Mass transfer around a cylinder in a nonlinear extensional flow

Abstract

In this theoretical report, we explored the transfer of mass around an infinite cylinder in a nonlinear extensional creeping flow, and at large Peclet numbers. First, we inspected the fluid mechanics problem, which is governed by a single dimensionless parameter: the nonlinear intensity of the flow (E). The fluid motion in the presence of the cylinder suggests interesting features such as closed circulations (E > 2/3) and separating surfaces (E < 0), both phenomena which are absent in the linear case (E = 0). Next, we examined the transfer of mass, where three different regions have been distinguished. In the first one (−2/9 < E < 2/3), which also includes the linear case, the thin concentration boundary layer, at each quarter, covers the entire cylinder surface. In the next one (E > 2/3), the closed circulation, which is in contact with the cylinder surface, reduces the length of the concentration boundary layer. In the last one (E < −2/9), separating surfaces touching the surface of the cylinder and creating, at each quarter, two concentration boundary layers flowing in opposite directions. There is a range (−0.340 < E < 0), where the mass transfer is lower than the linear case, with a minimum at E = −2/9 = −0.222. From this point, and in both directions, as |E| increases, the rate of mass transfer also increases.