Mass and Volume Conservation in Phase Field Models for Binary Fluids - Volume 13 Issue 4 - Jie Shen, Xiaofeng Yang, Qi Wang

We investigate recovery of multispecies oral biofilms following chlorhexidine gluconate (CHX) and CHX with surface modifiers (CHX-Plus) treatment. Specifically, we examine the percentage of viable bacteria in the biofilms following their exposure to CHX and CHX-Plus for 1, 3 and 10 minutes, respectively. Before antimicrobial treatment, the biofilms are allowed to grow for three weeks. We find that (a). CHX-Plus kills bacteria in biofilms more effectively than the regular 2% CHX does, (b). cell continues to be killed for up to one week after exposure to the CHX solutions, (c). the biofilms start to recover after two weeks, the percentage of the viable bacteria recovers in the 1 and 3 minutes treatment groups but not in the 10 minutes treatment group after five weeks and the biofilms fully return to the pretreatment levels after eight weeks. To understand the mechanism, a mathematical model for multiple bacterial phenotypes is developed, adopting the notion that bacterial persisters exist in the biofilms together with regulatory quorum sensing molecules and growth factor proteins. The model reveals the crucial role played by the persisters, quorum sensing molecules and growth factors in biofilm recovery, accurately predicting the viable bacterial population after CHX treatment.

We study a diffusive Lotka-Volterra competition system with advection under Neumann boundary conditions. Our system models a competition relationship that one species escape from the region of high population density of their competitors in order to avoid competition. We establish the global existence of bounded classical solutions to the system over one-dimensional finite domains. For multi-dimensional domains, globally bounded classical solutions are obtained for a parabolic-elliptic system under proper assumptions on the system parameters. These global existence results make it possible to study bounded steady states in order to model species segregation phenomenon. We then investigate the one-dimensional stationary problem. Through bifurcation theory, we obtain the existence of nonconstant positive steady states, which are small perturbations from the positive equilibrium; we also rigourously study the stability of these bifurcating solutions when diffusion coefficients of the escaper and its competitor are large and small respectively. In the limit of large advection rate, we show that the reaction-advection-diffusion system converges to a shadow system involving the competitor population density and an unknown positive constant. Existence and stability of positive nonconstant solutions to the shadow system have also been obtained through bifurcation theories. Finally, we construct infinitely many single interior transition layers to the shadow system when crowding rate of the escapers and diffusion rate of their interspecific competitors are sufficiently small. The transition-layer solutions can be used to model the interspecific segregation phenomenon.

We articulate and apply the generalized Onsager principle to derive transport equations for active liquid crystals in a fixed domain as well as in a free surface domain adjacent to a passive fluid matrix. The Onsager principle ensures fundamental variational structure of the models as well as dissipative properties of the passive component in the models, irrespective of the choice of scale (kinetic to continuum) and of the physical potentials. Many popular models for passive and active liquid crystals in a fixed domain subject to consistent boundary conditions at solid walls, as well as active liquid crystals in a free surface domain with consistent transport equations along the free boundaries, can be systematically derived from the generalized Onsager principle. The dynamical boundary conditions are shown to reduce to the static boundary conditions for passive liquid crystals used previously.