Brownian motion suspension rheology, effect

Phenomenologically, the viscous stress is the stress which vanishes instantaneously when the flow is stopped. On the other hand the elastic stress does not vanish until the system is in equilibrium. The elastic stress is dominant in concentrated polymer solutions, while viscous stress often dominates in the suspensions of larger particles for which the Brownian motion is not effective. Whichever stress dominates, the rheological properties can be quite complex since both and are functions of the configuration of the beads and therefore depend on the previous values of the velocity gradient. Note that the viscous stress only appears in the system with rigid constraints.t... 

Brownian motion must be taken into account for suspensions of small (submicron-sized) particles. By their very nature, such stochastic Brownian forces favor the ergodicity of any configurational state. Although no completely general framework for the inclusion of Brownian motion will be presented here, its effects will be incorporated within specific contexts. Especially relevant, in the present rheological context, is the recent review by Felderhof (1988) of the contribution of Brownian motion to the viscosity of suspensions of spherical particles. 

Before discussing theoretical models for the rheology of fiber suspensions and its connection to fiber orientation, there are three topics that must be discussed Brownian motion, concentration regimes, and fiber flexibility. Brownian motion refers to the random movement of any sufficiently small particle as a result of the momentum transfer from suspending medium molecules. The relative effect that Brownian motion may have on orientation of anisotropic particles in a dynamic system can be estimated using the rotary Peclet number, Pe s y Dm, where y is the shear rate and Ao is the rotary diffusivity, which defines the ratio of the thermal energy in the system to the resistance to rotation. Doi and Edwards (1988) estimated the rotary diffusivity, Ao, to be... 

---