Spreading and break-up of a drop in a gas stream

Based on the expansion of unknown functions in a series of a small parameter, an analytical method is developed for calculating the time-dependent motion and a spreading (up to the break-up) of a plane and axisymmetric drop in a gas stream. It is shown that the zero-order terms of expansion define a clear retardation of a drop as a solid sphere. The next terms of the series characterize deformation and spreading of the drop.Based on the solution of the boundary-value problem of drop spreading the infinite system of linear differential equations with constant coefficients is obtained. It is established that without viscosity the system contains a finite number of equations and permits an exact solution. The spreading of an ideal liquid drop with the surface tension force taken into account was investigated in detail. In the case of a water drop placed in nitrogen a comparison was made between the calculated results on drop shapes and experimental data obtained at different moments of time. The theory agrees with the experiment both qualitatively and quantitatively.