Two-Phase Nonturbulent Flow with Applications

Darko Mitrović,Andrej Novak

doi:10.1155/2015/439704

Abstract

We model dynamics of two almost immiscible fluids of different densities using the Stokes equations with the Dirac distribution representing the sink or source point. The equations are solved by regularizing the Dirac distribution and then using an iterative procedure based on the finite element method. Results have potential applications in water pollution problems and we present two relevant situations. In the first one, we simulate extraction of a light liquid trapped at the bottom of a pond/lake and, after being disturbed, it rises toward the surface. In the second case, we simulate heavy liquid leaking from a source and slowly dropping on an uneven bottom.

Highlights

Questions concerning transport of fluids are essential in environmental and industrial engineering
We model dynamics of two almost immiscible fluids of different densities using the Stokes equations with the Dirac distribution representing the sink or source point
The equations are solved by regularizing the Dirac distribution and using an iterative procedure based on the finite element method

Summary

Introduction

Questions concerning transport of fluids are essential in environmental and industrial engineering. Among many situations of interest, we will describe here two examples which we will put in the context of pollution problems In both situations, we have two fluids which are almost immiscible and have slightly different densities. We have two fluids which are almost immiscible and have slightly different densities This means that we assume almost sharp interface between the fluids and slow movements. Let us remark that the phenomenon is explained in [1] Another notable application of the model to be analyzed here is in solid Earth sciences. The mathematical problem is described by the Stokes and density advection-diffusion equations, similar to those used in geodynamics applications [4,5,6,7]. We will see how it spreads along through the water

Governing Equations

Solution Strategy

Simulations

Conclusion