On mass flux through a torus in Stokes flow
This is the last already posthumous paper of Professor Keith Stewartson, a man of great mathematical knowledge and physical insight, and a close friend of many of us all over the world. The paper has all features of Professor Stewartsons style of writing: clarity of problem presentation, elegance and simplicity (to the possible extent) of solution, results verifiable either by comparison with experimental findings or already existing theories. The problem considered is the following: the torus is posed axisymmetrically in the Stokes flow; what is the flux of fluid that actually passes through the gap at the center of the torus? Using the solution already available [\textit{S. R. Majumdar}, \textit{M. E. O'Neill}, Z. Angew. Math. Phys. 28, 541-550 (1977; Zbl 0374.76030)] two limiting cases are considered: when \(b/a<<1\) (a being the crossectional radius of the torus, b the radius of the hole) and \(a/b<<1.\) The first problem is treated in the frames of the lubrication theory, the second using the slender body theory. Results are compared with a general formal solution which enables to compute the flux for moderate sizes of the hole to a given accuracy.
torus is posed axisymmetrically in the Stokes flow
scientific article; zbMATH DE number 3868850
scientific article