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

Axisymmetric spreading of an idealised inviscid liquid drop impinging on a horizontal solid surface is analysed (including surface tension) using a bo undary integral method for Weber numbers (We), based on initial drop radius and impact velocity, ranging from 3 to 100. Progressive accumulation of li quid in a rim around the periphery of the spreading inviscid drop is predic ted. 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 greater than or equal to 10, the calculated reduction in drop height with t ime 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 n umber, and a simple model predicts a dimensionless limiting value of root 2 at large times as We --> infinity. 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 pri mary deformation. Derived values of the slope m can be fitted by m = 0.5WeR e(-0.5) for We less than about 40. Modification of the calculated inviscid spreading radius using a linear viscous correction provides an improved pre diction of drop spreading. (C) 1999 Elsevier Science Ltd. All rights reserv ed.