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Some low Reynolds number flows involving solid boundaries and porous media.

Stengel, Frank A.N. (1990) Some low Reynolds number flows involving solid boundaries and porous media. Doctoral thesis, University of Surrey (United Kingdom)..

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After a short introduction defining the notion of fluid and deriving the equation for the slow creeping motion of an incompressible Newtonian viscous fluid, the Stokes equation, the thesis moves on to describe flows around hollow surfaces. The surfaces studied are cylinders and surfaces of revolution and quantities such as drag and flux through the surface are calculated, whenever possible. The next chapter studies the slow creeping flow of a fluid in a porous medium and studies the different ways to model that flow. After finding the equations of the motion it goes on to investigate the boundary conditions arising by having a fluid passing from a ''free" medium to a porous medium. Chapter four describes the slow axisymmetric rotation of a solid above a porous bed of infinite thickness. Using Green's functions it derives an integral equation giving the surface stress on the solid, enabling therefore to find the drag on the solid, and to prove, in this case Brenner's asymptotic formula for the drag. It then goes on to make a complete study of the case of a disk by computing the velocity field and looking at the behaviour of the fluid far from the disk. Various graphs giving velocity profiles and functions associated with the drag are given. Chapter five describes the flow created by an axisymmetric stokeslet above a porous bed. It compares two models for the flow in the porous part, the Daicy and Brinkman models. At the same occasion it derives a new representation for the velocity field, in the case of the Binkman model. The last chapter sketches a description of the asymmetric flow generated by a stokeslet or a rotelet and of the problems encountered while trying to compute this flow. It criticizes in particular the new representation found in the previous chapter.

Item Type: Thesis (Doctoral)
Divisions : Theses
Authors :
Stengel, Frank A.N.
Date : 1990
Contributors :
Depositing User : EPrints Services
Date Deposited : 09 Nov 2017 12:16
Last Modified : 20 Jun 2018 11:10

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