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I) Particle free marginal layer. e. e. 13) =0 where kl = lim (- dF w/d¢ ) w ¢-+0 w (3. 15) 1. e. 5). 14) leads to (subscript s omitted) (3' 16) 38 D. Quemada where K is an integration constant. 17) Eq. e. 3), although these two equations are formally equivalent in the Einstein's limit. 17). 4). 3 . For higher concentration one can determine both k1 and K from 'experimental data. Alternatively one can find K ·k1 value - from a packing concentration limit, F(~ ) M '"' = K(k 1 ) ~ + - for a given ¢M' for which (3,18a) 0 Moreover many systems exhibit a smooth approach to zero of the slope dF/d~ as ~ + lim ~ M (dF/d~) , + such as 0 (3.

Diffi- culties in applying the Mooney equation, have been yet stressed (GILLESPIE, 1963) . 20) as a structural parameter, noticely in relation with the packing fraction $M . e. actual levels of parti- cle aggregation and deformation - can be described by tual packing concentration k($) or by an ac- (3. 24) which would be reached if particles at $ were packed without changing their actual (aggregated and eventually deformed) state, leading to infinite viscosity. It must be kept in mind that this actual packing $p will be usually different from the true one, $M , owing to structural modifications which would occur during the (true) rising of the tion.

For fixed properties of the whole system (concentration, temperature, suspending fluid characteristics ... ) and well-defined flow conditions, such an energy principle states that among all stationary solutions (onephase or two-phase viscometric flows), the actual solution (v,¢) is the one which minimizes the rate of energy dissipation (or more generally, the rate of entropy production). Therefore, any unsteady process lS ex- cluded from the present approach, especially mechanisms involved in the formation of the actual two-phase flow structure.

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