Shearing Phoresis

Authors: Söderholm,  L. H. S., Borg, K.
Document Type: Article
Pubstate: Submitted
Journal: Phys. Rev. E.
Year: 2002


An axially symmetric body small compared with the mean free path is free to move in a shearing gas. The body is treated as a test particle. The force and torque acting on the body are calculated. The body will be set in motion, which asymptotically will take place in one of the eigendirections of the rate of deformation tensor. The axis of the body then points in the same direction. For a velocity field $v_x(y)$ the final motion is parallel to one of the lines $x=y$ and $x=-y$, and the speed of the motion relative to the gas is given by \[ V=\frac\sqrt\frac\,\frac. \] Here $\mu$ is the viscosity of the gas, $p$ is the pressure, $\beta_N$ is a number close to unity, $T$ is the temperature, $m$ is the mass of a gas molecule, and $\alpha_$ is the accommodation coefficient of tangential momentum. The non-dimensional numbers $b_1$ and $b_3$ depend on the shape of the body. This speed is of the order of the mean free path of the gas multiplied by the shearing. -This means that there is a phenomenon of phoresis in a shearing gas, which is analogous to thermophoresis in a gas with a temperature gradient.