By C. M. Rodkiewicz (eds.)
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6), in the case of a suspension of non-interacting spheres, assuming that the . disturbance of streaming caused by the particles changes the original value y • y + dy , the shear rate increment of the shear rate to related to the increase of viscosity dn by dn/n sults from the conservation of the shear stress a = - dy/y = ny dy . be:mg , which re- in a Couette flow. 609 ... is an interaction constant. Finally, as col- lisions between spheres create doublets, triplets, ,,, a mean shape factor k for the suspension as a mixture of particles of various shapes .
Indeed such relations ~ = ~(~) must represent the strong increase in viscosity up to infinity, as ~ tends towards its maximum (packing) value ~M (Fig. 3). Fig. 3 Relative viscosity versus volume fraction~ of particles, in concentrated suspensions Infinite viscosity is found at packing concentration ~M . ~ - 1+~ 1 0~------------~------~ We shall give a detailled study of these equations and of some purely empirical relations. 1. Phenomenological equations A first group of studies refers to "effective medium" theories, considering the suspension with finite concentration ~ , a9 a fictive suspending fluid,having a (unknown) viscosity tal fraction of.
46 D. Quemada duration and speed (what can be fixed once for all) but also on particle deformabili ty (and aggregabili ty). 97 ~ ~ has been defined. , 1971). This can be understood as follows. Let number of particles suspended into the total volume ~ p V . Thus N ~ be = N~ p /V , being the particle volume. J! 27) Data are generally given using corrected hematocrit (See Fig. 1 for instance). 9. 01 (gr/100 ml)-1 . As hematocrit in pathologic situations varies about from,25 to need of an equation which covers the total range of variations in H led several authors to use equations for highly concentrated suspensions.
Arteries and Arterial Blood Flow by C. M. Rodkiewicz (eds.)