Abstract
In recent years, the investigation of various physiological processes, and also the problem of developing an artificial heart have stimulated studies in which blood flow in the heart, and also in the large arteries is treated as the flow of a viscous incompressible Newtonian liquid. Different assumptions have been made concerning the geometry of the heart. For example, in [1, 2] a sphere was used as model of a ventricle, the influence of the entrance and exit valves was not taken into account, and, since the Reynolds number is normally fairly high, the blood flow was treated as the flow of an ideal incompressible liquid. In the experimental study of [3], the ventricle was modeled by an ellipsoid and allowance was made for the influence of the entry mitral valve; a simplified cylindrical geometry was used in [4]. In the present paper, the model of the ventricle is a sphere. Allowance is made for the influence of an artificial entry ball valve. Configurations of this kind are encountered in an artificial heart with hydraulic drive. To use the problem as an analytic test in further computer calculations at high Reynolds numbers, and also to obtain analytic estimates for the trajectories of Lagrangian particles, the treatment is restricted to flows for which the influence of the nonlinear terms in the Navier-Stokes equations can be ignored.
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