Article pubs.acs.org/Langmuir
Sweating Liquid Micro-Marbles: Dropwise Condensation on Hydrophobic Nanoparticulate Materials Prasad S. Bhosale†,‡ and Mahesh V. Panchagnula§,* †
Department of Chemical Engineering, Tennessee Tech University, Cookeville, Tennessee 38501, United States Department of Chemical Engineering, University of Washington, Seattle, Washington 98195, United States § Department of Applied Mechanics, Indian Institute of Technology, Madras, Chennai 600 036, India ‡
S Supporting Information *
ABSTRACT: Liquid marbles have opened up several potential applications including biochemical batch reaction engineering and gas sensing. To be successful candidates in these applications, the ability to prepare liquid marbles of controlled sizes and in a continuous process is crucial. This has been the missing link in the science leading to these applications. In the current study, we present a remarkably simple process driven by condensation on a nanoparticulate matrix to continuously produce liquid marbles whose mean size can be controlled in the range of diameters from 3 to 1000 μm, while the distribution width is also controllable independently. We experimentally demonstrate the physics involved in this condensation-driven marble formation process using two fluidsglycerol and ethylene glycolwhich span an order of magnitude in viscosity. Hydrophobic fumed silica nanoparticulate material is used as the encapsulating medium owing to its intertwined agglomerate nature. We show that the primary mechanism causing the formation of liquid marbles is droplet nucleation followed by growth driven by condensation. Drop coalescence in dense droplet ensembles is the secondary mechanism, which attempts to destroy the distribution width controllability. From a physics perspective, it will be demonstrated that strong coalescence dominated growth gives rise to a hitherto unreported, significantly higher rate of growth.
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INTRODUCTION
control over both the mean marble diameter as well as the marble size distribution. Since the first studies by Aussillous and Quéré,5,6 the process of preparing liquid marbles has been one where a drop of a metered volume is first placed in a particulate material and allowed to “roll” until the particulate medium completely encapsulates the liquid.13 The particulate layer and the liquid marble are held in tact mainly due to the reduced surface free energy when a thin layer of powder is covered on the liquid surface. A serious shortcoming of this process is that it is not scalable to produce large numbers of liquid marbles continuously.14 Other scalable processes such as the use of blenders15 do not provide control over marble size and distribution width. Besides, the smallest drop that can be metered so reproducibly is on the order of 10 μm.16 It is known that smaller liquid marbles tend to be more mechanically stable owing to the increased mass of the encapsulating (particulate) sheath material per unit liquid volume.17 Even if one could meter drops in this size range of 1−10 μm in a continuous fashion (at a substantial energetic cost, which scales with liquid viscosity), a stable particulate layer is not guaranteed due to the
Liquid marbles have been presented as candidates in such important applications as gas sensing,1−3 storage,4 and bulk liquid transport since Aussillous and Quéré5,6 first proposed them. Since then, there has been growing interest in them due to potential applications for controlled manipulation of small liquid droplets in microfluidics,7 electrochemical/magnetic8,9/ gravitational actuation,6 and drug encapsulation.10 For example, hollow granules formed by liquid marbles’ evaporation are currently being investigated for tablet manufacturing in the pharmaceutical industry.11,12 To be successful candidates in these applications, the ability to prepare liquid marbles of controlled sizes and in a continuous process is crucial. In the current study, we present a remarkably simple process driven by condensation on a nanoparticulate matrix to continuously produce liquid marbles whose size can be controlled in the range of diameters from 3 to 1000 μm. We show that the primary mechanism causing the formation of liquid marbles is droplet nucleation followed by growth driven by condensation. From a physics perspective, it will be demonstrated that strong coalescence dominated growth gives rise to a hitherto unreported, significantly higher rate of growth. Through a combination of understanding derived from these two physical processes, we will show that the proposed process provides © 2012 American Chemical Society
Received: February 3, 2012 Revised: September 18, 2012 Published: September 20, 2012 14860
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inherent variability in the rolling process. This is the primary limitation restricting advancement in employing liquid marbles in the lab. We will substantially address this limitation through a novel marble creation process. As mentioned before, our process of creating the liquid marbles takes advantage of dropwise condensation in a particulate matrix followed by self-assembled encapsulation. Drop-wise condensation on sessile surfaces has been studied by various researchers for more than 200 years.18 Beysens and coworkers18−21 studied dew growth for isolated drops and showed that the mean drop diameter, ⟨D⟩ ∼ t1/3, where t is time. In the regime where dew growth is dominated by coalescence, they showed that the mean diameter ⟨D⟩ ∼ t. The fastest growth rate is achieved when the role of drop mobility and consequent coalescence activity is dominant in relation to condensation, which happens to be the case with liquid marbles. For this case, we will show that their result still does not represent the limiting fastest growth rate and that the value of the power law exponent could be much higher (≈1.6). It must be noted that Binks et al.,22 who studied ripening in oil/ water emulsions, also found similar exponents of their swelling fraction (1 when dominated by coalescence and 1/3 when coalescence is mitigated). The key to the physical process governing the self-assembly of liquid marbles is particle transport at the liquid vapor interface driven by condensation-induced surface fluid flow. Gokhale et al.23 were among the few to have indirectly studied drop-internal flows in a condensing sessile drop. The complementary problem of flows in evaporating sessile drops is however well investigated. Particularly, evaporation of droplets containing colloidal nano and micro particles has been the focus of many studies over the last two decades.24−26 At the beginning of the past decade, Deegan et al.27,28 described internal flows in an evaporating sessile drop containing colloidal particles (coffee ring effect). Potential applications of this process include simple evaporation-based self-assembly processes for nanoparticles, monolayers, or thin film deposition.24,28 Interestingly, very few studies have focused on condensation on droplets with particles at the interface.
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Figure 1. Schematic of the experimental setup showing (i) a heating pad, (ii) glass vial with fluid, whose interface is covered with the particulate material, and (iii) an optical microscope. (inset) Image depicting colorless marbles formed by the condensation process when the parent material was glycerol with a soluble dye.
microscope. This experiment was repeated over a temperature range of 60−220 °C. A sequence of images was captured over time and thus obtained images were processed using ImageJ software to measure rate of formation of marbles and their size distribution. In the end, stable liquid marbles were produced and recovered from the sweating process. They were tested following the methodology employed by Lafuma and Quéré29 for rupture strength and found to be robust. To measure vapor condensation efficiency, the vial set up with excess amount of hydrophobic power was used. A thick layer of hydrophobic powder (35 mg nHMDS on 3 g glycerol) at the surface allows higher vapor condensation. Liquid marbles formed in the powder layer were scoped out of the vial into a Petri dish. The excess amount of hydrophobic powder was then blown away using an air stream. The amount of liquid evaporated and converted into liquid marbles was calculated by weighing glycerol in the vial and marbles produced. Simulation Method. A simulation of drop nucleation, growth, and coalescence was performed to understand the experimental results. Consider a unit cube in three-dimensional space (or a unit square in two-dimensional space). Drops are allowed to nucleate at rate, ṅ0 and of diameter Dmin. Following Beysens, the diameter of an isolated drop is allowed to increase in time such that, D (t) = Dmin + Kt1/3. When two drops touch each other, they are allowed to instantaneously coalesce to be replaced by a single drop, such that the coalesced drop contains the same liquid volume as the two precursor drops. In addition, the center of the coalesced drop is placed at the center of mass of the two drops prior to coalescence. This simulation was carried forward in time until the volume fraction of liquid inside the unit cube approached unity (one large drop). Numerically, the nucleation process was initiated by generating three random numbers for the three coordinates describing the center of the drop. The drop was placed at that location of diameter Dmin. For a nondimensional time step of 1, ṅ0 drops were so placed at each time increment. The number of trials to place these drops exclusive of existing drops was limited to about 10ṅ0 in the interest of computer efficiency. The diameters of all of the drops in the system were updated following the t1/3 law stated above. When two drops intersected, they were allowed to coalesce into one drop. Since the liquid volume was continuously being added to the system, the liquid volume fraction continues to increase and the unit cube is likely to reach a condition when further nucleation is not possible within the number of specified trials. The simulation is stopped at that point.
MATERIALS AND METHODS
Nanoparticulate Hexamethyldisilazane (nHMDS) treated fumed silica powder (BET surface area 225 m2/g) was obtained from Cabot Corp. as commercial products TS 530.18 μPTFE powder with an average particle size of 7 to 12 μm (0.8−4.5 m2/g specific surface area) was obtained from DuPont Corp. Ethylene glycol, glycerol, and all other chemicals were obtained from Fisher Scientific. Large liquid marbles (where required) were prepared by embedding liquid drops (water, glycerol, and ethylene glycol) of desired size on hydrophobic particulate material placed in a glass dish. The particles self-assemble on the liquid−vapor interface causing the drop to render it nonwetting. The experimental apparatus consisted of a glass vial containing a liquid covered with particles at the interface that are a few hundred micrometers in thickness. The set up was placed under an optical microscope in a planar setup, as shown in Figure 1. A glass vial (1.5 cm diameter and 1.5 cm height) was filled with approximately 3 g of liquid (glycerol, ethylene glycol, or water). A thin layer of hydrophobic powder was spread on the liquid-free surface. The glass vial was placed on a heating pad and heated from the bottom. The liquid temperature was monitored continuously using a thermocouple. Approximately 10 min after the start of heating, the liquid vapor released at the free surface is condensed and enveloped by the particulate material at the surface, thereby forming liquid micromarbles. The liquid marble formation was observed using a Nikon Eclipse model LV100 optical 14861
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Figure 2. (a) Sweating process on a glycerol-nHMDS “rolled” liquid marble placed on a 195 °C hot plate (images captured every 10 min). Scanning Electron Micrographs of (b) “rolled” versus (c) “sweated” liquid marble formed by condensation. (d) ESEM micrograph of a liquid marble ≈300 μm in diameter formed by condensation. (e) Time series of images of a μPTFE−glycerol liquid marble on a hot plate at 220 °C.
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RESULTS AND DISCUSSION The initial study focused on the behavior of liquid marbles on hot surfaces, as shown in the time sequence for glycerol with nHMDS in Figure 2(a). As the parent marble is heated on a hot plate, small liquid droplets start to appear at the interface, selfencapsulate free particulate material and grow over time. As the heating process is continued, both the daughter marble count and their size increase. Eventually, the daughter marbles roll down the curved parent marble surface. This process continued until the primary marble was completely converted into small secondary marbles. This process gives the appearance that the parent marbles are sweating; we therefore termed the process as sweating liquid marbles. The curved liquid−vapor interface however did not lend itself well to imaging. Hence, a planar test set up was designed. The schematic of that test set up shown in Figure 1 consisted of the liquid−vapor interface covered with a few hundred micrometer thick layer of the particulate material. When the liquid is heated from bottom, the vapor diffuses through the particulate matrix and in the process, cools and condenses in the particulate medium resulting in selfencapsulation into a liquid marble. To ascertain that the mass transport is vapor-phase mediated and not temperature gradient induced liquid wicking, a simple experiment was conducted with a planar particulate as the material interface. The parent liquid was prepared with a colored dye as shown in the inset in Figure 1. The sweated daughter marbles were however clear, indicating that they were the result of condensation. What follows herein is a description of the results obtained from this setup. Figure 2(b)−(d) show micrographs obtained using an Environmental Scanning Electron Microscope of the interfacial structure of the rolled versus sweated liquid marbles. The image in Figure 2(b) shows dark spots indicating exposed liquid. When such a marble is allowed to bounce on a substrate, it is likely to rupture due to the liquid making contact with the
substrate. However, the uniformity of the particulate sheath is clearly noticeable in the case of the marble formed by condensation. The gray shade of the marble in this case is indicative of the more uniform coverage of the particulate material. The nanoparticulate material forms an interweaved layer protecting the marble against rupture.17 Two types of hydrophobic particles, nanoparticulate treated fumed silica (nHMDS) and microparticulate polytetrafluoroethylene (μPTFE) powders were studied in conjunction with three liquidsglycerol, ethylene glycol, and water. Scanning Electron Micrographs showing the morphology of the above particulate materials can be found in Bhosale et al.17 The μPTFE material consisted of irregular shaped single particles, whereas nHMDS was observed to show long intertwined chains. The sample set of liquids chosen in this study represents variation in viscosity, saturation vapor pressure, and surface tension. Sweating marbles formed with μPTFE powder were fragile and unstable and hence are not being reported in detail for brevity. See Figure 2(e) for a time series of images. As can be observed from this time series, the sweating process is far less organized and controllable with μPTFE than with nHMDS. In addition, our previous studies have shown mechanical robustness of nHMDS coated marbles over μPTFE.17 The nanoparticulate nHMDS forms a stronger and transparent elastic membrane around liquid drops producing transparent and mechanically robust marbles. The rest of the work is devoted to results using nHMDS as the encapsulating agent. Figure 3 shows a time series of optical micrographs of the visible particle interface taken every 15 min at glycerol interface coated with nHMDS powder and heated to 100 °C. The sequence of images demonstrates sweating marble formation, growth and coalescence. Initially marbles formed at random points on the particulate material surface; over time, these marbles grow and start to coalesce before forming bigger marbles, while new sweating marbles are formed. This process 14862
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Figure 3. Optical micrographs of glycerol-nHMDS surface taken every 15 min representing formation, growth, and coalescence of sweating marbles. Scale bar on images a, b, and c is 120 μm; d, e, and f is 240 μm; and g, h, and i is 480 μm. This time series was obtained at a heating pad temperature of 100 °C. See SI videos for a time sequence video of this process. (j) Optical micrograph of ethylene glycol-nHMDS surface obtained at 90 °C. Scale bar on image is 480 μm.
fumed silica regions (which are hydrophilic). The saturated vapor preferentially condenses on the hydrophilic spots because of the associated free energy well.15 The number density of such hydrophilic surface defects controls the nucleation rate.18 In the current experiment, the nHMDS nanoparticulate material had a very high surface density of nucleation sites in relation to μPTFE17 and hence is more efficient with the transfer of mass from the vapor phase into daughter marbles. (ii). Growth by Condensation. This initial stage of marble growth where the number density of liquid marbles remains constant but the diameter increases is well studied. This regime has been characterized by a growth law for the average marble diameter, ⟨D⟩ ∼ t1/3 where t is time since nucleation. However, in the present case, owing to the large density of nucleation sites, the time span of pure (coalescence-less) growth of liquid marbles was quite small (∼1 min), similar to Narhe et al.20 The transition time from pure growth by condensation to growth by condensation plus weak coalescence is observed to occur at a time when the marbles coverage surface area fraction approaches the random packing limit (≈55%). The surface area fraction is herein calculated as the area in a given image covered by liquid marbles (visible as circles in Figure 3, for example) per unit total area of the image. When the surface area fraction is less than the random packing limit, the marble
is similar to that of droplet condensation, growth, and coalescence observed in dropwise condensation on hydrophobic surfaces.30 Secondary and tertiary marbles formed from further condensation around the daughter marbles can also be observed. Such self-similar condensation structure was observed by Beysens18 for the case of dew formation. The sweating phenomenon is induced by dropwise condensation30−32 on the hydrophobic powder with nucleation sites provided by the nanoscale hydrophilic spots on the nHMDS material. A similar time series obtained with ethylene glycol is presented and discussed in the Supporting Information, SI. The novel method being proposed to produce liquid marbles rests on three physical forces: (i) nucleation, (ii) growth by condensation, and (iii) growth by coalescence. We shall discuss these three physical processes with relevance to our application. (i). Nucleation. The process of heterogeneous nucleation in the nanoparticulate matrix governs the initial stage of marble formation. Owing to the slightly elevated temperature of the liquid (over the ambient temperature), the nanoparticulate matrix is infused with vapor at the saturation partial pressure. The particulate matrix itself is made of long chain nanoparticle chains of fumed silica that have been rendered hydrophobic by a silane surface treatment. The process of surface treatment leaves the chains hydrophobic but with spots of untreated 14863
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Figure 4. (a) Plot of the average marble diameter with time for glycerol-nHMDS system for heating at four different temperatures. The error bars indicate the width of the marble size distribution. (b) Marble size distribution evolution with time for glycerol-nHMDS system at 90 °C. (c) Plot of the average marble diameter with time for ethylene glycol-nHMDS for two temperatures. (d) Marble size distribution evolution with time for ethylene glycol-nHMDS system.
Figure 5. (a) Mean diameter (solid symbols) and surface area fraction (open symbols) versus time for ethylene glycol and glycerol at approximately 70 °C. (b) Plot of nondimensional mean diameter versus nondimensional time from simulations.
viscosity and high nucleation rates, for example, ethylene glycol at high temperatures. The increased rate in the strong coalescence regime is made possible due to compliance of the particulate substrate in the case of sweating liquid marbles. Beysens and co-workers18,21 have developed a general scaling law for a δD dimensional drops condensing onto a δs dimensional surface. They showed that ⟨D⟩ ∼ tβ, where β = δD/3(δD − δs). For example, threedimensional drops coalescing on a two-dimensional surface follows a linear scaling with time. This scaling law was derived from studies of coalescence of populations of sessile drops. The first difference between that and the present case lies in the somewhat compliant nature of the substrate. The particulate matrix on a liquid meniscus allows marbles to be partially staggered in the vertical direction. A phenomenological
number density remains approximately constant (since each daughter marble grows by condensation unbeknownst of the others). (iii). Growth by Coalescence. Understanding this stage is the most crucial to achieving control over marble size distribution. Previous studies by Beysens and co-workers18,21 who have studied “breathe figures” and other sessile drop condensation processes have concluded that under the simultaneous action of both coalescence and growth, ⟨D⟩ ∼ t. We show that for the case of liquid marbles embedded in a particulate matrix (of thickness ∼100 μm) this regime is in fact one of weak coalescence. A hitherto undiscovered second regime characterized by strong coalescence driven growth is reported herein where ⟨D⟩ ∼ tα (α = 1.6) (see Figures 4 and 5). This regime is particularly manifested with fluids of low 14864
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origins of this qualitative difference in order to define the control parameters for this process. Figure 5(a) presents both the glycerol and ethylene glycol mean diameter data at approximately the same temperature. The rates of growth show a linear pattern for both glycerol and ethylene glycol with the slopes being correlated to the higher rates of nucleation and condensation with the ethylene glycol. This can be explained by understanding the variation of surface area fraction. It can be noted from Figure 5 that the rate of increase of surface fraction is much higher for ethylene glycol versus glycerol. The higher rate of increase is due to a higher saturation vapor pressure of ethylene glycol (1 mmHg at 53 °C) than glycerol (1 mmHg at 125.5 °C),34 resulting higher rates of mass transfer by condensation. Therefore, the surface packing limit of ≈55% is reached in a shorter time for ethylene glycol. The random packing limit defines the limiting area fraction value beyond which coalescence is vastly encouraged thereby driving the system toward reduced surface area coverage. In contrast, the surface area fraction remains small ( 1 can be avoided. The overall process efficiency for conversion of bulk liquid into marbles can be quantified in terms of the mass of glycerol converted into daughter marbles at a given temperature and for a given heating time. As an example, the mass conversion efficiency was measured to be as high as 50% at 220 °C within two hours. Liquid marbles as small as 3 μm in diameter (and with a narrow size distribution) can be created by employing low heating temperatures over small times. A continuous marble production process would involve a low temperature (≈70 °C) heating step followed by a continuous daughter marble removal process, either mechanically or pneumatically. As has been shown before, the distribution width is sensitive to coalescence and hence one would achieve better control if this regime can be avoided. A secondary advantage of this process is that the average marble diameter could be kept small (2). This would increase the exponent in the power law description to be greater than 1. Figure 4 presents plots of the mean marble diameter and marble distribution versus time for glycerol and ethylene glycol. As expected, the rate of growth is an increasing function of the temperature. In addition, the rate of growth is linear for all temperatures similar to the observations of Beysens18 indicating only weak coalescence. As the temperature increases, the distribution width also increases. The distribution width is a strong function of the rate of marble coalescence. This is most remarkably observed in figure 4(a) where the slope of linear growth changes significantly for only a 10 °C change in heater temperature (from 90 to 100 °C). Higher heating temperatures cause faster evaporation, faster growth of liquid marbles, higher mean size and distribution width as well as lower energetic barriers to coalescence. The marble size distribution for glycerol is presented in figure 4(b). First, this plot further corroborates the onset of coalescence by the appearance of bimodality in the distribution at time, 24 min. Second, we can characterize the distribution width in terms of the Full Width at Half Maximum (fwhm). The fwhm divided by the mean diameter is an indicator the spread in the distribution. At the initial stages of nucleation and growth, where marbles are physically separated in space, they are nearly monodisperse (fwhm/mean
