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Exact solution for deep bed filtration with finite blocking time. (English) Zbl 1486.76079

Summary: An initial-boundary value problem for a quasilinear system describing deep bed filtration of a monodisperse suspension in a medium with pores of various sizes is investigated analytically. The filtration function is assumed to have power-law type while tending to zero with the power index lower than one. We found that this assumption has two consequences: (i) the blocking time is finite, and (ii) the characteristics issuing from the points where the retained particle concentration reaches its maximum are not uniquely determined. The exact solution is constructed by a modified method of characteristics, which removes the ambiguity by using an additional blocking line equation derived from the original problem. The weak singularity of the solution on the blocking line is described. A simple sufficient coefficient condition for the unique solvability of the problem is derived.

MSC:

76S05 Flows in porous media; filtration; seepage
76T20 Suspensions
35Q35 PDEs in connection with fluid mechanics
65M25 Numerical aspects of the method of characteristics for initial value and initial-boundary value problems involving PDEs
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