Theory Of Orthogonal Flow In
Elastic Chambers And Bio-bags
Author(s)
K. Kosorin
Abstract
This study presents a theory of the orthogonal flow of Newtonian fluid in an
elastic chamber. The elastic chamber is a space bounded by a movable material
boundary S that has a single orifice and is pliable with respect to normal forces.
The characteristic feature of this flow is that the fluid motion is perpendicular to
moving S and S to the one-parameter level surfaces Si inside the chamber. The
orthogonal flow domain is confined to such parts of the chamber interior V, for
which the level function exists defining the system of level surfaces Si, by
means of the equation (x,y,z)=
i with the set of constant parameters
i,
i=1,2…,. This flow property enables us to define the three-component
velocity field a(u,v,w) by the single vector q normal to Si for whole V. By
means of vector algebra and the Navier-Stokes description of the shear stress
tensor, a mathematical formulation of the mass and momentum conservation
laws for orthogonal flow has been derived as the main result of the theory. The
certainty and the uncertainty of the direction field of flow were used as the
determining factors in this process. A constitutive form of the level function
(x,y,z) as the tool for obtaining the system of level surfaces Si for chambers of
real geometry has been proposed and applied for the sphere and slanted ellipsoid
chambers.
The study of liquor dynamics effects on hydrocephalus development in the
system of brain ventricles inspired this work. It is assumed that the orthogonal
flow theory can effectively simplify the mathematical description of a certain
kind of fluid flow in elastic chambers as well as in some cavities and bags of live
organisms.
Keywords: single-orifice elastic chamber, orthogonal flow, directional cosines,
directional field of flow, level function, level surface system, stream lines,
intrinsic derivatives, constitutive form of level function, Navier-Stokes equations.
Keywords
single-orifice elastic chamber, orthogonal flow, directional cosines,
directional field of flow, level function, level surface system, stream lines,
intrinsic derivatives, constitutive form of level function, Navier-Stokes equations
Related Book
Other papers in this volume
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