Non-aqueous phase liquid drop formation within a water saturated fracture

This work focuses on the mechanisms of non-aqueous phase liquid (NAPL) drop formation within a single fracture fed from a NAPL reservoir by way of a circular orifice, such as a pore. The fracture is assumed to be fully saturated, the relative wettability of the system is assumed water-wet, and the water velocity profile within the fracture is described by a Poiseuille flow. The size of the NAPL drops is investigated for various water flow velocities and NAPL entrance diameters. A force balancing method was used to determine the radii of detached drops. The drop sizes calculated from the model developed here are shown to be in agreement with available experimental drop size data. It is shown that at low Reynolds numbers the buoyancy force is the dominant force acting on the drop during the formation process and at high Reynolds numbers the viscous forces dominate. A simplified expression relating the geometry of the fractured system to the drop radii is developed from the model equations, and it is shown to predict drop radii that match well with both the model simulations and the available experimental data.     

A unique behavior of water drops induced by low-density polyethylene surface with a sharp wettability transition

A low-density polyethylene (LDPE) surface with a sharp wettability gradient and high hysteresis was prepared, on which a unique behavior of water drops was found. The water contact angle of one water drop on the less hydrophobic region was larger than that on the more hydrophobic end, which was much different from the general phenomenon. The unique behavior is believed to be induced by the high hysteresis of the LDPE surface and the sharp change in wettability. The driving and hysteresis forces acting on the water drops were calculated and analyzed in detail. The reasons resulting to such a unique phenomenon were further explained.     

微液滴的非机械驱动

微液滴的非机械驱动是操纵微小尺雨液体流动的新方法。本文介绍当前有关微液滴非机械驱动的研究进展，包括：利用电化学方法产生并消耗表面活性分子来产生表面张力梯度；把表面浸润性梯度和温度梯度相结合；通过光敏化合物偶氮部分顺反异构的转换导致表面自由能的变化，最后由光照来驱动微液滴，以及利用固体基片上的亲水疏水条纹构建微芯片上实验室的液体非机械输送网络。     

Rheo-optical determination of the interfacial tension in a dispersed blend

In this work, we present two novel methods to determine the interfacial tension of a disperse polymer blend through rheo-optical measurements of flow-induced single drop distortions. A counter-rotating shearing device with transparent plates is used to measure drop distortions. The cell geometry allows for a top view of the deforming drop, i.e., along the velocity gradient direction. Such a view is the only possible option for all currently available commercial rheo-optical instruments. Two different quantities are monitored, namely, the drop axis along the vorticity direction, and the rotation period of the drop surface. We use drops of a polyacrilamide aqueous solution (a shear thinning liquid) immersed in a polyisobutene matrix. Experimental results are interpreted in terms of theories for Newtonian liquids, where the relevant parameter is the Capillary number. If an appropriate viscosity ratio is chosen, that accounts for the shear thinning behaviour of the drop phase, good agreement is found between measurements and theoretical predictions. As a result, a robust estimate of the blend interfacial tension, that makes use only of the information acquired from top view experiments, is obtained.     

Ratcheting motion of liquid drops on gradient surfaces

The motions of liquid drops of various surface tensions and viscosities were investigated on a solid substrate possessing a gradient of wettability. A drop of any size moves spontaneously on such a surface when the contact angle hysteresis is negligible; but it has to be larger than a critical size in order to move on a hysteretic surface. The hysteresis can, however, be reduced or eliminated with vibration that allows the drop to sample various metastable states, thereby setting it to the path of global energy minima. Significant amplification of velocity is observed with the frequency of forcing vibration matching the natural harmonics of drop oscillation. It is suggested that the main cause for velocity amplification is related to resonant shape fluctuation, which can be illustrated by periodically deforming and relaxing the drop at low frequencies.     

Particle motions in sheared suspensions

The effects of diffusion out of and into drops undergoing equatorial collision in laminar shear flow were studied. With an electric field perpendicular to the direction of flow, diffusion into undeformed drops enhanced coalescence, while diffusion from the drops inhibited it. With marked outward diffusion, drops having a collision angle greater than 83° assumed a stable alignment in opposition to the velocity gradient for several minutes and then rotated to become a permanent head-on collision doublet. With inward diffusion the separation of drop centers increased along the paths of approach and the apparent angle of collision decreased. The phenomena were explained qualitatively on the basis of surface flow arising from concentration gradients at the drop surfaces. Stable multiplets were formed on collision of highly deformed drops as a result of hydrodynamic forces both with and without diffusion.     

Motion of a drop on a solid surface due to a wettability gradient

The hydrodynamic force experienced by a spherical-cap drop moving on a solid surface is obtained from two approximate analytical solutions and used to predict the quasi-steady speed of the drop in a wettability gradient. One solution is based on approximation of the shape of the drop as a collection of wedges, and the other is based on lubrication theory. Also, asymptotic results from both approximations for small contact angles, as well as an asymptotic result from lubrication theory that is good when the length scale of the drop is large compared with the slip length, are given. The results for the hydrodynamic force also can be used to predict the quasi-steady speed of a drop sliding down an incline.     

The effects of the column pressure drop on retention and efficiency in packed and open tubular supercritical fluid chromatography

The effects of the pressure drop across the column on retention and efficiency in SFC have been studied. Numerical methods are described which enable the prediction of hold-up time and pressure drop in both packed and open tubular columns. Predictions of both hold-up time and pressure drop are in good agreement with experimental data. The density gradient along the column can be calculated using the numerical methods and a procedure is described which enables the calculation of the overall capacity factors of the solutes from the density profile in the column. Significant variations of the capacity factor are observed along the column. The effect of the density gradient along the column on local diffusivity and dispersion is studied. The column efficiency in systems with significant pressure drops is affected by changes in: the linear velocity of the mobile phase; the diffusion coefficients; and the capacity factors of the solutes along the column. The overall efficiency of the chromatographic system can be calculated if, as is the case for open tubular columns, adequate plate height equations are available.     

The dynamics of evaporating sessile droplets

Experiments on sessile drops evaporating in a normal atmosphere without an applied thermal gradient are reported and compared with an available theoretical model. The liquids used are alkanes; water; and, more recently, polydimethylsiloxane oligomers. The substrates are silicon wafers, completely wetted by the liquid. Experiments with hanging drops allow us first to discard any influence of convection in the gas phase on the drop dynamics. The model assumes the process to be controlled by the stationary diffusion of the evaporating molecules in the gas phase. For alkanes and water, and in a limited range of drop sizes where gravity can be ignored, the model accounts very well for the dynamics of the drop radius, and rather well for the contact angle. This is no longer the case with the polydimethylsiloxane oligomers, where the very small contact angles require a more elaborated analysis of the drop edge. The text was submitted by the authors in English.     

Size-selective sliding of sessile drops on a slightly inclined plane using low-frequency AC electrowetting

When placed on an inclined solid plane, drops often stick to the solid surface due to pinning forces caused by contact angle hysteresis. When the drop size or the plane's incline angle is small, the drop is difficult to slide due to a decrease in gravitational force. Here we demonstrate that small drops (0.4-9 μL) on a slightly inclined plane (~12°, Teflon and parylene-C surface) can be mobilized through patterned electrodes by applying low-frequency ac electrowetting under 400 Hz (110-180 V(rms)), which has a mechanism different from that of the high-frequency ac method that induces sliding by reducing contact angle hysteresis. We attribute the sliding motion of our method to a combination of contact angle hysteresis and interfacial oscillation driven by ac electrowetting instead of the minimization of contact angle hysteresis at a high frequency. We investigated the effects of ac frequency on the sliding motion and terminal sliding of drops; the terminal sliding velocity is greatest at resonance frequency. Varying the electrowetting number (0.21-0.56) at a fixed frequency (40 Hz) for 5 μL drops, we found an empirical relationship between the electrowetting number and the terminal sliding velocity. Using the relationship between the drop size and ac frequency, we can selectively slide drops of a specific size or merge two drops along an inclined plane. This simple method will help with constructing microfluidic platforms with sorting, merging, transporting, and mixing of drops without a programmable control of electrical signals. Also, this method has a potential in heat transfer applications because heat removal capacity can be enhanced significantly through drop oscillation.     

Experimental investigation on thermocapillary drop migration at large Marangoni number in reduced gravity

Results from a space experiment on thermocapillary drop migration conducted on board the Chinese spacecraft ShenZhou-4 are presented in this paper. In the experiment, isolated drops of Fluorinert liquid moved in a matrix liquid of 5cst silicone oil at values of the Marangoni numbers (Ma) ranging up to 5500 and the interferometry images showed the temperature distribution inside the test cell. The drop migration velocity was measured. The experimental results show that the scaled drop migration velocity V/V(YGB) obviously decreases with Ma increasing the values up to 5500. The space experimental results are also compared with those from our early experiments, other space experiments, and some theoretical predictions.     

The drop size in membrane emulsification determined from the balance of capillary and hydrodynamic forces

Here, we investigate experimentally and theoretically the factors that determine the size of the emulsion droplets produced by membrane emulsification in "batch regime" (without applied crossflow). Hydrophilic glass membranes of pore diameters between 1 and 10 mum have been used to obtain oil-in-water emulsions. The working surfactant concentrations are high enough to prevent drop coalescence. Under such conditions, the size of the formed drops does not depend on the surfactant type and concentration, on the interfacial tension, or on the increase of viscosity of the inner (oil) phase. The drops are monodisperse when the working transmembrane pressure is slightly above the critical pressure for drop breakup. At higher pressures, the size distribution becomes bimodal: a superposition of a "normal" peak of monodisperse drops and an "anomalous" peak of polydisperse drops is observed. The theoretical model assumes that, at the moment of breakup, the hydrodynamic ejection force acting on the drop is equal to the critical capillary force that corresponds to the stability-instability transition in the drop shape. The derived equations are applied to predict the mean size of the obtained drops in regimes of constant flow rate and constant transmembrane pressure. Agreement between theory and experiment is established for the latter regime, which corresponds to our experimental conditions. The transition from unimodal to bimodal drop size distribution upon increase of the transmembrane pressure can be interpreted in terms of the transition from "dripping" to "jetting" mechanisms of drop detachment.     

Motion of drops on a surface induced by thermal gradient and vibration

It is well known that a liquid drop with a low contact angle (approximately 45 degrees ) and low wetting hysteresis moves toward the colder region of a temperature gradient substrate as a result of the thermal Marangoni force. A moderately sized water drop, however, usually does not move on such a surface because of the overwhelming effect of hysteresis. The water drop can, however, be forced to move when it is vibrated on a temperature gradient surface with its velocity exhibiting maxima at the respective Rayleigh frequencies. A simple model is presented that captures the dependence of drop velocity on hysteresis, vibration amplitude, and the forcing and resonance frequencies of vibration.     

Time-varying migration process of moving neutralization boundary on the immobilized pH gradient strip in the weak-base rehydration buffer

This paper quantificationally probes into time-varying migration processes of moving neutralization boundary (MNB) on immobilized pH gradient (IPG) strip in ammonia-rehydration buffers. The time-varying migration processes are determined by both time-varying dissociation equilibria of ammonia and position-varying pH environments formed by immobilized carrier ampholytes (CAs) on the IPG strip. Thus, the local dissociation equilibria of ammonia and the position-varying pH are introduced into the recursion equation of position of MNB migrations. The theoretical position-time curves and the velocity-time curves of MNB migrations obtained by the recursion approach were satisfactorily validated by a series of images of boundary migrations from the IPG-MNB experiments by using rehydration buffers with different ammonia concentrations on pH 3-6 IPG strips. The results achieved herein have significant evidence to a quantificational understanding of the mechanism of MNB and IEF.     

Measurement of dynamical forces between deformable drops using the atomic force microscope. I. Theory

Recent experimental developments have enabled the measurement of dynamical forces between two moving liquid drops in solution using an atomic force microscope (AFM). The drop sizes, interfacial tension, and approach velocities used in the experiments are in a regime where surface forces, hydrodynamics, and drop deformation are all significant. A detailed theoretical model of the experimental setup which accounts for surface forces, hydrodynamic interactions, droplet deformation, and AFM cantilever deflection has been developed. In agreement with experimental observations, the calculated force curves show pseudo-constant compliance regions due to drop flattening, as well as attractive pull-off forces due mainly to hydrodynamic lubrication forces.     

Drop mixing in a microchannel for lab-on-a-chip platforms

We present theory, simulations, and experiments for discrete drop mixing in microchannels. The drops are placed sequentially in a channel and then moved at a set velocity to achieve mixing. The mixing occurs in three different regimes (diffusion-dominated, dispersion-dominated, and convection-dominated) depending on the Péclet number (Pe) and the drop dimensions. Introducing the modified Péclet number (Pe*), we show asymptotic curves that can be used to predict the mixing time and the required distance for mixing for any of the three regimes. Simulations of the mixing experiments using COMSOL agree with the theoretical limits. In our experimental work, we used a polydimethylsiloxane (PDMS) microchannel with a membrane air bypass valve to remove the air between drops. This approach enables precise control of the mixing and merging site. Experimental, simulation, and theoretical results all agree and show that mixing can occur in fractions of a second to hours, depending on the parameters used.     

Advancing contact lines on chemically patterned surfaces

We report an experimental investigation on advancing contact lines of large drops spreading on chemically patterned surfaces. The model substrates were prepared using microphotolithography allowing precise control of the position and the size of the wettability patterns. Experiments were performed exploring different surface geometries: from ordered to disordered fields of defects and from low to high surface densities. The shape of the contact line between two isolated defects was investigated as a function of the distance. Portions of the contact line on the defects and on the matrix were studied during spreading experiments and were related to the apparent contact angles measured from the final thickness of the drops. A modified Cassie equation based on the line fraction of defects is proposed.     

Several surfaces with special wettability: Influence on spreading and motion of W/O emulsion droplets

Physical and chemical modifications were made on the surface of the aluminum sheet to change the surface properties and superhydrophobic–hydrophilic wettability gradient surface was made on the perspex surface by using microstructure-pattering technique and self-assembled-monolayer method. By using high-speed video camera system and optical tensiometer, this paper discusses the influence of special surfaces with different wettability on spreading and motion of water, oil, and W/O emulsion droplets both experimentally and theoretically. In addition, the paper also discusses the influence of the superhydrophobic–hydrophilic wettability gradient on fluidity of W/O emulsion droplets and the coalescence process of droplets. The results showed that the contact angle of W/O emulsion droplets on the modified surfaces was related to the water and oil distribution at the three-phase line. On the wettability gradient surface, the droplet moved spontaneously when the droplet was located at the junction of the gradient. A quasi-steady theoretical model was used to analyze the driving and resistant forces acting on a droplet to improve the understanding of the self-transport behavior of the droplets.     

Membrane emulsification using membranes of regular pore spacing: Droplet size and uniformity in the presence of surface shear

During membrane emulsification it is shown that the size of the drops formed at the membrane surface may increase with increasing dispersed phase injection rate through the membrane, or it may decrease, depending on the prevailing conditions. This is illustrated using a paddle stirrer positioned above flat disc membranes with regular arrays of pores of 20 μm diameter and spacing between the pores of 80 and 200 μm. In the former case an additional mechanism for drop detachment is the push-off force, which is determined by the geometry of the drops as they deform at the membrane surface. When dispersing sunflower oil in to aqueous solutions containing Tween 20, drop sizes between 60 and 200 μm were produced, and in the case of the membrane when the push-off force was working the Coefficient of Variation of the drops formed was below 10%. The push-off force may be added to the shear-drag force to predict drop detachment. For the 200 μm pore spaced membrane this force is much less prominent than the 80 μm spaced membrane. The capillary-shear model has been modified to include this push-off force. The experimental study required the use of very low dispersed phase injection rates as well as very high rates. Hence, two different types of pumps were used to provide these: a peristaltic and syringe pumps. A small study comparing the drop size, and size distributions, showed that the pump type did not influence the drops produced by the membrane emulsification process.