Boundary elements method for microfluidic two-phase flows in shallow channels

In the following work we apply the boundary element method to two-phase flows in shallow microchannels, where one phase is dispersed and does not wet the channel walls. These kinds of flows are often encountered in microfluidic Lab-on-a-Chip devices and characterized by low Reynolds and low capillary numbers. Assuming that these channels are homogeneous in height and have a large aspect ratio, we use depth-averaged equations to describe these two-phase flows using the Brinkman equation, which constitutes a refinement of Darcy's law. These partial differential equations are discretized and solved numerically using the boundary element method, where a stabilization scheme is applied to the surface tension terms, allowing for a less restrictive time step at low capillary numbers. The convergence of the numerical algorithm is checked against a static analytical solution and on a dynamic test case. Finally the algorithm is applied to the non-linear development of the Saffman-Taylor instability and compared to experimental studies of droplet deformation in expanding flows.Comment: accepted for publication, Computers and Fluids 201

Influences of surfactant on the breakup of a fluid jet in viscous surrounding

The effect of insoluble surfactant on the breakup of a fluid jet surrounded by another viscous fluid at low Reynolds number is studied both theoretically and experimentally. Equations governing the evolution of the interface and surfactant concentration are derived using a long wavelength approximation for the case of an inviscid jet and a slightly viscous jet surrounded by a more viscous fluid. These one dimensional partial differential equations governing the evolution of the slender jet are solved numerically for given initial interfacial perturbations and surfactant concentration. It is found that the presence of insoluble surfactant at the interface retards the pinch-off. The influence of surface diffusion of surfactant on the jet deformation is studied by varying surface Peclet number. It is found that greater diffusion of surfactant causes the jet to pinch faster. To check the predictions of our model, we performed experiments both for clean interface and as well as in presence of surfactants. The experimental results support the prediction of the theoretical model that the presence of surfactant slows down the pinch-off process. Results of the long wavelength model are also compared against the numerical simulations of the full problem. The solution of the full problem shows similar behavior to the simplified long wavelength model

A computational fluid dynamics study of two-phase flows in the presence of surfactants

Drop formation in co-flowing fluids and drops rising in a tube are important in applications such as microencapsulation and enhanced oil recovery. A hybrid volume-of-fluid method with a front-tracking scheme is developed to study two-phase flows in the presence of surfactants at finite Reynolds numbers. Both fluids can be Newtonian or shear-thinning, and surfactants are soluble in the adsorption-desorption limit. A drop in the co-flowing geometry typically breaks up at the primary neck. The drop breaks faster with smaller volumes as the outer flow rate increases or the drop viscosity decreases. When surfactants are present, they accumulate in the neck region resulting in Marangoni stresses that slow down the neck thinning rate. This results in longer breakup times with larger drop volumes. At high surfactant coverages, the primary neck formation slows down enough and breakup occurs at the secondary neck. Increasing outer co-flowing flow weakens the retarding effect of the high surfactant coverage leading to breakup again at the primary neck. The adsorption-desorption kinetics also affects the neck breakup position, and the primary drop volume and breakup time depend non-linearly on the Biot number. The presence of a confining wall may lower the value of the critical equilibrium fractional coverage required for the drop to enter the no-necking regime. As the drop becomes more shear-thinning, the drop breaks up faster with a shorter remnant drop length. Multiple satellite drops are observed at breakup with strongly shear-thinning drop fluid at high coverage of soluble surfacants. The buoyancy-driven motion of drops in a tube is investigated by determining the steady shapes and velocities of the drops as a function of the drop size. Higher buoyancy force leads to larger deformation of drops and increased terminal velocities. Higher inertia increases the terminal velocity of drops and results in the development of negative curvatures at the rear of the drop. The non-uniform distribution of surfactants at the interface gives rise to Marangoni stresses that retard the drop motion though the drop shapes remain unaffected

A mathematical formulation of the boundary integral equations for a compressible stokes flow

A general boundary integral formulation for compressible Stokes flows is theoretically described within the framework of hydrodynamic potentials. The integral equation is implemented numerically to the study of drop expansion in compressible viscous flows. Marker point positions on the drop interface are involved by using the boundary integral method for calculation of fluid velocity. Surface discretization is adaptive to the instantaneous drops shapes. The interplay between viscous and surface tension and its influence on the evolving emulsion microstructure during its expansion is fundamental to the science and technology of foam processing. In this article the method is applied for 3D simulations of emulsion densification that involves an uniform expansion of a viscous fluid containing spherical drops on a body centered cubic lattice (BCC)

Surfactants, Thermal And Surface Energy Effects On Emulsions’ Transport Properties: A Study Using Lattice Boltzmann Method

This work aims to provide an efficient Gunstensen LBM based CFD model, capable of solving complex problems related to droplets behavior in shear and parabolic flows. Thermal conditions determine the outcome of the physical and transport properties of emulsions during their various processing phases. A better understanding of the intricate relationship between thermal, surfactants and hydrodynamics can help in the optimization of these processes during the production of emulsions. To investigate the outcome of coupling thermal, surfactants and hydrodynamics on emulsions behavior, a robust quasi-steady thermal-surfactants numerical scheme is presented and used here. To validate the model, the rheological behavior of oil-in-water system was investigated. The numerical results matched well the experimental results of the similar oil-in-water system under steady-state thermal conditions. Furthermore, it is shown that the proposed numerical model can handle cases with transient thermal conditions while maintaining good accuracy. The model has been improved to study the combined effects of temperature, and contact angle on the movement of slugs and droplets of oil in water (O/W) system flowing between two parallel plates and in 3D confined flow study. This is found in the enhanced oil recovery technique which includes thermal, contact angle and surfactant effects for breaking up trapped crude oil. The model static contact angle due to the deposition of the O/W droplet on a flat surface with simulated hydrophilic characteristic at different fluid temperatures, matched very well the proposed theoretical calculation. Furthermore, the model was used to simulate the dynamic behavior of droplets and slugs deposited on the domain\u27s upper and lower surfaces, while subjected to parabolic flow conditions. The model accurately simulated the contact angle hysteresis for the dynamic droplets cases. It was also shown that at elevated temperatures the required power to transport the mixture diminished remarkably. The aim is to improve our understanding of the underlying physics associated with the secondary and tertiary extraction process of trapped crude oil in wells by injecting hot water. Finally, the model was utilized for the investigation of the flow behavior of O/W emulsions with the goal of delineating the best practices for transporting these emulsions in circular ducts. The effects of temperature, volume fraction, flow pressure gradient, and surfactants concentration are investigated in a Poiseuille flow setup. A dimensionless power number ratio was introduced and successfully used for guiding the selection of the most cost-efficient means for transporting O/W emulsion