Instabilities of complex fluids with partially structured and partially random interactions

We develop a theory for thermodynamic instabilities of complex fluids composed of many interacting chemical species organised in families. This model includes partially structured and partially random interactions and can be solved exactly using tools from random matrix theory. The model exhibits three kinds of fluid instabilities: one in which the species form a condensate with a local density that depends on their family (family condensation); one in which species demix in two phases depending on their family (family demixing); and one in which species demix in a random manner irrespective of their family (random demixing). We determine the critical spinodal density of the three types of instabilities and find that the critical spinodal density is finite for both family condensation and family demixing, while for random demixing the critical spinodal density grows as the square root of the number of species. We use the developed framework to describe phase-separation instability of the cytoplasm induced by a change in pH.

Automated summary

This theory model explores thermodynamic instabilities of complex fluids consisting of interacting chemical species organized in families, with family condensation, family demixing, and random demixing as three types of fluid instabilities. The critical spinodal density of these instabilities is determined, showing finite values for family condensation and family demixing, while increasing as the square root of the number of species for random demixing. The developed framework is used to describe phase-separation instability of the cytoplasm induced by a change in pH.