Pattern formation in a coupled driven diffusive system

We investigate pattern formation in a driven mixture of two mutually repulsive particle species via a field-based lattice model (FLM), a hybrid model that combines aspects of the driven Widom-Rowlison lattice gas (DWRLG) and its statistical field theory [Dickman and Zia Phys. Rev. E 97, 062126 (2018)2470-004510.1103/PhysRevE.97.062126; Lavrentovich, Dickman, and Zia, Phys. Rev. E 104, 064135 (2021)2470-004510.1103/PhysRevE.104.064135]. We find that the FLM effectively captures the bulk behavior of the DWRLG in both low- and high-density phases, suggesting that phase transitions in these models may share a common universality class. Under the effect of a drive, the FLM additionally reveals an intermediate regime, not reported in previous DWRLG studies, characterized by irregular stripes with widely fluctuating widths, contrasting with the regular, well-ordered stripes found at higher densities. In this intermediate phase, the system exhibits long-range order predominantly perpendicular to the drive direction. To construct a continuum description, we derive two coupled partial differential equations for the particle densities via a gradient expansion of the FLM mean mass-transfer equations, supplemented with additive noise. Designing a numerical solver using the pseudospectral method with dealiasing and stochastic time differencing, we reproduce the low-density microemulsion phase (characterized by a nonzero characteristic wavenumber q^{*}) and stripes perpendicular to the drive at high density. We identify the nonzero difference in the characteristic velocities of the sum and difference of the particle densities as a necessary condition for perpendicular stripe formation in the high-density phase. The continuum model exhibits novel behaviors not observed in the FLM, such as stripes aligned parallel to the drive, and chaotic patterns. This work highlights how the interplay of external drive, particle interactions, and noise can lead to a rich phenomenology in strongly driven binary mixtures.