Rheology of self-assembled fluids

Abstract

We investigate the rheological properties of a Landau–Ginzburg model that has competing interaction terms. These interactions have earlier been shown to produce mesoscopic ordering and such models have been helpful in explaining microemulsion behavior. Our present study is based on time-dependent Landau–Ginzburg equations for the order parameter and velocity field. The possible influence of hydrodynamic fluctuations, though discussed, is neglected in our treatment. General expressions for the excess viscosity and the first normal stress coefficient are derived in terms of the quasistatic structure factor. For steady shear flows and in the mean field approximation, explicit relations are given in two space dimensions for a nonconserved order parameter and in three space dimensions for a conserved order parameter. The former case is the easiest one to study numerically in computer simulations. Our numerical results show that mean field theory for the excess viscosity is satisfactory at some distance from the ‘‘transition’’ curve to the lamellar phase. The normal stress coefficient turns out to be very small. It only becomes appreciable close to the phase boundary. Here the nonlinear dependencies of excess viscosity and stress coefficient on the shear rate become important. To explain the general behavior we have considered terms up to fourth order in the shear rate. Computer simulations as well as mean field theory indicate that the quadratic corrections to both coefficients are negative in the microemulsion region. With increasing shear rate one therefore first enters a regime of shear-thinning. The quartic corrections are found to be positive, so further increase of the shear rate will lead to shear-thickening.

Rheology of active polar emulsions: from linear to unidirectional and inviscid flow, and intermittent viscosity

“…Lowering k φ from positive to negative values leads the system to move from pure ferromagnetic phase to configurations where interfaces between components are favoured [53][54][55][56][57] . In the Appendix Adimensional Numbers we will show that, for a symmetric composition of the mixture, the system sets into a lamellar phase modulated at wavenumber κ = |k φ |/2c, when a < k 2 φ /4c + β 2 /k P (see panels (a) and (b) of Fig.…”

Three-dimensional simulation of hexagonal phase of a specific polymer system under shear: The dynamic density functional approach

“…8,11 During the last couple of years the time evolution of morphologies in complex liquids in external flows has been studied by computer simulation techniques using timedependent Landau-Ginzburg models. 1, [12][13][14][15] These models are based on traditional free energy expansion methods [16][17][18] which contain only the basic physics of phase separation 19 and are not well suited for specific applications. In contrast to these phenomenological theories we do not truncate a free energy expansion, but retain the full polymer path integral by a numerical procedure.…”

Dynamic Density Functional Theory for Sheared Polymeric Systems

“…However, in the weak segregation regime the basic features of the process of alignment in flow (regardless of fine details of orientational transitions) can be described accurately by a diffusion‐convection equation, with an imposed velocity profile, see Equation (1) 1,3,4. It was convincingly shown by many authors that this equation can describe rather well many physically relevant phenomena in sheared inhomogeneous fluids 18,20,28–36. Moreover, if the polymers are of equal bulk viscosity, the approximation becomes even better.…”