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Breakup and Disruption of Drops in Shearing and Extensional Particulate Flows

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Abstract

When biological cells approach regions with high strain-rates, the membrane deformation can surpass the yielding point, leading to cell lysis. In the interest of enhancing such effects, drop dynamics is studied. Here, bending stiffness and viscoelastic area compression of the membrane are not considered. Surface-tension force is used to model planar tensile stresses instead. Breakup of drops has been shown to depend on the type of flow, the Reynolds number, Re , the capillary number, Ca , the viscosity ratio, the density ratio, and the Stokes number (particulate flows). In simple shear flows at low Re and low Ca, breakup is not possible. The main purpose of this work is to find conditions that enhance drop disruption under such flows. While the deformation of drops and elastic capsules in simple shear flows and particulate flows have been subject of research, less attention has been given to the deformation of drops in particulate simple shear flows that are initially quiescent. The effects of rigid particles on drops are studied numerically for several flow conditions and the deformation is analyzed using the particle-particle distance. It is observed a decrease in deformation as Re (moderate regime) increases for different initial position of the particles. Drop deformation increases with Ca, meanwhile larger and denser particles are preferred to induce drop puncturing. Without particles, the conditions for drop breakup are found when the walls are closely located. Similarly, a gravity-driven particulate flow is studied and the dependence on the Bond number is shown. The problem of drop splitting in sudden expansions is also analyzed, showing dependence on the expansion ratio. The conservation laws are solved numerically using finite volumes and the Crank-Nicolson scheme. Velocities are corrected with SIMPLEC. The interface is tracked with the volume-of-fluid method, reconstructed with the piecewise linear interface calculation algorithm (PLIC), and fluxed based on the defined donating region (DDR). A High-Resolution technique (SMART) is employed to discretize advection terms. A continuum surface force (CSF) models surface tension. Rigid particles are introduced in the domain with the Lagrange multiplier method.

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