CONFINED SUSPENSIONS
The
rheology of suspensions becomes more intricate when they are confined.
In particular the effect of walls can change the usual viscosity laws
such as the ones initially proposed by Batchelor and Green (1972) which
give the viscosity in terms of the concentration phi
only. Following the simulations of Davit Y. and Peyla P., EPL, 83
(2008) 64001, we proposed to investigate the corrections of the
viscosity of confined suspensions by including corrections terms of the
reduced gap h/d (h is the gap, d the diameter of particles).
Thus, one finds, for semi-dilute suspensions:
These results have been confirmed exerimentally usual monodisperse
particles (different sizes) in PDMS. The above coefficients were
determined experimentally and confirmed previous results.
Left.
Reduced viscosity vs. volume fraction.
Right. Values of coefficients a1 and a2 as functions of h/d