Instabilities of complex fluids with partially structured and partially random interactions

TL;DR

This paper presents a theoretical framework for analyzing thermodynamic instabilities in complex fluids with mixed structured and random interactions, revealing three distinct instability types and their critical conditions.

Contribution

It introduces an exactly solvable model using random matrix theory to classify and analyze three types of fluid instabilities based on species interactions.

Findings

Identifies three instability types: family condensation, family demixing, and random demixing.

Determines finite critical spinodal densities for family condensation and demixing.

Shows critical density for random demixing increases with the square root of species number.

Abstract

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.