Some comments on the Resistance Experienced by a Porous Sphere Moving in a Viscous Incompressible Fluid at Low Reynolds Numbers
The formulae for viscous drag force experienced by a porous sphere falling in a viscous fluid at low Reynolds numbers which have been given by several authors are compared with one another and with the Stokes formula. The problem of these formulae, justified to apply in the cases of real porous media is discussed. It is shown that in many cases of standard porous material (for example sand, felt the differences between the viscous drag force due to the Stokes formula and others are non-essential, independently of the forms of boundary conditions and filtration equation by the use of which these formulae were obtained. A fibrous medium with very large porosity (for example cotton) is given as an example of the porous medium in the case of which some of these formulae may have a practical meaning. A new proposition of an experimental method of determining both the constant appearing in the Beavers-Joseph condition and the effective viscosity in the Brinkman equation is given.
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