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Theory of orthogonal flow in elastic chambers and bio-bags

机译：弹性腔和生物袋中正交流的理论

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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 characteristicfeature of this flow is that the fluid motion is perpendicular to moving S and S to the one-parameter level surfaces S, inside the chamber. The orthogonal flow domain is confined to such parts of the chamber interior V, for which the level function φ exists defining the system of level surfaces S_i by means of the equation φ(x,y,z)=φ_i with the set of constant parameters φ_i i=l,2...,∞. This flow property enables us to define the three-component velocity field a(u,v,w) by the single vector q normal to S, 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 φ(x,y,z) as the tool for obtaining the system of level surfaces S_i 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.
机译：这项研究提出了弹性室内牛顿流体正交流动的理论。弹性腔是由可移动材料边界S〜界定的空间，该边界具有单个孔口，并且相对于法向力柔顺。这种流动的特征是，流体运动垂直于将S和S移至腔室内的单参数水平面S上。正交流域限于腔室内部V的这些部分，对于这些部分，存在水平函数φ，该水平函数通过方程φ（x，y，z）=φ_i与一组常数参数一起定义水平表面S_i的系统φ_ii = l，2 ...，∞。这种流动特性使我们能够通过垂直于S的单个矢量q来定义整个V的三分量速度场a（u，v，w）。通过矢量代数和切应力张量的Navier-Stokes描述该理论的主要结果是，得出了正交流的质量和动量守恒律的数学公式。流场方向性的确定性和不确定性被用作该过程的决定因素。已经提出了水平函数φ（x，y，z）的本构形式，作为用于获得用于实际几何形状的腔的水平表面S_i的系统的工具，并将其应用于球体和倾斜的椭圆腔。酒动力学对脑室系统脑积水发展的影响的研究激发了这项工作。假设正交流理论可以有效地简化在弹性腔室以及某些生物腔体和袋子中某种流体流动的数学描述。

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