On pressure-driven Hele–Shaw flow of power-law fluids

Validerad;2022;Nivå 2;2022-09-26 (hanlid)
We analyze the asymptotic behavior of a non-Newtonian Stokes system, posed in a Hele–Shaw cell, i.e. a thin three-dimensional domain which is confined between two curved surfaces and contains a cylindrical obstacle. The fluid is assumed to be of power-law type defined by the exponent 1< p<∞. By letting the thickness of the domain tend to zero we obtain a generalized form of the Poiseuille law, i.e. the limit velocity is a nonlinear function of the limit pressure gradient. The flow is assumed to be driven by an external pressure which is applied as a normal stress along the lateral part of the boundary. On the remaining part of the boundary we impose a no-slip condition. The two-dimensional limit problem for the pressure is a generalized form of the p′-Laplace equation, 1/p+1/p'=1, with a coefficient called ‘flow factor’, which depends on the geometry as well as the power-law exponent. The boundary conditions are preserved in the limit as a Dirichlet condition for the pressure on the lateral boundary and as a Neumann condition for the pressure on the solid obstacle.

Manjate, SalvadorLuleå tekniska universitet,Matematiska vetenskaper,Department of Mathematics and Informatics, Eduardo Mondlane University, Maputo, Mozambique(Swepub:ltu)salman (author)
Wall, PeterLuleå tekniska universitet,Matematiska vetenskaper(Swepub:ltu)wall (author)
Luleå tekniska universitetMatematiska vetenskaper (creator_code:org_t)

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NATURAL SCIENCES: NATURAL SCIENCES; and Mathematics; and Mathematical Ana ...

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