Boundary integral prediction of the spreading of an inviscid drop impacting on a solid surface

Abstract

Axisymmetric spreading of an idealised inviscid liquid drop impinging on a horizontal solid surface is analysed (including surface tension) using a boundary integral method for Weber numbers ( We), based on initial drop radius and impact velocity, ranging from 3 to 100. Progressive accumulation of liquid in a rim around the periphery of the spreading inviscid drop is predicted. The effect diminishes with increasing Weber number, and is negligible when We=50. It is concluded that the experimentally observed rim at Weber numbers exceeding this value is due solely to viscous retardation. For We⩾10, the calculated reduction in drop height with time is found to be almost independent of Weber number, and agrees extremely well with experimental data despite the absence of viscous effects in the calculations. The inviscid spreading rate increases with increasing Weber number, and a simple model predicts a dimensionless limiting value of 2 at large times as We→∞. The viscous reduction in the radius of spreading, determined by subtracting the measured and calculated (inviscid) values, is found to be approximately linear in time during most of the primary deformation. Derived values of the slope m can be fitted by m=0.5We Re −0.5 for We less than about 40. Modification of the calculated inviscid spreading radius using a linear viscous correction provides an improved prediction of drop spreading.