Maximum spreading of an impacting drop

Abstract

The maximum diameter of a drop impacting on a flat solid surface is studied theoretically assuming axi-symmetric spreading without splashing. The energy balance between the initial state of the drop (sphere diameter d0) and that a maximum spread (contact diameter dm) is closed by two novel concepts. For the gas-liquid surface area, an approximate spherical cap model is proposed. Energy loss by viscous dissipation is related to the total energy dissipation when the drop has come to rest. The fractional dissipation upon maximum spread is modelled as a function of an impact parameter (P) that combines the power laws of the capillary and viscous regimes depending on a regime discrimination parameter (A). Exponents of the Weber (We) and Reynolds (Re) numbers in P=WeRe−2/5 are determined by asymptotic analysis. The parameter A is determined from experimental data as a function of the advancing contact angle (θa). In this way, an explicit model for the maximum spread factor (βm=dm/d0) is proposed which includes the scaling laws βm∼We1/2, βm∼We1/4 and βm∼Re1/5 and is in good agreement with experimental data for wide ranges of We, Re and θa.