Host: The Japan Society of Mechanical Engineers
Name : [in Japanese]
Date : November 11, 2020 - November 13, 2020
Jet with Re < 1 is observed downstream of valves in lymphatic vessels of mice and it is an impending research target in developing treatment of noninvasive cancer, especially breast cancer. Traits of the jet are that the pressure and velocity greatly vary at the jet exit because of flows with angle change of ninety degree at the exit periphery. A new theory of Stokesian free jet is presented as a model of the jet from a lymphatic valve to predict the pressure in the jet region. Navier-Stokes equations and continuity equation, expressed by the spherical coordinates, are solved under the Stokes approximation by taking radial pressure and velocity variations at the exit into account. Flow field is divided into two regions by the hemisphere with its origin at the exit center and the exit radius, inner region and outer one. The former is inside the hemisphere and the latter is outside it. The pressures in both regions are given by Legendre polynomials up to the eleventh degree, multiplied by powers of the radial distance, and the velocity components are expanded by two series of unknown functions of the angle, multiplied by the powers of the distance. The outer-region solutions are patched with those in the inner-region ones over the hemisphere, resulting in reasonable solutions for the free jet.
