Component-Based Software Model for Numerical Simulation of Constrained Oscillations of Liquid Drops and Layers

Abstract

AbstractThe study of microhydrodynamic processes have not only practical significance, but also have a wide field for theoretical approaches and numerical investigation. The article deals with a numerical investigation of constrained oscillation of a liquid drop on a substrate, which harmonically oscillates, and oscillation of the liquid layer located on the surface of a bending plate. Forced vibrations of the cantilevered plate are excited by the piezoelectric element. The mathematical model is based on a system of Navier–Stokes equations for an immiscible incompressible two-phase mixture. The problem of numerical simulation of the interaction between a deformed solid and a fluid layer is a Fluid-Structure Interaction problem and requires a solution of both the elastodynamic and the hydrodynamics equations. The partitioned approach to solving fluid-interaction problems is one of the most common. Its allows solving each of the physical problems independently, using specific numerical schemes and a proprietary parallelism model. The elastodynamic problem taking into account geometric and physical nonlinearity is solved by the finite element method. The proposed mathematical models allow us to study the dynamics of the free surface of small liquid volumes and the processes of redistribution of a liquid layer on a flexible vibrating base.