Gravitational instability in suspension flow

The gravity-driven flow of non-neutrally buoyant suspensions is shown to be unstable to spanwise perturbations when the shearing motion generates a density profile that increases with height. The instability is simply due to having heavier material over light – a Rayleigh–Taylor-like instability. The wavelength of the fastest growing disturbance is on the order of the thickness of the suspension layer. The parameters important to the problem are the angle of inclination of the layer relative to gravity, the relative density difference between the particles and the fluid, the ratio of the particle size to the thickness of the layer and the bulk volume fraction of particles. The instability is illustrated for a range of these parameters and shown to be most pronounced at intermediate values thereof. This instability mechanism may play an important role in pattern formation in multiphase flows

Microrheology of colloidal dispersions by Brownian dynamics simulations

We investigate active particle-tracking microrheology in a colloidal dispersion by Brownian dynamics simulations. A probe particle is dragged through the dispersion with an externally imposed force in order to access the nonlinear viscoelastic response of the medium. The probe’s motion is governed by a balance between the external force and the entropic “reactive” force of the dispersion resulting from the microstructural deformation. A “microviscosity” is defined by appealing to the Stokes drag on the probe and serves as a measure of the viscoelastic response. This microviscosity is a function of the Péclet number (Pe=Fa∕kT)—the ratio of “driven” (F) to diffusive (kT∕a) transport—as well as of the volume fraction of the force-free bath particles making up the colloidal dispersion. At low Pe—in the passive microrheology regime—the microviscosity can be directly related to the long-time self-diffusivity of the probe. As Pe increases, the microviscosity “force-thins” until another Newtonian plateau is reached at large Pe. Microviscosities for all Péclet numbers and volume fractions can be collapsed onto a single curve through a simple volume fraction scaling and equate well to predictions from dilute microrheology theory. The microviscosity is shown to compare well with traditional macrorheology results (theory and simulations)

Second normal stress jump instability in non-Newtonian fluids

An instability mechanism is shown to operate in complex, non-Newtonian fluids in which a jump in normal stresses occurs between two fluids. Fluids with a negative second normal stress difference can be unstable with respect to transverse or spanwise perturbations. The mechanism appears to be generic, although the details will depend on the specific flow and the nature of the complex fluid. The instability mechanism is illustrated for two-layer Couette and falling film flows of viscous suspensions

Second normal stress jump instability in non-Newtonian fluids

An instability mechanism is shown to operate in complex, non-Newtonian fluids in which a jump in normal stresses occurs between two fluids. Fluids with a negative second normal stress difference can be unstable with respect to transverse or spanwise perturbations. The mechanism appears to be generic, although the details will depend on the specific flow and the nature of the complex fluid. The instability mechanism is illustrated for two-layer Couette and falling film flows of viscous suspensions