Phoresis in a Shearing Gas

Authors: Söderholm,  L. H. S., Borg, K.
Document Type: Conference
Pubstate: Published
Journal: Rarefied Gas Dynamics
Volume: 23   242-249
Year: 2003


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. This force and torque will set the body 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 is given by \[ V=\frac\left(\frac\right)^b_1v_. \] Here $\mu$ is the viscosity of the gas, $p$ is the pressure, $\beta_N$ is a number close to unity, $T$ is the temperature and $m$ is the mass of a gas molecule. The non-dimensional number $b_1$ depends on the shape of the body. This speed is of the order of the mean free path of the gas multiplied by the shearing. There will be no motion for a body, which is reflection symmetric in a plane orthogonal to the axis of symmetry. 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.