Capillary driven molten metal flow over topographically complex substrates

A theoretical model of a capillary driven flow of liquid metal through topography features of rough surfaces has been verified by a study of molten solder (Sn-Pb) spreading over Cu₆Sn₅/Cu₃Sn/Cu intermetallic (IMC) substrates. Flow through microgrooves over a rough IMC substrate is considered as spreading through an isotropic porous medium featuring a network of open microgrooves having predefined free-flow area cross sections. The relative margin of deviation between theoretically predicted and empirically determined locus of points of triple line locations is within the range of 5-15%. This margin supports the validity of the developed, analytically formulated square root power law model for a whole spreading domain in terms of (i) geometry of topographical features of the rough surface (i.e., effective intrinsic permeability, porosity/tortuosity, and microchannel cross section geometry), (ii) wetting/spreading features (equilibrium contact angle and filling factor), and (iii) molten metal/substrate properties (viscosity and surface tension). Experimental data involving triple line kinetics represent the data set of locations of the triple line versus time obtained by in situ monitoring of the spreading of molten metal systems over IMC substrates by using the controlled atmosphere hot stage microscopy.