Mathematics Colloquia and Seminars

Return to Colloquia & Seminar listing

Steady-streaming refers to the secondary time independent flow superimposed on the primary oscillatory flow. Specifically, we consider steady streaming induced by oscillatory flow past a cylinder between two plates. While known since the 1930s, this phenomena has received renewed interests recently for possible applications in particle manipulations and non-Newtonian flows. Here, we use a combination of Fourier series and an asymptotic expansion to study the confinement effects for viscous steady-streaming. The successive equations for the Fourier coefficients resulting from the asymptotic expansion are then solved numerically using finite element methods. We use our model to test the possible breaking of the four-fold symmetry around the cylinder due to the domain shape. Finally, we utilize the tangential steady- streaming velocity along the radial chord at an angle of $\pi$/4 to better analyze our solutions over an extensive range of oscillating frequencies and multiple levels in the z-direction. Further insights can be gained by a two dimensional analysis in an infinite domain. Finally, we'll discuss extensions to non-Newtonian flows and preliminary results.