We extend the energetic variational approach so it can be applied to a chemical reaction system with general mass action kinetics. Our approach starts with an energy-dissipation law. We show that the chemical equilibrium is determined by the choice of the free energy and the dynamics of the chemical reaction is determined by the choice of the dissipation. This approach enables us to couple chemical reactions with other effects, such as diffusion and drift in an electric field. As an illustration, we apply our approach to a nonequilibrium reaction-diffusion system in a specific but canonical setup. We show by numerical simulations that the input-output relation of such a system depends on the choice of the dissipation.

We prove the existence of a well order reconstruction solution (WORS)-type Landau--de Gennes critical point on a square domain with an isotropic concentric square inclusion, with tangent boundary conditions on the outer square edges. There are two geometrical parameters---the outer square edge length $\lambda$, and the aspect ratio $\rho$, which is the ratio of the inner and outer square edge lengths. The WORS exists for all geometrical parameters and all temperatures, and is globally stable for either $\lambda$ small enough or for $\rho$ sufficiently close to unity. We study three different types of Landau--de Gennes critical points in this setting: critical points with the minimal two degrees of freedom consistent with the imposed boundary conditions, critical points with three degrees of freedom, and critical points with five degrees of freedom. We identify the competitors for the WORS in the two- and three-dimensional settings. In the three-dimensional setting, we numerically find up to $28$ critical points for moderately large values of $\rho$, of which diagonal solutions are global energy minimizers when they exist. We find two nonenergy minimizing critical points with five degrees of freedom for very small values of $\rho$, with an escaped profile around the isotropic square inclusion.

In this paper, we summarize some recent advances related to the energetic variational approach (EnVarA), a general variational framework of building thermodynamically consistent models for complex fluids, by some examples. Particular focus will be placed on how to model systems involving chemo-mechanical couplings and non-isothermal effects.

When an orientationally ordered system, like a nematic liquid crystal (LC), is confined on a self-closing spherical shell, topological constraints arise with intriguing consequences that depend critically on how the LC is aligned in the shell. We demonstrate reversible dynamic tuning of the alignment, and thereby the topology, of nematic LC shells stabilized by the nonionic amphiphilic block copolymer Pluronic F127. Deep in the nematic phase, the director (the average molecule orientation) is tangential to the interface, but upon approaching the temperature $T_{\mathrm{NI}}$ of the nematic-isotropic transition, the director realigns to normal. We link this to a delicate interplay between an interfacial tension that is nearly independent of director orientation, and the configuration-dependent elastic deformation energy of an LC confined in a shell. The process is primarily triggered by the heating-induced reduction of the nematic order parameter, hence realignment temperatures differ by several tens of degrees between LCs with high and low $T_{\mathrm{NI}}$, respectively. The temperature of realignment is always lower on the positive-curved shell outside than at the negative-curved inside, yielding a complex topological reconfiguration on heating. Complementing experimental investigations with mathematical modeling and computer simulations, we identify and investigate three different trajectories, distinguished by their configurations of topological defects in the initial tangential-aligned shell. Our results uncover a new aspect of the complex response of LCs to curved confinement, demonstrating that the order of the LC itself can influence the alignment and thereby the topology of the system. They also reveal the potential of amphiphilic block copolymer stabilizers for enabling continuous tunability of LC shell configuration, opening doors for in-depth studies of topological dynamics as well as novel applications in, e.g., sensing and programed soft actuators.