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EXACT SOLUTION FOR DEEP BED FILTRATION WITH FINITE BLOCKING TIME

SIAM Journal on Applied Mathematics. 2020. Vol. 80. No. 5. P. 2120–2143.
Nazaikinskii V., BEDRIKOVETSKY P., LIUDMILA I. KUZMINA, OSIPOV Y.

An initial-boundary value problem for a quasilinear system describing deep bed ltra-
tion of a monodisperse suspension in a medium with pores of various sizes is investigated analytically.
The ltration 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 nite,
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 modi ed 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 sucient coecient condition for the unique solvability of the problem is derived.

Research target: Mathematics
Priority areas: mathematics
Language: English
Full text
DOI
Text on another site
Keywords: method of characteristics exact solutiondeep bed fi ltration,quasilinear hyperbolic systemunique solvability
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