Abstract: Ring formation in an evaporating sessile drop is a hydrodynamic process in which solids dispersed in the drop are advected to the contact line. After all the liquid evaporates, a ring-shaped deposit is left on the substrate that contains almost all the solute. Here I show that the drop itself can generate one of the essential conditions for ring formation to occur: contact line pinning. Furthermore, I show that when self-induced pinning is the only source of pinning an array of patterns---that include cellular and lamellar structures, sawtooth patterns, and Sierpinski gaskets---arises from the competition between dewetting and contact line pinning.

Abstract: A new bulk microphysical parameterization for large-eddy simulation (LES) models of the stratocumulus-topped boundary layer has been developed using an explicit (drop spectrum resolving) microphysical model as a data source and benchmark for comparison. The liquid water is divided into two categories, nonprecipitable cloud water and drizzle, similar to traditional Kessler-type parameterizations. The cloud condensation nucleus (CCN) count, cloud/drizzle water mixing ratios, cloud/drizzle drop concentrations, and the cloud drop integral radius are predicted in the new scheme. The source/sink terms such as autoconversion/accretion of cloud water into/by drizzle are regressed using the cloud drop size spectra predicted by an explicit microphysical model. The results from the explicit and the new bulk microphysics schemes are compared for two cases: nondrizzling and heavily drizzling stratocumulus-topped boundary layers (STBLs). The evolution of the STBL (characterized by such parameters as turbulence...

Abstract: We describe an experimental technique for the production of highly monodisperse emulsions (with minimum achievable polydispersities <3%). The phase to be dispersed is introduced into a coflowing, surfactant-laden continuous phase via a tapered capillary. Drops detach from the capillary when the streamwise forces exceed the force due to interfacial tension. Drop size is a function of the capillary tip diameter, the velocity of the continuous phase, the extrusion rate, and the viscosities and interfacial tension of the two phases. Emulsions composed of a variety of fluids and with drop sizes ranging from 2 to 200 μm have been produced using this technique.

Abstract: We are interested in the amount of fluid left behind a drop moved inside a capillary tube. Long ago, Taylor showed that for very viscous liquids moved at small velocities, the film thickness is a monotonic increasing function of the capillary number. New data obtained with liquids of low viscosity are reported here and compared with Taylor’s law. Two successive effects are observed: above a threshold in capillary number, the film is thicker than a Taylor film; at a very high speed, the deposition law becomes a decreasing function of the drop velocity. Both behaviors are analyzed thanks to scaling arguments and shown to be consequences of inertia.

Abstract: Controlling the impact of drops onto solid surfaces is important for a wide variey of coating and deposition processes--for example, the treatment of plants with herbicides and pesticides requires precise targeting in order to meet stringent toxicological regulations. However, the outer wax-like layer of the leaves is a non-wetting substrate that causes sprayed droplets to rebound; often less than 50% of the initial spray is retained by the plant. Although the impact and subsequent retraction of non-wetting aqueous drops on a hydrophobic surface have been the subjects of extensive experimental and theoretical work, non-newtonian rheological effects have not been considered in any detail. Here we report that, by adding very small amounts of a flexible polymer to the aqueous phase, we can inhibit droplet rebound on a hydrophobic surface and markedly improve deposition without significantly altering the shear viscosity of the solutions. Our results can be understood by taking into account the non-newtonian elongational viscosity, which provides a large resistance to drop retraction after impact, thereby suppressing droplet rebound.

Abstract: The type and stability of Pickering emulsions stabilised by disc-like Laponite RD clay particles are described. By establishing the phase diagram of aqueous dispersions as a function of clay and salt (NaCl) concentration, we deduce that toluene-in-water (o/w) emulsions, stable to creaming and coalescence for at least 6 months, are only formed under conditions where the colloidal particles are flocculated. The initial average drop diameter is independent of clay concentration but depends markedly on oil volume fraction, ranging from 10 to 28 μm. Changes in the drop size distributions with time are shown to be due to Ostwald ripening, which, due to the irreversible nature of particle adsorption at oil/water interfaces, is rapid at first and ceases completely at long times. It is suggested that ripening is arrested when the Laplace pressure inside drops of different sizes becomes equal. For optimum conditions, emulsions prepared using a variety of oils including non-polar alkanes and polar alcohols are always o/w even at high oil phase volume fraction, reflecting the hydrophilic nature of this synthetic clay in oil–water systems.

Abstract: Ceramic foams are prepared as positive images of corresponding plastic structures and exhibit bed porosities as high as 80–90%. This makes them attractive as catalyst supports in processes where high pressure drop in the reactor tube is a problem. In this research, pressure drop relationships were examined for 10, 30, 45 and 65 pores per inch (PPI) ceramic foam samples made from 92.0 and 99.5% α-Al2O3 and from ZrO2 stabilized with Mg, Ca, and La2O3. Pore distributions were determined with imaging analysis, using digital techniques. Pressure drop measurements confirmed that ceramic foams follow the Forscheimer relationship and may be interpreted with the Ergun model, in which the pressure drop is the sum of viscous and inertial terms. The Ergun parameters, α and β, are not constant, α decreases from 8.05 to 2.88 and β increases from 0.0338 to 0.111 as the pore density increases from 10 to 65 PPI. Empirical equations were developed for these parameters in terms of the mean pore size and the bed porosity, and these indicated a dependence on the media properties. Calculated pressure drop from these equations were within 15% of measured values. Up to 15 wt.% γ-Al2O3 washcoat was added to 30 PPI samples of α-Al2O3 foams. Nitrogen BET surface areas increased from about 2 m2 g−1 in the unwashcoated samples to almost 15 m2 g−1 at the highest loading. Both α and β increase linearly with the BET surface area, α by only about 50% but β by a factor of 8. This suggests that roughness introduced by the washcoat plays a dominant role in the turbulent resistance.

Abstract: A spherical drop, placed in a second liquid of the same density, is subjected to shearing between parallel plates. The subsequent flow is investigated numerically with a volume-of-fluid (VOF) method. The scheme incorporates a semi-implicit Stokes solver to enable computations at low Reynolds number. Our simulations compare well with previous theoretical, numerical, and experimental results. For capillary numbers greater than the critical value, the drop deforms to a dumbbell shape and daughter drops detach via an end-pinching mechanism. The number of daughter drops increases with the capillary number. The breakup can also be initiated by increasing the Reynolds number.

Abstract: Liquid films with thicknesses on the order of 1 mm were commonly used for the study of drop impingement onto a wetted surface. This is because films thinner than 1 mm are difficult to generate and measure due to capillary meniscus. In this work a novel method to produce thin films of well-defined thickness has been developed. Also a reliable process with minimum uncertainty to determine film thickness was proposed. New splashing phenomena were observed for drop impact onto thin films. It is found that the critical splash level (the threshold Weber number) is insensitive to film thickness for a given solid surface if the film is sufficiently thin. It is also shown that the critical splash level increases with liquid viscosity.

Abstract: When a drop is deposited gently onto the surface of a layer of the same liquid, it sits momentarily before coalescing into the bottom layer. High-speed video imaging reveals that the coalescence process is not instantaneous, but rather takes place in a cascade where each step generates a smaller drop. This cascade is self-similar and we have observed up to six steps. The time associated with each partial coalescence scales with the surface tension time scale. The cascade will, however, not proceed ad infinitum due to viscous effects, as the Reynolds number of the process is proportional to the square root of the drop diameter. Viscous effects will therefore begin to be important for the very smallest drops. This cascade is very similar to the one observed previously by Charles and Mason [J. Colloid Sci. 15, 105 (1960)] for two immiscible liquids, where one of the liquids replaces the air in our setup.

Abstract: Experiments and modeling of the drainage of the thin liquid film between two deformable spherical drops approaching each other at constant velocity in another liquid are being presented. Two numerical models based on the lubrication theory have been developed considering the cases of immobile or mobile drop interfaces. The absolute film thickness and the thinning rate have been measured using laser interferometry for a wide range of capillary numbers. In all studied cases, the model with immobile interfaces was found to give the best predictions of the experimental time evolution of the film thickness and radial expansion. These results made it possible to derive a typical time scale of the drainage process.

Abstract: In the present work, contact angles formed by drops of diethylene glycol, ethylene glycol, formamide, diiodomethane, water, and mercury on a film of polypropylene (PP), on plates of polystyrene (PS), and on plates of a liquid crystalline polymer (LCP) were measured at 20°C. Then the surface energies of those polymers were evaluated using the following three different methods: harmonic mean equation and geometric mean equation, using the values of the different pairs of contact angles obtained here; and Neumann's equation, using the different values of contact angles obtained here. It was shown that the values of surface energy generated by these three methods depend on the choice of liquids used for contact angle measurements, except when a pair of any liquid with diiodomethane was used. Most likely, this is due to the difference of polarity between diiodomethane and the other liquids at the temperature of 20°C. The critical surface tensions of those polymers were also evaluated at room temperature according to the methods of Zisman and Saito using the values of contact angles obtained here. The values of critical surface tension for each polymer obtained according to the method of Zisman and Saito corroborated the results of surface energy found using the geometric mean and Neumann's equations. The values of surface energy of polystyrene obtained at 20°C were also used to evaluate the surface tension of the same material at higher temperatures and compared to the experimental values obtained with a pendant drop apparatus. The calculated values of surface tension corroborated the experimental ones only if the pair of liquids used to evaluate the surface energy of the polymers at room temperature contained diiodomethane. © 2000 John Wiley & Sons, Inc. J Appl Polym Sci 76: 1831–1845, 2000

Abstract: The basic problem of the impact and solidification of molten droplets on a substrate is of central importance to a host of processes. An important and novel such process in the area of micromanufacturing is solder jetting where microscopic solder droplets are dispensed for the attachment of microelectronic components. Despite the recent appearance of a few numerical studies focusing on the complex transient aspects of this process, no analogous experimental results have been reported to date to the best of our knowledge. Such a study is reported in this paper. Eutectic solder (63Sn37Pb) was melted to a preset superheat and used in a specially designed droplet generator to produce droplets with diameters in the range 50-100 μm. In a first series of experiments, the size, temperature, and impacting speed of the molten droplets were maintained constant. The primary variable was the temperature of the substrate that was controlled in the range from 48°C to 135°C. The dynamics of molten solder microdroplet impact and solidification on the substrate was investigated using a flash microscopy technique. The time for the completion of solidification from the moment of a solder droplet impact on the substrate varies between 150 μs and 350 μs. The dynamic interaction between the oscillation in the liquid region and the rapid advance of the solidification front was visualized, quantified, and presented in this paper. In a second series of experiments, the evolution of the wetting angle between the spreading drop and the substrate was recorded and analyzed. No quantitative agreement with Hoffman's correlation for wetting was found. It was established that the wetting angle dynamics is strongly coupled with the evolution of the droplet free surface. Two successive regimes were distinguished during the spreading. The influence of the initial impact velocity and substrate temperature on the dynamics of the measured wetting angle was described in both regimes. To the best of our knowledge, this study presents the first published experimental results on the transient fluid dynamics and solidification of molten microdroplets impacting on a substrate at the above-mentioned time and length scales that are directly relevant to the novel solder jetting technology.

Abstract: Numerical simulations have been used to investigate the flow regimes resulting from the impact of a 2.9 mm water drop on a deep water pool at velocities in the range 0.8–2.5 m/s. The results were used to identify the conditions leading to the formation of vortex rings, entrapment of a bubble during cavity collapse and the formation of vertical Rayleigh jets. Bubble entrapment and the associated growth of a thin high speed jet were shown to be the result of a capillary wave that propagates down the walls of the crater resulting from drop impact. Although the existence of a capillary waves is a necessary condition for bubble entrapment, bubbles will only occur when the wave speed and maximum crater size is such that the wave reaches the bottom of the crater before collapse has resulted in the formation of a thick Rayleigh jet. Simulations also clarified the conditions for which drop impact leads to axi-symmetric vortex rings. Results not reported previously, include the observation that a single drop can pr...

Abstract: We studied the dynamics of spontaneously spreading drops of viscous liquids over several decades of time. We show that there exist at least two different time scale behaviors which are compatible with the recently proposed combined theory of spreading dynamics.

Abstract: An apparatus for setting up crystallisation experiments comprises a mother liquor drop station that removes mother liquor from a plurality of wells of a multi well plate and delivers submicroliter volumes of mother liquor to a plurality of different drop regions at the same time. The apparatus also comprises a molecule drop station that delivers submicroliter volumes of a solution containing a molecule to be crystallized to the drop regions. Fig 6a

Abstract: The distribution of charge z and radii R in clusters electrosprayed from formamide solutions of tetraheptylammonium bromide was investigated by selecting those within a narrow range of electrical mobilities Z(1) in a first differential mobility analyzer (DMA), reducing their charge to unity by passage through a neutralizing chamber containing a radioactive (alpha) source, and measuring the mobilities Z(z) of the resulting discrete set of singly charged clusters in a second DMA. After correcting for the polarization contribution to cluster drag, the tandem DMA data yield the range of radii present at detectable levels for each charge state up to z = 9. Because small ion evaporation from electrospray drops leads to charge loss when a drop reaches a certain critical radius R(crit)(z), the measured maximum and minimum cluster radii associated with a given z can be used to infer the activation energy Delta for ion evaporation as a function of drop charge and curvature. These results confirm the Iribarne-Thomson ion-evaporation mechanism, and support earlier theoretical expressions for the functional form of Delta(z,R). The different phenomenon of ion evaporation from metastable multiply charged dry clusters is also observed at characteristic times of 1 s. Its activation energy is estimated as approximately 0.3 eV larger than for ion evaporation from the drops. This new process complicates the interpretation of the present measurements in terms of ion evaporation from liquid surfaces, but introduces no radical change in the picture. It helps understand why salt clusters with more than two or three charges are harder to see in mass spectrometers than in mobility studies under ambient conditions. Copyright 2000 John Wiley & Sons, Ltd.

Abstract: An experimental study was made to measure the performance of wire mesh mist eliminator as a function of broad ranges of operating and design conditions. The experiments were carried out in an industrial scale layered type demister pad made of 316 L stainless steel wires. The demister performance was evaluated by droplet separation efficiency, vapor pressure drop of wet demister, and flooding and loading velocities. These variables were measured as a function of vapor velocity (0.98–7.5 m/s), packing density (80.317–208.16 kg/m 3 ), pad thickness (100–200 cm), wire diameter (0.2–0.32 mm), and diameter of captured droplets (1–5 mm). All the measurement results lie in ranges where, in practice, the wire mesh mist eliminator predominates. The experimental results indicate that the separation efficiency increases with both the maximum diameter of capture water droplets and the vapor velocity and with the decrease of wire diameter. The pressure drop for the dry demister is relatively low and depends only on the vapor velocity. The pressure drop increases linearly up to the loading point, thereafter; the rate of increase is larger. Beyond the flooding point, the increase rate is significant even for the slightest rise in the vapor velocity. The flooding velocity diminishes with the beef-up of the packing density and with the decrease of the wire diameter. Three empirical correlations were developed as a function of the design and operating parameters for the separation efficiency, pressure drop for the wet demister in the loading range, and the flooding and loading velocities. These correlations are sufficiently accurate for practical calculations and demister design. The temperature depression corresponding to the pressure drop in a wire mesh mist eliminator systems installed in a typical multi stage flash desalination plant was estimated from the developed correlation. A good agreement was obtained between the design values and the correlation predictions.

Abstract: The aim of this paper is to compute the friction felt by a solid particle, of radius a, located across a flat or spherical interface of radius R, and moving parallel to the interface. This spherical interface can be a molecular film around an emulsion or aerosol droplet, the membrane of a vesicle or the soap film of a foam bubble. For simplicity, the acronym VDB is used to refer to either vesicle, drop, or bubble. The theory is designed as a tool to interpret surface viscosimetry experiments involving spherical probes attached to films or model membranes, taking care of the finite-size effects when the film encompasses a finite fluid volume. The surface of the VDB is a two-dimensional fluid, characterized by dilational (ηsdil) and shear (ηssh) surface viscosities. The particle intercepts a circular disc in the interface, whose size depends on the particle penetration inside the VDB. The three-dimensional fluids inside and outside the interface may be different. The analysis holds in the low Reynolds number and low capillary number regime. A toroidal (x1,x2,φ) coordinate system is introduced, which considerably simplifies the geometry of the problem. Then the hydrodynamic equations and boundary conditions are written in x1,x2,φ. The solution is searched for the first-order Fourier component of the velocity field in the radial angle φ. Reformulating the equations in “two-vorticity-one-velocity” representation, one basically ends up with a set of equations in x1,x2 only. This set is numerically solved by means of the Alternating-Direction-Implicit method. Numerical results show that the particle friction is influenced both by the viscosity and by the finiteness of the VDB volume. Finite-size effects have two origins: a recirculation effect when a/R is not very small, and an overall rotation of the VDB-particle complex when ηs is very large. In principle, the theory allows for a quantitative determination of ηs whatever a/R, including the limit a/R=0 (flat interface).

Abstract: Drop testing of micro-machined accelerometers (experimental samples) from the height of a table top shows that a moderate impact can result in large percentage of device malfunctions (as much as 50%) which render the devices unusable. This paper is a first attempt at providing a detailed analysis of the consequences of dropping a micro-machined transducer structure to a solid surface. The theoretical analysis is composed of two parts; first, a micro-machined structure is treated as a single degree of freedom oscillator consisting of a mass, a spring and a dashpot, whose motion is governed by an ordinary differential equation. Then the flexibility of the micro-machined structure is examined by solving a governing partial differential equation. It was found that for a nominal micro-machined transducer structure, the drop induced proof-mass travel and the deflection of the structure itself can be as large as 20% of its lateral dimension depending on the structural rigidity. The drop induced acceleration or deceleration depends on drop height as well as structural properties such as mass, spring constant, flexural rigidity, and geometrical dimensions. It is shown that a table-top drop can generate decelerations ranging from tens of thousands to hundreds of thousands of g's.

Abstract: Trains of juxtaposed drops in a tube are described and found to move spontaneously, in wetting conditions, because of their asymmetry. We focus on the coating properties of these devices, and show in particular that highly viscous species can be (self-) transported, thanks to the lubricating film left by the first drop. Different properties of these systems are finally displayed, which stress their versatility towards microfluidics applications.

Abstract: The steady thermocapillary motion of a spherical drop in a uniform temperature gradient is treated in the situation where convective transport of energy is predominant in the drop phase as well as in the continuous phase, i.e., when the Marangoni numbers are large. It is assumed that the Reynolds numbers in both phases are large as well; to leading order, the velocity fields are given by a potential flow field in the continuous phase and Hill’s vortex inside the drop. The migration velocity of the drop is obtained by equating the rate at which work is done by the thermocapillary stress to the rate of viscous dissipation of energy. The analysis deals with an asymptotic situation wherein convective transport of energy dominates with conduction playing a role only where essential. This leads to thin thermal boundary layers both outside and within the drop. The method of matched asymptotic expansions is employed to solve the conjugate heat transfer problem in the two phases. It is shown that the demand for energy within the drop, necessary to increase its temperature at a steady rate as it moves into warmer surroundings, results in a large temperature difference between the surface of the drop and its interior. The variation of temperature over the drop surface is large as well, and leads to a linear increase of the migration velocity of the drop with increasing Marangoni number. This result is strikingly different from that for the limiting case when the viscosity and thermal conductivity inside the drop become negligible compared to the corresponding properties in the continuous phase. This limit, which holds for a gas bubble, is recovered correctly from the analysis.