where [[sigma].sub.s], [[tau].sub.f], [d.sub.s], and [d.sub.f] are the wall structure, fluid stress
tensors, and wall displacement, respectively.
Structural displacement and fluid stress at time t are assumed to be [[d.bar].sup.-1.sub.s] = [[d.bar].sup.0.sub.s] = [sup.t] [[d.bar].sub.s] and [[[tau].bar].sup.0.sub.s] = [sup.t][[d.bar].sub.f] [[d.bar].sup.1.sub.s] = [sup.t][[d.bar].sub.s] = [[[tau].bar].sup.0.sub.s], = [tau] [[[tau].bar].sub.f].
(1) Based on the provided structural displacement, fluid solution vector [X.sup.k.sub.f] can be obtained by fluid equation [F.sub.f][[X.sup.k.sub.f], [[lambda].sub.d] [[d.bar].sup.k-1.sub.s] 1 + (1 - [[lambda].sub.d]) [[d.bar].sup.k- 2.sub.s]=0 and the fluid stress [[[tau].bar].sup.k.sub.f] can be further calculated as well.
where [[rho].sub.f] is the fluid density, [[tau].sub.f] is the fluid stress
tensor, [f.sup.B.sub.f] are the body forces per unit volume, v is the fluid velocity vector, [[??].sub.f] is the moving coordinate velocity, and v - [[??].sub.f] is the relative velocity of the fluid with respect to the moving coordinate velocity.
(4) The fluid stress at the interface did not have to be computed explicitly.
The hydrodynamic part, consisting of the fluid stress acting on the interface and the viscoelastic terms, is treated together with the fluid.
1/R, similar to those of Figure 5, were constructed for various specific values of the measured fluid stress
. Again, evaluation of the slopes of the resulting curves allowed calculation of the presumed slip velocity of the fluid at the die exit.
In stage 2, the applied pressure is carried partly as particle network stress [P.sub.p], which consolidates the cake if it exceeds the compressive yield stress, and rest as fluid stress [P.sub.f].
Consequently, Equation (5) underestimates the fluid stress at the start of stage 2, which in reality should be equal to the applied pressure.
In particular, we focus on the evaluation of the local fluid stresses at the surface of an object and on the evaluation of the total fluid forces acting on the object body, as the integration of the local stresses.
The fluid force acting on a solid body is evaluated by integrating the fluid stresses over the body surface:
(13) is a system of three equations for the particle fluctuating velocity correlations (i = j) that can be solved once those expressions for the fluid stresses
and [k.sup.d]are provided.