Sloshing characteristics of viscoelastic liquids in a rectangular container with a floating flexible plate

Abstract

The study examines the sloshing behavior of two superposed viscoelastic fluid layers governed by Walter’s liquid ‘B” model within a rectangular tank, subjected to horizontal vibrations. Our investigation is extending to take into account the influence of a flexible plate floating on the top fluid layer, where a modified membrane equation is used to model the stress balance on the surface. Additionally, an insoluble surfactant exists at the liquid–liquid interface within the flow system. The problem’s mathematical model is linked with the linearized Navier–Stokes equation for viscoelastic fluids, along with boundary conditions, which are solved using Laplace transform. Durbin’s numerical inverse Laplace transform scheme is used to numerically calculate solutions of the governing equations in the time domain. Graphical representations of the numerical results are included to investigate the free surface profiles, sloshing forces and moments skeletons and evolution of surface concentration under horizontal excitations, examining their behavior in relation to uniform thickness and structural rigidity of the floating elastic plate; Marangoni number and the relaxation times coefficients of the fluids. The results showed that both the thickness and structural rigidity of the floating elastic enhances the wave stability of both free surfaces of liquids, and it also causes a significant decrease in the forces acting on the walls of the container, which constitutes a safety factor to maintain the integrity of the container. On the other hand, increasing the viscoelastic parameters stimulates the sloshing waves and increases the compressive forces on the walls of the container.