Spherical expansion of the vapor plume into ambient gas: an analytical model

A simplified model of plume expansion into ambient atmosphere is presented which is based on the laws of mass, momentum, and energy conservation. In the course of expansion, the energy is redistributed between the thermal and kinetic energies of the plume and (internal and external) shock waves (SW). The expansion is described by ordinary differential equations for the characteristic radii (contact surface, position of the SWs). The initial stage is similar to inertial expansion into vacuum, with radius R proportional to t. Internal SW propagates inwards from the contact surface. Later expansion follows a point-blast model with R proportional to t(2/5). Here the homogenized plume is decelerated and heated because of the counter-pressure of the ambient gas, which forms external SW. At a certain distance from the target, the plume stops (and even contracts), while external SW weakens and detaches from the contact surface. Analytical formulas for the transitional stages of expansion are discussed, and theoretical predictions are compared with experimental results of laser ablation of steel and YBCO in Ar.