DRAG FORCES ON NON-SPHERICAL PARTICLES IN THE FREE MOLECULAR REGIME

The evaluation of the drag force on non-spherical particles is of great importance in a wide range of areas. In the present paper, a general analytical expression for the drag force on non-spherical particles in the free molecular regime is obtained based on the gas kinetic theory. The obtained expression is applicable to rigid convex non-spherical particles suspending in a diluted gas, wherein multiple collisions between the gas molecules and the particle are ignored. Based on the Maxwellian scattering model, i.e., specular and diffusion collisions between gas molecule and the particle, the general analytical expression for the drag force on particles can be derived by evaluate the momentum transfer between the gas molecules and the particle upon gas-particle collisions. As examples, the expressions for drag force on several common non-spherical particles, such as spheres, cylinders, ellipsoids and cones, are also presented, which are consistent with the results in open literatures. It is found that the drag force on non-spherical particles depends on the geometric shape and orientation. However, the specific expressions for drag force on non-spherical particles are mathematically too complex to be employed in practical application. Considering that the particle is expected to undergo a rapidly rotation in the case of weak potential field in the free molecular regime, so the distribution of the particle orientation should be a uniformly random distribution. Then, the expression of the orientation-averaged drag force on non-spherical particles can be derived by introducing the random orientation distribution of the particle. It is found that the orientation-averaged drag force is proportional to the surface area of the non-spherical particle, and the corresponding coefficient is independent of the particle size or shape. The findings in the present paper can be employed to simplify the calculation of the drag forces on non-spherical particles in the free molecular regime.