Modeling and Computations of Cellular Dynamics Using Complex-fluid Models

Cells are fundamental units in all living organisms as all living organisms are made up of cells of different varieties. The study of cells is therefore an essential part of research in life science. Cells can be classified into two basic types: prokaryotic cells and eukaryotic cells. One typical organisms of prokaryotes is bacterium. And eukaryotes mainly consist of animal cells. In this thesis, we focus on developing predictive models mathematically to study bacteria colonies and animal cell mitotic dynamics. Instead of living alone, bacteria usually survive in a biofilm, which is a microorganism where bacteria stick together by extracellular matrix primarily made up of extracellular polymeric substances (EPS) that the bacteria excrete. By treating the biofilm and solvent as a fluid mixture, we have developed a mathematical modeling framework and computational tool to investigate the mechanisms of biofilm formation and function. The bacteria in biofilms can be categorized into various types either by their persistence to antimicrobial treatments or by their reactions to quorum sensing molecules. We have studied dynamics of 3D heterogeneous biofilm formation under hydrodynamic stress, investigated the pros and cons of quorum sensing mechanism in an aqueous environment subject to hydrodynamic impact, explored the mechanism of antimicrobial persistence, looked into optimal dosing strategies, and examined the impact of cell motility on the development of biofilm morphology. As an integral part of the study, we have also validated our model of biofilm persistence to antimicrobial treatment against the experimental results obtained in our collaborators’ laboratory. Using the validated model, we then have probed the scenario of biofilm relapse after the antimicrobial treatment. These studies have demonstrated that our model and computational package can be an effective tool for analyzing the mechanism of biofilm formation and function. During an eukaryotic cell cycle, mitosis is a process in which a mother cell divides into two genetically identical daughter cells. In the initial stage of mitosis, the mother cell, spreaded on a substrate, undergoes a dramatic shape change by detaching from the substance and forming a spherical shape. During the late stage of mitosis, a contractile ring forms on the cell division plane, splitting the mother cell into two identical daughter cells. This late stage of mitotic process is also known as cytokinesis for eukaryotic cells. We have developed a modeling framework for simulating the space-time evolution of cell morphology, cell motility and mitotic dynamics of eukaryotic cells by a multiphase field complex fluids approach. In order to solve the complex cellular dynamics models, we have developed a series of efficient, energy law preserving, stable schemes and implemented them on GPU clusters for high-performance computing. The models have shown qualitative agreement with experiments on cell rounding, movement, wrinkling, blebbing, and dividing processes

A Second Order Fully-discrete Linear Energy Stable Scheme for a Binary Compressible Viscous Fluid Model

We present a linear, second order fully discrete numerical scheme on a staggered grid for a thermodynamically consistent hydrodynamic phase field model of binary compressible fluid flow mixtures derived from the generalized Onsager Principle. The hydrodynamic model not only possesses the variational structure, but also warrants the mass, linear momentum conservation as well as energy dissipation. We first reformulate the model in an equivalent form using the energy quadratization method and then discretize the reformulated model to obtain a semi-discrete partial differential equation system using the Crank-Nicolson method in time. The numerical scheme so derived preserves the mass conservation and energy dissipation law at the semi-discrete level. Then, we discretize the semi-discrete PDE system on a staggered grid in space to arrive at a fully discrete scheme using the 2nd order finite difference method, which respects a discrete energy dissipation law. We prove the unique solvability of the linear system resulting from the fully discrete scheme. Mesh refinements and two numerical examples on phase separation due to the spinodal decomposition in two polymeric fluids and interface evolution in the gas-liquid mixture are presented to show the convergence property and the usefulness of the new scheme in applications

Numerical study of surface tension driven convection in thermal magnetic fluids

Microgravity conditions pose unique challenges for fluid handling and heat transfer applications. By controlling (curtailing or augmenting) the buoyant and thermocapillary convection, the latter being the dominant convective flow in a microgravity environment, significant advantages can be achieved in space based processing. The control of this surface tension gradient driven flow is sought using a magnetic field, and the effects of these are studied computationally. A two-fluid layer system, with the lower fluid being a non-conducting ferrofluid, is considered under the influence of a horizontal temperature gradient. To capture the deformable interface, a numerical method to solve the Navier???Stokes equations, heat equations, and Maxwell???s equations was developed using a hybrid level set/ volume-of-fluid technique. The convective velocities and heat fluxes were studied under various regimes of the thermal Marangoni number Ma, the external field represented by the magnetic Bond number Bom, and various gravity levels, Fr. Regimes where the convection were either curtailed or augmented were identified. It was found that the surface force due to the step change in the magnetic permeability at the interface could be suitably utilized to control the instability at the interface.published or submitted for publicationis peer reviewe

Numerical approximations for a three-component Cahn–Hilliard phase-field model based on the invariant energy quadratization method

How to develop efficient numerical schemes while preserving the energy stability at the discrete level is a challenging issue for the three component Cahn-Hilliard phase-field model. In this paper, we develop first and second order temporal approximation schemes based on the "Invariant Energy Quadratization" approach, where all nonlinear terms are treated semi-explicitly. Consequently, the resulting numerical schemes lead to a well-posed linear system with the symmetric positive definite operator to be solved at each time step. We rigorously prove that the proposed schemes are unconditionally energy stable. Various 2D and 3D numerical simulations are presented to demonstrate the stability and the accuracy of the schemes