Stresslet resistance functions for low Reynolds number flow using deforming spheres
The stresslets of two rigid spheres in an ambient pure straining flow are obtained at low Reynolds number by defining and solving an equivalent problem of flow around deforming spheres. If the spheres are separated by a small gap, the stresslet of each sphere (the symmetric first moment of the surface stress) is a singular function of the gap width. For spheres in an ambient pure straining flow, the singularities manifest themselves as the slow convergence of numerical calculations. The methods of lubrication theory are used to calculate the singularities in the stresslets and it is shown that these new singularities can be related to singularities already found in other resistance functions. It is also shown that the singular terms can be used to improve the rate of convergence of series expressions for the stresslets. The series expressions then become valid for all separations of the spheres.
scientific article; zbMATH DE number 4095033