The emergence of supramolecular forces from lattice kinetic models of non ideal fluids: applications to the rheology of soft glassy meterials

A systematic study for a single-specie lattice Boltzmann model with frustrated-short range attractive and mid/long-range repulsive-interactions is presented. The equilibrium analysis is performed along the guidelines proposed by [X. Shan, Phys. Rev. E 77, 066702 (2008)] and allows us to determine the surface tension density and the resulting disjoining pressure developing in a thin film when two interfaces overlap. Numerical simulations of confined flows are then performed with a multicomponent model and are successfully tested against the recent suggestion by Bocquet and coworkers on the existence of a cooperative length underlying the non-local rheology of highly confined soft-glassy materials [Goyon et al., Nature 454, 84-87 (2008); Soft Matter 6, 2668-2678 (2010)].