Effects of inertia on the deformation of drops enclosed by elastic interfaces in linear shear flow

Abstract

Droplets enclosed by elastic interfaces can be extensively found in nature and engineering applications. For instance, oil-water droplets in petroleum engineering can be surrounded by Asphaltene thin film; biological cells are usually surrounded by elastic biological membranes consisting of lipid bilayers with spectrin proteins; droplets enclosed by polymer membranes or lipid bilayers are also widely found in materials science and engineering. This type of droplets is also an excellent structure for encapsulation, transport and release of active agents due to the presence of elastic interface, thus they are widely used in applications such as cosmetics and drug delivery. To study the deformation behavior of single droplet enclosed by complex interfaces under shear flow is fundamental for understanding rheological characteristics of droplet suspensions and for developing droplet-based substance transport technologies. The presence of various molecules confers the drop interfaces various special mechanical properties, such as resistances to shear deformation, area dilatation and bending deformation. Those special mechanical properties significantly influence the transport characteristics of momentum and energy between droplets and surrounding fluids, thus conventional theories based on surface tension are no longer valid for understanding the dynamics of droplets enclosed by elastic interfaces. Generally, the deformation of droplets enclosed by elastic interfaces under shear flow is mainly governed by the coupling of fluid inertia, interface elasticity and fluid viscosity. Current literatures mostly focus on the deformation of drops with elastic interfaces with inertia neglected, which is based on the assumption of Stokes flow. However, the effects of fluid inertia are of great importance in many cutting edge technologies and in vivo bioprocesses, such as inertial microfluidic technologies for separation and manipulation of droplets, blood flow with moderate Reynolds number in arterial vessel. As such, in this study, a three-dimensional direct numerical simulation model able to simultaneously consider fluid inertia and interface elasticity is developed for two-phase flow by combining the front tracking method and the finite element method. Using this model, we study the effects of particle Reynolds number on the deformation behavior of elastic interface enclosed drops in linear shear flow. It is found that oscillations in transient deformation are presented at high Reynolds numbers, and the amplitude and period of such oscillations increase with the Reynolds number. Both the maximum deformation and steady-state deformation increase with the Reynolds number. Besides, the three-dimensional shapes of drops are alternated with the Reynolds number increased. The physical mechanisms underlying the effects of fluid inertia on the deformation of elastic interface enclosed droplets are also discussed by analyzing the distribution of streamline and pressure inside and outside the droplets at different Reynolds number. In summary, the fluid inertia has significant influences on the deformation behavior of elastic interface enclosed drops, especially at moderate to high Reynolds numbers. These results provide new insights into the deformation and motion of droplets enclosed by elastic interfaces under shear flow. Besides, the numerical method developed in the present study can be further used to study the flow characteristics of complex droplet suspensions such as blood and crude oil emulsions and to develop microfluidic technologies for manipulation and separation of complex droplets such as blood cells.