Nonreciprocal Model B: the role of mobilities and nonreciprocal interfacial forces

Abstract

We study a non-reciprocal version of Model B, as the continuum theory for non-reciprocal particle mixtures. In contrast to non-reciprocal Cahn–Hilliard models, it is important in this context to consider the dependence of mobility coefficients on the local concentrations. We show that a homogeneous state that is linearly stable for one form of the mobility can be unstable for a different form of mobility, an effect that would be impossible in equilibrium and implies a crucial role for mobilities in non-reciprocal mixtures. For unstable homogeneous states we study the spinodal dynamics governing the onset of phase separation. We find, again in contrast to non-reciprocal Cahn–Hilliard models, that exceptional point transitions between static and oscillatory instabilities are generically avoided by transitions where the spinodal lengthscale changes discontinuously. At these transitions we find intricate spinodal dynamics with two competing lengthscales, one governing a static instability and the other an oscillatory instability, i.e. one that generates travelling waves. We demonstrate that, depending on the interaction strengths, more complex transitions can occur in the spinodal dynamics, including coexistence of three lengthscales and lines of discontinuous transitions, terminated by critical points, between distinct static instabilities. Finally, we explore the effects of additional non-reciprocity in the interfacial chemical potentials, which would generically be expected when obtaining Model B by coarse graining from a non-reciprocal particle model. We show that interfacial non-reciprocity can increase the region in the spinodal phase diagram where oscillatory instabilities occur, but only up to a certain boundary that we establish analytically and demonstrate numerically.