Dr. Nick Cogan (Dept. of Mathematical Sciences, FSU) 

11/4/2021  3:10pm

Abstract:

Multiphase models have been extensively used to describe the dynamics in applications where multicomponent physics play a role. Rather than resolve the components at the microscope, macroscopic closure laws  are used along with, often heuristic, assumptions. Multiphase models have the advantage of substantially simplifying numerical simulations by avoiding explicit treatment of interfaces and being amendable to standard numerical methods. In this talk, we will describe two applications where multiphase models were applied. We will outline what has been done and directions that we are working on. 

 

Biofilms are composed of bacteria enmeshed in a self-produced polymer network. The network is composed of multiple types of polymers with  very different structures and functions. Many multiphase models have considered the polymer network as a homogenous network. We describe previous work and how this leads to incorporating current understanding to develop biofilm control methods. 

 

The second application is focused on the interaction between physics and chemistry. The origins of life are rooted in the organization from small molecules to larger molecules into self-assemblies. This organization requires energetic input that appears to have been driven by temperature and pressure differentials near hydrothermic vents. It has been hypothesized that the building blocks of life originated at the interface between high temperature water exacting into the oceans via these vents. A recent study focused on the development of a solid membrane via a simplified chemical precipitate reaction. The aims are to understand the physical interaction between the precipitating solid and the fluid dynamics as the membrane barrier is formed. We introduce a slight change in the standard formulation and show that this model is compatible with Darcys’ law and standard porous media equations in different limits. We also provide numerical and  linearization results indicating the affect of a developing solid within a flowing liquid.