Descripción
Convection in colloidal suspensions of solid particles is characterized by the inter-
play between thermophoresis, sedimentation and Brownian diffusion. Their coupled
effects is represented by a dimensionless parameter B and experiments by Chang et al.
(2008) have shown that for a given set of experimental parameters, B a function of
the particle radius rp with the function B(rp) having the shape of an inverted parabola
with two roots in the range 5nm less than or equal to rp less than or equal to 125nm. We investigate both the linear and nonlinear convection in a suspension of solid particles using a particulate medium in a Rayleigh-Bénard geometry set-up. The analysis focuses on the particle dominated convection regime for which the onset is steady and to disturbances having infinitely
long wavelength. For 0< B<<1, which corresponds to particle size near the two
roots of B(r), we retrieve the instability threshold conditions for the binary mixture
model. For B = O(1), we show that, unlike the binary mixture model, the conditions
for instability onset can be mapped to corresponding experimental parameters. A non-
linear evolution equation is derived and its predictions compared to those of a similar
equation for the binary mixture case.