 90°, the characteristic length for solute diffusion is the radius of curvature h* = κdrop as shown in Fig. 7(b). Further work is currently being sought on the theoretical modelling of the vapor absorption process.


image file: c8cp04504f-f7.tif
Fig. 7 Characteristic droplet length, h*, for solute diffusion within the LiBr–H2O droplets (a) on hydrophilic glass substrate, and (b) on hydrophobic PTFE substrates.

Fig. 8 shows the evolution of the characteristic lengths for droplets on a hydrophilic glass substrate and on a hydrophobic PTFE substrate in time at 45 °C and 60% RH (Fig. 8(a)) and at 45 °C and 90% RH (Fig. 8(b)). It shows that on glass substrates the characteristic length (droplet height) decreases along with time at 60% RH as a consequence of the reported droplet spreading. While at 90% RH the characteristic length actually increases due to the greater amount of absorbed water vapor when compared to 60% RH. By comparison, on PTFE substrates the characteristic length (radius of curvature) increases to greater extent when compared to the characteristic length reported on hydrophilic glass substrates (Fig. 8). On PTFE substrates, at 60% RH the characteristic length increases from about 1.18 mm to about 1.4 mm in 3500 seconds, while at 90% RH, the characteristic length increases from about 1.1 mm to about 1.7 mm in 7000 seconds.


image file: c8cp04504f-f8.tif
Fig. 8 Evolution of characteristic lengths for solute diffusion within the LiBr–H2O droplets, versus time (s), on (triangles) hydrophilic glass substrates and on (circles) hydrophobic PTFE at (a) 45 °C and 60% RH, and at (b) 45 °C and 90% RH.

The characteristic time τ for mass diffusion defined in eqn (3), accounts for how long it takes for the water molecules to diffuse over the distance h*, hence as h* increases so does τ, and droplet saturation is reached later on the hydrophobic case. At 45 °C and 60% RH, for the same diffusion coefficient, τPTFE/τglasshPTFE*/hglass* ∼ 1.96. This estimation remarkably agrees with the experimental results where it takes 1650 seconds and 900 seconds for the droplets to reach equilibrium on PTFE substrate and on glass substrate respectively, i.e., τPTFE/τglass = 1650/900 ∼ 1.83.

The above analysis clearly demonstrates that surface wettability has a strong impact on the mechanisms of growth and spreading of hygroscopic lithium bromide desiccant droplets. Due to the shorter characteristic length for solute diffusion, droplets on hydrophilic glass substrate show faster vapor absorption rates. Since the efficiency and dehumidification capacity of packed towers are closely related to the vapor absorption rate of the liquid desiccant, for industrial applications, we then propose hydrophilic inner packing as the optimum configuration to further enhance the efficiency and dehumidification capacity of such systems.

4.2. Mechanisms of droplet spreading during vapor absorption

As described in Section 3, on hydrophilic glass substrates LiBr–H2O droplets show a clear spreading trend with monotonically increasing contact radius and decreasing contact angle (Fig. 2), while on hydrophobic PTFE substrates no apparent additional spreading is observed (Fig. 3). We note here that right after droplet deposition, there is a competition between capillary and viscous dissipation forces occurring within the first instant after deposition prompting the spherical cap shape of the droplet. This initial transient spreading differs from the timescales of spreading reported on hydrophilic glass substrates upon vapor absorption. In previous literature, droplet spreading phenomenon is reported in the droplet deposition process.53 In those studies, the droplet spreading is due to competition between capillary driving forces and viscous dissipation, and takes place within the first seconds right after droplet deposition following Tanner's law:54R(t) ∝ t1/10. The time scale of spreading is in the order of milliseconds for low viscosity liquids such as water in air on boro-silicate glass substrates53 or hexadecane on copper and/or glass.55 However, in our work LiBr–H2O droplets spread along with a time scale ca. 102–103 s greater than for early regimes of spreading. Therefore, classical droplet spreading described by Tanner's law cannot be used to explain the spreading of the TCL observed during vapor absorption on a hydrophilic substrate.

Next, to elucidate the different spreading behavior depending on the substrate wettability reported in our study, we look into the different binary interactions at the TCL. Seemingly, to the phenomena taking place during receding stick-slip earlier reported in literature, during vapor absorption on a hydrophobic PTFE surface the TCL remains pinned to the surface because of the intrinsic energy barrier presumably induced by substrate heterogeneities.16,56,57 Then, the contact angle increases to account for the increase in droplet volume. As the contact angle deviates from that of equilibrium, the droplet gains certain excess of free energy.57,58 As the excess of free energy overcomes the intrinsic energy barrier induced by the solid substrate the jump or slip of the contact line takes place.15,16,57,58 Next, we provide a qualitative local force balance at the TCL for establishing the different nature of the intrinsic energy barrier depending on the wettability of the surface, similar to the one proposed by Shanahan.16,57,58Fig. 9 presents schematic of the droplet profile at equilibrium contact angle, θ0, and at slightly larger contact angle when respect to the equilibrium one, θ0 + δθ, due to vapor absorption on (a) hydrophilic glass and (b) on hydrophobic PTFE substrates. At the equilibrium state, the profile of a droplet on a smooth ideal surface follows the balanced Young's equation, γSGγSL = γLG[thin space (1/6-em)]cos[thin space (1/6-em)]θ0, which accounts for the respective binary surface tensions: solid–gas, γSG, solid–liquid, γSL, and liquid–gas, γLG.59 As conveyed above, after the deposition of a desiccant droplet on a substrate in the presence of a humid environment, the droplet volume will increase due to vapor absorption. Within a finite short time, δt, and assuming the droplet contact line as pinned, the contact angle will increase due to volume expansion to (θ0 + δθ). Moreover, since the solution near the droplet surface gets diluted due to water absorption, the liquid-gas surface tension γLG will decrease by δγLG. Due to the variations in both the contact angle and the liquid–gas surface tension, the force balance at the TCL is altered, and as a consequence an extra horizontal force, δF, arises which tends to depin the contact line. By neglecting the second order small quantity, δF can be derived as eqn (4):

 
δF = (γLG − δγLG)[thin space (1/6-em)]cos(θ0 + δθ) − γLG[thin space (1/6-em)]cos[thin space (1/6-em)]θ0 ≈ −γLG[thin space (1/6-em)]sin[thin space (1/6-em)]θ0δθ − δγLG[thin space (1/6-em)]cos[thin space (1/6-em)]θ0(4)


image file: c8cp04504f-f9.tif
Fig. 9 Schematic of droplet profiles at the equilibrium state and at a slightly different contact angle when compared to equilibrium one (θ0θ0 + δθ) due to vapor absorption on (a) hydrophilic glass substrate and on (b) hydrophobic PTFE substrate.

On hydrophilic substrates, the droplet contact angle is smaller than 90°, and the value of cos[thin space (1/6-em)]θ0 is positive. In this case, the absolute value of the depinning force can be expressed as |δF|θ<90° = |γLG[thin space (1/6-em)]sin[thin space (1/6-em)]θ0δθ| + |δγLG[thin space (1/6-em)]cos[thin space (1/6-em)]θ0|. While on hydrophobic substrates, the contact angle is larger than 90°, and the absolute value of the depinning force can be then expressed as |δF|θ>90° = |γLG[thin space (1/6-em)]sin[thin space (1/6-em)]θ0δθ| − |δγLG[thin space (1/6-em)]cos[thin space (1/6-em)]θ0|. Therefore, for the same change in the contact angle, the depinning force is larger on hydrophilic substrates than on hydrophobic ones: |δF|θ<90° > |δF|θ>90°. Then, for an identical intrinsic energy barrier, ∂U/∂r, it is easier for the TCL to advance on hydrophilic glass substrates.

Fig. 10 shows the evolution of liquid–air surface tension, γLG, along with vapor absorption for the six experimental conditions studied by assuming the solute distribution within the droplet as homogenous.60 Depending on the experimental condition investigated, γLG of LiBr–H2O droplet decreases as water vapor is absorbed. In addition, as for common fluids, at higher temperature, LiBr–H2O droplets have smaller surface tension than at low temperatures. Moreover, as absorption takes place, the surface tension decreases with time and changes in surface tension are more marked at higher ambient humidity conditions as shown in Fig. 10. In the extreme case of 45 °C and 90% RH, the surface tension decreases from ca. 88.04 mN m−1 to ca. 74.78 mN m−1, which is still larger than that of pure water droplet at 45 °C (γLG,water,45°C ≈ 69.14 mN m−1[thin space (1/6-em)]61). The decrease in the droplet surface tension partly accounts for the contact angle decrease during vapor absorption. Nevertheless, the decrease in contact angle during vapor absorption is about 30°, which cannot be accounted for by the contact angle change caused purely by the decrease in surface tension. Therefore, additional explanations are expected.


image file: c8cp04504f-f10.tif
Fig. 10 Evolution of surface tension of LiBr–H2O droplets along with time during vapor absorption on a hydrophilic glass substrate.

Compared to hydrophobic PTFE substrates, the hydrophilic nature of glass substrates induces higher adhesion force to water molecules.62 Therefore, in humid environments, water molecules may accumulate near the glass surface due to adsorption.63 In the presence of a LiBr–H2O droplet, the surface near the contact line will absorb more water vapor and induce both density gradient and surface tension gradient along the droplet interface. In previous literature, droplet spreading has been observed under surface tension gradients induced by localized surfactant addition,64 as well as by an imposed temperature gradient.65 Therefore, the density gradient and surface tension gradient induced by non-uniform absorption across the droplet surface can be another plausible reason for the droplet spreading observed in this study.

Furthermore, when looking into a moving contact line, a precursor film is usually considered to be ahead of the visible droplet bulk.66–68 In previous studies, the existence of precursor film has been verified by advanced experimental techniques such as atomic force microscopy (AFM),69 and epifluorescence inverted microscopy,70 amongst others.71Fig. 11 shows the proposed schematic of the continuous transition from the macroscopic droplet profile to the microscopic precursor film at the triple contact line for a spreading droplet on a hydrophilic substrate. The length of the diffusive precursor film is proportional to the square root of time and can be expressed as eqn (5).70

 
image file: c8cp04504f-t3.tif(5)
where Lp is the precursor film length, A is the Hamaker constant, η is viscosity, hc is the cutoff thickness, and t is time.


image file: c8cp04504f-f11.tif
Fig. 11 Schematic of microscopic features in the vicinity of the advancing contact line on a hydrophilic substrate as: precursor film ahead of the visible macroscopic droplet,70 wedge region and macroscopic droplet. Macroscopic droplet profile is also included along.

For droplets on a hydrophobic PTFE substrate, due to the larger droplet curvature, the cutoff thickness is larger than that of droplets on hydrophilic glass.72 According to eqn (5), the length of the precursor film is inversely proportional to the square root of the cutoff thickness, hence the length of precursor film will be longer on a hydrophilic glass substrate than on a PTFE hydrophobic one. During experiments, vapor absorption happens both at the macroscopic droplet interface and at the precursor film. As vapor absorption proceeds, the precursor film will gradually grow thicker, with the inner side merging with the droplet bulk, and the outer side stretching forward. Since the precursor film typically extends more on hydrophilic substrates than that on hydrophobic ones, the precursor film develops more rapidly, and the triple contact line thus advances further, which is put forward as an additional mechanism for the greater droplet spreading observed on hydrophilic substrates.

5. Conclusions

The present study provides novel fundamental insights in vapor absorption process into single liquid hygroscopic desiccant droplets providing a new sub-topic of research on droplets. The effect of substrate wettability and ambient conditions are explored. Typically, on hydrophilic glass substrates, LiBr–H2O droplets show a spreading trend during vapor absorption. While on hydrophobic PTFE substrates, the smaller decrease in the contact angle along with an increasing contact radius evidences the lower spreading behavior when compared to hydrophilic glass. Moreover, the final volume expansion ratio of droplet is only function of relative humidity regardless of ambient temperature and surface wettability.

Depending on the wettability of the substrate, the kinetics of vapor absorption are found to differ. On hydrophilic glass substrates, LiBr–H2O droplets reach equilibrium with the ambient much quicker when compared to hydrophobic PTFE substrates. This is attributed to the shorter characteristic length for solute diffusion, which is further demonstrated by evaluating the characteristic time for solute diffusion within the droplet.

Besides, the apparent droplet spreading on hydrophilic glass substrates is explained based on a force balance analysis at the triple contact line, by the evolution of liquid–gas droplet surface tension, and by the development of a precursor film during vapor absorption.

To summarize, the vapor uptake into single liquid desiccant droplets and the mechanisms of droplet growth and spreading are revealed. The presented findings are of great significance both for a more accurate prediction of the vapor absorption process and for the optimization of dehumidification devices.

Conflicts of interest

The authors declare that they have no conflict of interests.

Acknowledgements

The authors gratefully acknowledge the support received by the International Institute for Carbon-Neutral Energy Research (WPI-I2CNER) and the Inter Transdisciplinary Energy Research Support Program from Kyushu University. ZW acknowledges the support received by the Japanese Society for the Promotion of Science (JSPS). DO gratefully acknowledges the support received from JSPS KAKENHI (grant no. JP16K18029 and JP18K13703). KS acknowledges the support from EPSRC through the grant EP/N011341/1. All the authors thank Dr Prashant Valluri of the University of Edinburgh for his insights on the precursor film theory.

References

  1. J. Park and J. Moon, Control of colloidal particle deposit patterns within picoliter droplets ejected by ink-jet printing, Langmuir, 2006, 22(8), 3506–3513 CrossRef CAS PubMed .
  2. C. J. Brinker, Y. Lu, A. Sellinger and H. Fan, Evaporation-induced self-assembly: nanostructures made easy, Adv. Mater., 1999, 11(7), 579–585 CrossRef CAS .
  3. T. Ming, X. Kou, H. Chen, T. Wang, H. L. Tam, K. W. Cheah, J. Y. Chen and J. Wang, Ordered gold nanostructure assemblies formed by droplet evaporation, Angew. Chem., 2008, 120(50), 9831–9836 CrossRef .
  4. V. Dugas, J. Broutin and E. Souteyrand, Droplet evaporation study applied to DNA chip manufacturing, Langmuir, 2005, 21(20), 9130–9136 CrossRef CAS PubMed .
  5. K. Sefiane, S. K. Wilson, S. David, G. J. Dunn and B. R. Duffy, On the effect of the atmosphere on the evaporation of sessile droplets of water, Phys. Fluids, 2009, 21(6), 062101 CrossRef .
  6. K. Sefiane, Effect of nonionic surfactant on wetting behavior of an evaporating drop under a reduced pressure environment, J. Colloid Interface Sci., 2004, 272(2), 411–419 CrossRef CAS PubMed .
  7. F. Girard, M. Antoni, S. Faure and A. Steinchen, Influence of heating temperature and relative humidity in the evaporation of pinned droplets, Colloids Surf., A, 2008, 323(1), 36–49 CrossRef CAS .
  8. Y. Fukatani, D. Orejon, Y. Kita, Y. Takata, J. Kim and K. Sefiane, Effect of ambient temperature and relative humidity on interfacial temperature during early stages of drop evaporation., Phys. Rev. E, 2016, 93(4), 043103 CrossRef PubMed .
  9. G. McHale, S. Aqil, N. J. Shirtcliffe, M. I. Newton and H. Y. Erbil, Analysis of droplet evaporation on a superhydrophobic surface, Langmuir, 2005, 21(24), 11053–11060 CrossRef CAS PubMed .
  10. N. D. Patil, P. G. Bange, R. Bhardwaj and A. Sharma, Effects of substrate heating and wettability on evaporation dynamics and deposition patterns for a sessile water droplet containing colloidal particles, Langmuir, 2016, 32(45), 11958–11972 CrossRef CAS PubMed .
  11. G. J. Dunn, S. K. Wilson, B. R. Duffy, S. David and K. Sefiane, The strong influence of substrate conductivity on droplet evaporation, J. Fluid Mech., 2009, 623, 329–351 CrossRef CAS .
  12. X. Zhong and F. Duan, Disk to dual ring deposition transformation in evaporating nanofluid droplets from substrate cooling to heating, Phys. Chem. Chem. Phys., 2016, 18(30), 20664–20671 RSC .
  13. L. Bansal, S. Chakraborty and S. Basu, Confinement-induced alterations in the evaporation dynamics of sessile droplets, Soft Matter, 2017, 13(5), 969–977 RSC .
  14. W. Xu, R. Leeladhar, Y. T. Kang and C. H. Choi, Evaporation kinetics of sessile water droplets on micropillared superhydrophobic surfaces, Langmuir, 2013, 29(20), 6032–6041 CrossRef CAS PubMed .
  15. A. Askounis, D. Orejon, V. Koutsos, K. Sefiane and M. E. Shanahan, Nanoparticle deposits near the contact line of pinned volatile droplets: size and shape revealed by atomic force microscopy., Soft Matter, 2011, 7(9), 4152–4155 RSC .
  16. D. Orejon, K. Sefiane and M. E. Shanahan, Stick–slip of evaporating droplets: substrate hydrophobicity and nanoparticle concentration, Langmuir, 2011, 27(21), 12834–12843 CrossRef CAS PubMed .
  17. C. Antonini, J. B. Lee, T. Maitra, S. Irvine, D. Derome, M. K. Tiwari, J. Carmeliet and D. Poulikakos, Unraveling wetting transition through surface textures with X-rays: Liquid meniscus penetration phenomena, Sci. Rep., 2014, 4, 4055 CrossRef CAS .
  18. Y. O. Popov, Evaporative deposition patterns: Spatial dimensions of the deposit., Phys. Rev. E, 2005, 71, 036313 CrossRef .
  19. M. E. R. Shanahan, K. Sefiane and J. R. Moffat, Dependence of Volatile Droplet Lifetime on the Hydrophobicity of the Substrate, Langmuir, 2011, 27(8), 4572–4577 CrossRef CAS .
  20. J. M. Stauber, S. K. Wilson, B. R. Duffy and K. Sefiane, On the lifetimes of evaporating droplets, J. Fluid Mech., 2014, 744, R2 CrossRef .
  21. J. M. Stauber, S. K. Wilson, B. R. Duffy and K. Sefiane, On the lifetimes of evaporating droplets with related initial and receding contact angles, Phys. Fluids, 2015, 27, 122101 CrossRef .
  22. F. G. H. Schofield, S. K. Wilson, D. Pritchard and K. Sefiane, The lifetimes of evaporating sessile droplets are significantly extended by strong thermal effects, J. Fluid Mech., 2018, 851, 231–244 CrossRef .
  23. M. A. Saada, S. Chikh and L. Tadrist, Evaporation of a sessile drop with pinned or receding contact line on a substrate with different thermophysical properties, Int. J. Heat Mass Transfer, 2013, 58, 197–208 CrossRef .
  24. L. Mei and Y. J. Dai, A technical review on use of liquid-desiccant dehumidification for air-conditioning application, Renewable Sustainable Energy Rev., 2008, 12(3), 662–689 CrossRef CAS .
  25. K. J. Chua, S. K. Chou and W. M. Yang, Advances in heat pump systems: A review, Appl. Energy, 2010, 87(12), 3611–3624 CrossRef CAS .
  26. Z. Wang, X. Zhang and Z. Li, Evaluation of a flue gas driven open absorption system for heat and water recovery from fossil fuel boilers., Energy Convers. Manage., 2016, 128, 57–65 CrossRef .
  27. K. Parham, M. Khamooshi, D. B. K. Tematio, M. Yari and U. Atikol, Absorption heat transformers–a comprehensive review, Renewable Sustainable Energy Rev., 2014, 34, 430–452 CrossRef CAS .
  28. K. J. Chua, S. K. Chou and W. M. Yang, Liquid desiccant materials and dehumidifiers – A review, Renewable Sustainable Energy Rev., 2016, 56, 179–195 CrossRef .
  29. H. Hu and R. G. Larson, Evaporation of a sessile droplet on a substrate, J. Phys. Chem. B, 2002, 106(6), 1334–1344 CrossRef CAS .
  30. X. H. Liu, Y. Zhang, K. Y. Qu and Y. Jiang, Experimental study on mass transfer performances of cross flow dehumidifier using liquid desiccant, Energy Convers. Manage., 2006, 47(15), 2682–2692 CrossRef .
  31. G. A. Longo and A. Gasparella, Experimental and theoretical analysis of heat and mass transfer in a packed column dehumidifier/regenerator with liquid desiccant, Int. J. Heat Mass Transfer, 2005, 48(25), 5240–5254 CrossRef CAS .
  32. Y. J. Dai and H. F. Zhang, Numerical simulation and theoretical analysis of heat and mass transfer in a cross flow liquid desiccant air dehumidifier packed with honeycomb paper, Energy Convers. Manage., 2004, 45(9), 1343–1356 CrossRef CAS .
  33. A. A. Al-Farayedhi, P. Gandhidasan and M. A. Al-Mutairi, Evaluation of heat and mass transfer coefficients in a gauze-type structured packing air dehumidifier operating with liquid desiccant, Int. J. Refrig., 2002, 25(3), 330–339 CrossRef CAS .
  34. X. H. Liu, X. M. Chang, J. J. Xia and Y. Jiang, Performance analysis on the internally cooled dehumidifier using liquid desiccant, Build. Environ., 2009, 44(2), 299–308 CrossRef .
  35. Y. Yin, X. Zhang, G. Wang and L. Luo, Experimental study on a new internally cooled/heated dehumidifier/regenerator of liquid desiccant systems., Int. J. Refrig., 2008, 31(5), 857–866 CrossRef CAS .
  36. Z. Wang, X. Zhang and Z. Li, Investigation on the coupled heat and mass transfer process between extremely high humidity air and liquid desiccant in the counter-flow adiabatic packed tower, Int. J. Heat Mass Transfer, 2017, 110, 898–907 CrossRef CAS .
  37. S. Jain, S. Tripathi and R. S. Das, Experimental performance of a liquid desiccant dehumidification system under tropical climates, Energy Convers. Manage., 2011, 52(6), 2461–2466 CrossRef CAS .
  38. Y. Luo, H. Yang, L. Lu and R. Qi, A review of the mathematical models for predicting the heat and mass transfer process in the liquid desiccant dehumidifier., Renewable Sustainable Energy Rev., 2014, 31, 587–599 CrossRef CAS .
  39. S. Jeong and S. Garimella, Falling-film and droplet mode heat and mass transfer in a horizontal tube LiBr/water absorber, Int. J. Heat Mass Transfer, 2002, 45(7), 1445–1458 CrossRef CAS .
  40. S. A. Abdul-Wahab, M. K. Abu-Arabi and Y. H. Zurigat, Effect of structured packing density on performance of air dehumidifier, Energy Convers. Manage., 2004, 45(15–16), 2539–2552 CrossRef CAS .
  41. D. Bonn, J. Eggers, J. Indekeu, J. Meunier and E. Rolley, Wetting and spreading, Rev. Mod. Phys., 2009, 81(2), 739–805 CrossRef CAS .
  42. C. Liu, E. Bonaccurso and H. J. Butt, Evaporation of sessile water/ethanol drops in a controlled environment, Phys. Chem. Chem. Phys., 2008, 10(47), 7150–7157 RSC .
  43. X. Qu, E. J. Davis and B. D. Swanson, Non-isothermal droplet evaporation and condensation in the near-continuum regime, J. Aerosol Sci., 2001, 32(11), 1315–1339 CrossRef CAS .
  44. Y. Kita, Y. Okauchi, Y. Fukatani, D. Orejon, M. Kohno, Y. Takata and K. Sefiane, Quantifying vapor transfer into evaporating ethanol drops in humid atmosphere, Phys. Chem. Chem. Phys., 2018, 20, 19430–19440 RSC .
  45. S. Nath, C. E. Bisbano, P. Yue and J. Boreyko, Duelling dry zones around hygroscopic droplets, J. Fluid Mech., 2018, 855, 601–620 CrossRef .
  46. J. M. Wimby and T. S. Berntsson, Viscosity and density of aqueous solutions of lithium bromide, lithium chloride, zinc bromide, calcium chloride and lithium nitrate. 1. Single salt solutions, J. Chem. Eng. Data, 1994, 39(1), 68–72 CrossRef CAS .
  47. R. J. Hopkins and J. P. Reid, Evaporation of ethanol/water droplets: examining the temporal evolution of droplet size, composition and temperature, J. Phys. Chem. A, 2005, 109(35), 7923–7931 CrossRef CAS .
  48. J. R. E. Christy, Y. Hamamoto and K. Sefiane, Flow Transition within an Evaporating Binary Mixture Sessile Drop, Phys. Rev. Lett., 2011, 106, 205701 CrossRef .
  49. S. Dehaeck, C. Wylock and P. Colinet, Evaporating cocktails, Phys. Fluids, 2009, 21, 091108 CrossRef .
  50. E. L. Cussler, Diffusion: Mass Transfer in Fluid Systems, Cambridge University Press, Cambridge Series in Chemical Engineering, 2009 Search PubMed .
  51. V. M. M. Lobo, A. C. F. Ribeiro and L. M. P. Verissimo, Diffusion coefficients in aqueous solutions of potassium chloride at high and low concentrations, J. Mol. Liq., 1998, 78(1–2), 139–149 CrossRef CAS .
  52. H. S. Harned and A. L. Levy, The Differential Diffusion Coefficient of Calcium Chloride in Dilute Aqueous Solutions at 25°, J. Am. Chem. Soc., 1949, 71(8), 2781–2783 CrossRef CAS .
  53. S. Mitra and S. K. Mitra, Understanding the early regime of drop spreading, Langmuir, 2016, 32(35), 8843–8848 CrossRef CAS PubMed .
  54. L. H. Tanner, The spreading of silicone oil drops on horizontal surfaces, J. Phys. D: Appl. Phys., 1979, 12(9), 1473 CrossRef CAS .
  55. R. Ruiter, P. Colinet, P. Brunet, J. H. Snoeijer and H. Gelderblom, Contact line arrest in solidifying spreading drops, Phys. Rev. Fluids, 2017, 2, 043602 CrossRef .
  56. M. E. R. Shanahan, Meniscus Shape and contact angle of a slightly deformed axisymmetric drop, J. Phys. D: Appl. Phys., 1989, 22, 1128–1135 CrossRef .
  57. M. E. R. Shanahan, Simple Theory of “Stick-Slip” Wetting Hysteresis, Langmuir, 1995, 11(3), 1041–1043 CrossRef CAS .
  58. M. E. R. Shanahan and K. Sefiane, in Contact Angle Wettability and Adhesion. ed. K. L. Mittal, Taylor & Francis Group Koninklijke Brill NV, Leiden The Netherlands, 2009, vol. 6, pp. 19–32 Search PubMed .
  59. T. Young, An essay on the cohesion of fluids, Philos. Trans. R. Soc. London, 1805, 95, 65–87 CrossRef .
  60. W. Yao, H. Bjurstroem and F. Setterwall, Surface tension of lithium bromide solutions with heat-transfer additives, J. Chem. Eng. Data, 1991, 36(1), 96–98 CrossRef CAS .
  61. G. J. Gittens, Variation of surface tension of water with temperature, J. Colloid Interface Sci., 1969, 30(3), 406–412 CrossRef CAS .
  62. Y. I. Tarasevich and E. V. J. Aksenenko, Interaction of water molecules with hydrophilic and hydrophobic surfaces of colloid particles, J. Water Chem. Technol., 2015, 37(5), 224–229 CrossRef .
  63. Marianne K. Bernett and W. A. Zisman, Effect of adsorbed water on wetting properties of borosilicate glass, quartz, and sapphire, J. Colloid Interface Sci., 1969, 29(3), 413–423 CrossRef CAS .
  64. A. Chengara, A. D. Nikolov and D. T. Wasan, Spreading of a water drop triggered by the surface tension gradient created by the localized addition of a surfactant, Ind. Eng. Chem. Res., 2007, 46(10), 2987–2995 CrossRef CAS .
  65. A. L. Bertozzi, A. Münch, X. Fanton and A. M. Cazabat, Contact line stability and undercompressive shocks in driven thin film flow, Phys. Rev. Lett., 1998, 81(23), 5169 CrossRef CAS .
  66. L. Leger, M. Erman, A. M. Guinet-Picard, D. Ausserre and C. Strazielle, Precursor film profiles of spreading liquid drops., Phys. Rev. Lett., 1988, 60(23), 2390–2393 CrossRef CAS .
  67. H. P. Kavehpour, B. Ovryn and G. H. McKinley, Microscopic and Macroscopic Structure of the Precursor Layer in Spreading Viscous Drops, Phys. Rev. Lett., 2003, 91(19), 196104 CrossRef .
  68. P. Colinet and A. Rednikov, Chapter 4 – Precursor Films and Contact Line Microstructures Droplet Wetting and Evaporation, Oxford, 2015, pp. 31–56 Search PubMed .
  69. H. Xu, D. Shirvanyants, K. Beers, K. Matyjaszewski, M. Rubinstein and S. S. Sheiko, Molecular motion in a spreading precursor film, Phys. Rev. Lett., 2004, 93(20), 206103 CrossRef .
  70. A. Hoang and H. P. Kavehpour, Dynamics of nanoscale precursor film near a moving contact line of spreading drops, Phys. Rev. Lett., 2011, 106(25), 254501 CrossRef CAS PubMed .
  71. H. Ghiradella, W. Radigan and H. L. Frisch, Electrical resistivity changes in spreading liquid films, J. Colloid Interface Sci., 1975, 51(3), 522–526 CrossRef CAS .
  72. A. Carré, J. C. Gastel and M. E. Shanahan, Viscoelastic effects in the spreading of liquids, Nature, 1996, 379, 432–434 CrossRef .

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