Evaluation of the surface tension measurement of axisymmetric drop shape analysis (ADSA) using a shape parameter

A quantitative criterion called “shape parameter” to evaluate the quality of surface tension measurement of Axisymmetric Drop Shape Analysis (ADSA) is presented. ADSA is a powerful technique for the measurement of interfacial tensions and contact angles of pendant drops, sessile drops, and bubbles. Despite the general success of ADSA, deficient results may be obtained for drops close to spherical shape. Therefore, the “shape parameter” was used to determine the range of drop shapes in which ADSA succeeds or fails. The “shape parameter” is a dimensionless parameter that expresses quantitatively the difference in shape between a given experimental profile and an inscribed circle. The surface tension measurements of ADSA were evaluated for both pendant drop and constrained sessile drop configurations using the shape parameter. Different shapes of the pendant drop were studied using different sizes and materials of holders. For each drop configuration, a “critical shape parameter” was defined based on the minimum value of the shape parameter that guarantees an error of less than ±0.1 mJ/m². Furthermore, the effects of the type of liquid and constellation on the “critical shape parameter” were studied.     

Development of a new methodology to study drop shape and surface tension in electric fields

Development of a new methodology for the study of both shape and surface tension of conducting drops in an electric field is presented. This methodology, called axisymmetric drop shape analysis-electric fields (ADSA-EF), generates numerical drop profiles in an electrostatic field, for a given surface tension. Then, it calculates the true value of the surface tension by matching theoretical profiles to the shape of experimental drops, using the surface tension as an adjustable parameter. ADSA-EF can be employed to simulate and study drop shapes in the electric field and to determine its effect on liquid surface tension. The method can also be used to measure surface tension in microgravity, where current drop-shape techniques are not applicable. The axisymmetric shape of the drop is the only assumption made in the development of ADSA-EF. The new scheme is applicable when both gravity and electrostatic forces are present. Preliminary measurements using ADSA-EF suggest that the surface tension of water increases by about 2% when an electric field with the magnitude of 10(6) V/m is applied.     

Total Gaussian curvature,drop shapes and the range of applicability of drop shape techniques

Drop shape techniques are used extensively for surface tension measurement. It is well-documented that, as the drop/bubble shape becomes close to spherical, the performance of all drop shape techniques deteriorates. There have been efforts quantifying the range of applicability of drop techniques by studying the deviation of Laplacian drops from the spherical shape. A shape parameter was introduced in the literature and was modified several times to accommodate different drop constellations. However, new problems arise every time a new configuration is considered. Therefore, there is a need for a universal shape parameter applicable to pendant drops, sessile drops, liquid bridges as well as captive bubbles. In this work, the use of the total Gaussian curvature in a unified approach for the shape parameter is introduced for that purpose. The total Gaussian curvature is a dimensionless quantity that is commonly used in differential geometry and surface thermodynamics, and can be easily calculated for different Laplacian drop shapes. The new definition of the shape parameter using the total Gaussian curvature is applied here to both pendant and constrained sessile drops as an illustration. The analysis showed that the new definition is superior and reflects experimental results better than previous definitions, especially at extreme values of the Bond number.     

Polymer nanodroplets forming liquid bridges in chemically structured slit pores: a computer simulation

Using a coarse-grained bead-spring model of flexible polymer chains, the structure of a polymeric nanodroplet adsorbed on a chemically decorated flat wall is investigated by means of molecular dynamics simulation. We consider sessile drops on a lyophilic (attractive for the monomers) region of circular shape with radius R(D) while the remaining part of the substrate is lyophobic. The variation of the droplet shape, including its contact angle, with R(D) is studied, and the density profiles across these droplets also are obtained. In addition, the interaction of droplets adsorbed on two walls forming a slit pore with two lyophilic circular regions just opposite of one another is investigated, paying attention to the formation of a liquid bridge between both walls. A central result of our study is the measurement of the force between the two substrate walls at varying wall separation as well as the kinetics of droplet merging. Our results are compared to various phenomenological theories developed for liquid droplets of mesoscopic rather than nanoscopic size.     

Stability of the Shape of a Viscous Drop under Buoyancy-Driven Translation in a Hele-Shaw Cell

It has been shown (N. R. Gupta, A. Nadim, H. Haj-Hariri, and A. Borhan, J. Colloid Interface Sci. 218, 338 1999) that a circular drop translating in a Hele-Shaw cell under the action of gravity is linearly stable for nonzero interfacial tension. In this paper, we use the boundary integral method to examine the nonlinear evolution of the shape of initially noncircular drops translating in a Hele-Shaw cell. For prolate initial deformations, it is found that the drop reverts to a circular shape for all finite Bond numbers considered. Initially oblate drops, on the other hand, are found to become unstable and break up if the initial shape perturbation is of sufficiently large magnitude. The critical conditions for the onset of drop breakup are examined in terms of the magnitude of the initial deformation as a function of Bond number. Two branches of marginal stability are identified and the effects of viscosity ratio and asymmetric initial perturbations on the stability diagram are discussed. Copyright 2000 Academic Press.     

Desiccating colloidal sessile drop: dynamics of shape and concentration

Using lubrication theory, drying processes of sessile colloidal droplets on a solid substrate are studied. A simple model is proposed to describe temporal dynamics of both the shape of the drop and the volume fraction of the colloidal particles inside the drop. The concentration dependence of the viscosity is taken into account. It is shown that the final shapes of the drops depend on both the initial volume fraction of the colloidal particles and the capillary number. The results of our simulations are in a reasonable agreement with the published experimental data. Computations for the drops of aqueous solution of human serum albumin are presented.     

Three-dimensional equilibrium shapes of drops on hysteretic surfaces

In this paper, we study equilibrium three-dimensional shapes of drops on hysteretic surfaces. We develop a function coupled with the publicly available surface energy minimization code Surface Evolver to handle contact angle hysteresis. The function incorporates a model for the mobility of the triple line into Surface Evolver. The only inputs to the model are the advancing and receding contact angles of the surface. We demonstrate this model’s versatility by studying three problems in which parts of the triple line advance while other parts either recede or remain stationary. The first problem focuses on the three-dimensional shape of a static pendant drop on a vertical surface. We predict the finite drop volume when impending sliding motion is observed. In the second problem, we examine the equilibrium shapes of coalescing sessile drops on hysteretic surfaces. Finally, we study coalescing puddles in which gravity plays a leading role in determining the equilibrium puddle shape along with hysteresis.     

Recent progress in axisymmetric drop shape analysis (ADSA)

Axisymmetric Drop Shape Analysis (ADSA) is a powerful technique for the measurement of interfacial properties from the shape of drops/bubbles. It relies on the best fit between theoretical curves with known surface tension values and an experimental profile. Despite the general success of ADSA, inconsistent results are obtained for nearly spherical drop shapes. Since the source of this and possible other limitations are unknown, the entire ADSA technique including hardware and software is systematically scrutinized. The hardware consists of electronics, and optical and mechanical components that generate a digital image of a drop. Since the quality of images has a considerable impact on the surface tension measurements, general guidelines for the use of hardware components are developed to enhance the quality of the image. The scrutiny of the software of ADSA is significantly more involved. The software consists of image analysis and numerical schemes. One of the key elements is the modularization of the software, since a generic software package is not suitable for all experimental situations. As a result, a more versatile image analysis module is introduced. In this context a variety of state-of-the-art edge detection techniques are studied, and a more robust technique is adopted. The two existing ADSA numerical schemes are also compared systematically, and the more efficient one is implemented. It is shown that even this superior numerical scheme has convergence problems for nearly spherical drops. This difficulty is due to numerical truncation and accumulation of round-off errors, which are the ultimate limitation of all numerical schemes. This intrinsic limitation becomes more pronounced as drops become closer to spherical in shape, but there were no objective criteria available to define "close to spherical drops". Therefore, a quantitative criterion called shape parameter is introduced to identify the range of applicability of ADSA. The improved version of ADSA not only determines the interfacial properties more accurately but, through the shape parameter, also provides an a priori knowledge of the accuracy of the results.     

Impact of compound drops: a perspective

Drop interaction with solid surfaces upon impact has been attracting a growing community of researchers who are focusing more and more on ‘complex’ surfaces and ‘complex’ drops. Recently, we are observing an emerging research trend related to the investigation of compound drop impact. Compound drops consist of two or more distinct continuous phases sharing common interfaces, surrounded by a third phase. Examples are core–shell and Janus drops. In this review, we address the fundamental aspects of compound drop impact and discuss the current challenges related to experimental testing and numerical simulation of multiphase fluid systems. Furthermore, we provide a perspective on the technological relevance of understanding and controlling compound drop impact, ranging from 3D printing to liquid separation for water cleaning and oil remediation.     

Shaping of gelling biopolymer drops in an elongation flow

Shaping, defined as deformation in combination with gel formation of gelatine and kappa-carrageenan drops in an elongation flow, was studied. The focus was to investigate the possibility of shaping and fixating small drops in the diameter range 20 to 229 mum. In the shaping progress and the influence of experimental properties, the viscosity, temperature, and flow of the deforming fluid were examined on the final drop shape. In the experiments a hot emulsion of an aqueous biopolymer solution in silicone oil was injected into cold silicone oil where a deforming elongation flow field existed. After injection, a temperature decrease in the drops resulted in a gel formation of the biopolymer and a fixation of the deformed drop in the flow. The shape was measured and the effect on the drop aspect ratio was determined by image analysis. Over the total drop diameter range, kappa-carrageenan was more ellipsoid-shaped than gelatine, with a maximum aspect ratio of 6 compared to 4 for gelatine. For small drops, around 22 mum, it is possible to shape kappa-carrageenan, but for gelatine small drops tend to be unaffected. An increase in viscosity, temperature, and flow resulted in an increase in the final fixated shape of the drops. The differences in drop deformation between the biopolymers were explained by drop-viscosity/oil differences and differences in the kinetics of gel formation. The different gel formation kinetics resulted in a short, well-defined, shaping process for kappa-carrageenan, while for gelatine the process was more complex, with both deformation and relaxation present at different stages.     

Size-dependent surface tension and Tolman's length of droplets

A model for the size-dependent surface tension gammalv(D) of liquid droplets, free of any adjustable parameter, is presented in terms of the size-dependent surface energy gammasv(D). It is found that gammalv(D) drops monotonically with the size of the droplet in the nanometer region. Modeling predictions agree with computer simulations for sodium, aluminum, and water droplets. Meanwhile, the Tolman's equation is found to be valid for small particles, and the Tolman's length is always positive and becomes longer when the droplet size is decreased.     

Partial wetting of chemically patterned surfaces: the effect of drop size

Partial wetting of chemically heterogeneous substrates is simulated. Three-dimensional sessile drops in equilibrium with smooth surfaces supporting ordered chemical patterns are considered. Significant features are observed as a result of changing the drop volume. The number of equilibrated drops is found either to remain constant or to increase with growing drop volume. The shape of larger drops appears to approach that of a spherical cap and their three-phase contact line seems, on a larger scale, more circular in shape than that of smaller drops. In addition, as the volume is increased, the average contact angle of drops whose free energy is lowest among all equilibrium-shaped drops of the same volume appears to approach the angle predicted by Cassie. Finally, contrary to results obtained with two-dimensional drops, contact angle hysteresis observed in this system is shown to exhibit a degree of volume dependence in the advancing and receding angles. Qualitative differences in the wetting behavior associated with the two different chemical patterns considered here, as well as differences between results obtained with two-dimensional and three-dimensional drops, can possibly be attributed to variations in the level of constraint imposed on the drop by the different patterns and by the dimensionality of the system.     

A numerical study of the effect of insoluble surfactants on the stability of a viscous drop translating in a Hele-Shaw cell

A circular drop is a linearly stable solution for the buoyancy-driven motion of drops in a Hele-Shaw cell [Gupta et al. J. Colloid Interface Sci.218(1), 338 (1999)]. In the absence of surface-active agents, an initially prolate drop always goes to a steady circular shape while initially oblate drops exhibit complex dynamics [Gupta et al. J. Colloid Interface Sci.222, 107 (2000)]. In this study, the effect of insoluble surfactant impurities on the critical conditions for drop breakup is explored by using the Langmuir adsorption framework in conjunction with a physically based expression for the depth-averaged tangential stress exerted on a two-phase interface in a Hele-Shaw cell. It is shown that the presence of surfactants can have both a stabilizing and a destabilizing effect on the shape of the drop, depending on the Bond number, the magnitude of the initial perturbation, and the strength of surface convection. Similar to the clean drop dynamics, two marginally stable branches are found. Increasing the surface Peclet number results in the stabilization of the main branch while the secondary branch shifts to higher Bond numbers. The mode of breakup is also found to be strongly influenced by the strength of surface convection.     

Implementation and examination of a new drop shape analysis algorithm to measure contact angle and surface tension from the diameters of two sessile drops

The performance of a new algorithm developed to measure contact angle and surface tension of sessile drops is examined. To calculate the contact angle and surface tension, the new algorithm (ADSA-TD) requires the radius (contact or equatorial) and volume of two sessile drops of different sizes that are placed on the same surface. Initially, the algorithm was tested using synthetic drops (synthetic or theoretical drops are produced by numerical integration of the Laplace equation). The radii and volumes of synthetic drops were used as ADSA-TD inputs. The calculated contact angle (θ) and surface tension (γ) by ADSA-TD matched perfectly the assumed values of θ and γ used to produce the synthetic drops, confirming theoretically the validity of the new algorithm. In the next step, the sensitivity of the algorithm to input errors was examined. It was shown experimentally that both calculated contact angle and surface tension are affected by the errors in volume and radius. Besides the error in input values, it was shown that the size difference between the paired drops and the differences in their contact angles would affect the output of ADSA-TD. As it turns out, the calculated surface tension is so sensitive to the above factors that ADSA-TD does not appear to be promising as a surface tension measurement technique. However, ADSA-TD produced acceptable contact angle values as compared to measurements made by other proven techniques such as axisymmetric drop shape analysis-profile. Thus, ADSA-TD may be of interest as a contact angle measurement technique which does not require the liquid surface tension as input.     

Amphiphilic crescent-moon-shaped microparticles formed by selective adsorption of colloids

We use a microfluidic device to prepare monodisperse amphiphilic particles in the shape of a crescent-moon and use these particles to stabilize oil droplets in water. The microfluidic device is comprised of a tapered capillary in a theta (θ) shape that injects two oil phases into water in a single receiving capillary. One oil is a fluorocarbon, while the second is a photocurable monomer, which partially wets the first oil drop; silica colloids in the monomer migrate and adsorb to the interface with water but do not protrude into the oil interface. Upon UV-induced polymerization, solid particles with the shape of a crescent moon are formed; removal of fluorocarbon oil yields amphiphilic particles due to the selective adsorption of silica colloids. The resultant amphiphilic microparticles can be used to stabilize oil drops in a mixture of water and ethanol; if they are packed to sufficient surface density on the interface of the oil drop, they become immobilized, preventing direct contact between neighboring drops, thereby providing the stability.     

Microfluidic assembly of homogeneous and Janus colloid-filled hydrogel granules

The microfluidic assembly of colloid-filled hydrogel granules of varying shape and composition is described. First, drops are formed by shearing a concentrated colloidal microsphere-acrylamide suspension in a continuous oil phase using a sheath-flow device. Both homogeneous and Janus (hemispherically distinct) spheres and disks are produced by confining the assembled drops in microchannels of varying geometry. Next, photopolymerization is carried out shortly after drop breakup to preserve their morphology. Representative wet and dried granules are characterized using fluorescence and scanning electron microscopy, respectively. Our approach offers a facile route for assembling colloid-filled hydrogel granules with controlled shape and composition.     

Double emulsions with controlled morphology by microgel scaffolding

Double emulsions are valuable structures that consist of drops nested inside bigger drops; they can be formed with exquisite control through the use of droplet-based microfluidics, allowing their size, composition, and monodispersity to be tailored. However, only little control can be exerted on the morphology of double emulsions in their equilibrium state, because they are deformable and subject to thermal fluctuations. To introduce such control, we use droplet-based microfluidics to form oil-in-water-in-oil double emulsion drops and arrest their shape by loading them with monodisperse microgel particles. These particles push the inner oil drop to the edge of the aqueous shell drop such that the double emulsions adopt a uniform arrested, anisotropic shape. This approach circumvents the need for ultrafast polymerization or geometric confinement to lock such non-spherical and anisotropic droplet morphologies. To demonstrate the utility of this technique, we apply it to synthesize anisotropic and non-spherical polyacrylate-polyacrylamide microparticles with controlled size and shape.     

Collective behavior during the exit of a wetting liquid through a network of channels

The exit of a wetting fluid from a thin microchannel into a sudden expansion is studied experimentally. In the case of the exit from a single channel, the advancing interface converges to a parabolic shape after an initial transient, in accordance with the lubrication limit analysis of a spreading drop. The experiments are then repeated for the exit from two parallel channels. At early times, the two exiting drops behave independently and display the same evolution as a single exiting droplet, while at late times we recover a single parabolic profile. The transition between the early and late states is due to the merging of the two drops, which is associated with a sudden increase in the flow rate. This is the signature of a collective effect which acts to redistribute the fluid spatially. Finally, the experiment is generalized to the case of seven parallel channels where a cascade of two-by-two mergings is observed, indicating that local interactions dominate the dynamics which lead to the global state of the system.