Capillary Rise of Liquids over a Microstructured Solid Surface

Abstract

The location of the triple line as a function of time has been recorded for a series of organic liquids, with various surface tension to viscosity ratios, wicking upward a rough Cu(6)Sn(5)/Cu intermetallic (IMC) substrate. The complex topographical features of such an IMC rough surface are characterized by surface porosity and surface roughness. A theoretical model for wicking upward a rough surface has been established by treating the rough IMC surface as a two-dimensional porous medium featuring a network of open microtriangular grooves. The model is verified against experimental data. The study confirms that the kinetics of capillary rise of organic liquids in a nonreactive flow regime over a porous surface having arbitrary but uniformly distributed topographical features involves (i) surface topography metrics (i.e., permeability, tortuosity/porosity, and geometry of the microchannel cross section); (ii) wicking features (i.e., contact angle and filling factor); and (iii) physical properties of liquids (i.e., surface tension and viscosity). An excellent agreement between theoretical predictions and experimentally obtained data proves, for a selected filling factor η, validity of the analytically established model. Scaled data sets show that, for a given rough surface topography, (i) wicking kinetics of considered liquids depend on properties of liquids, that is, surface tension to viscosity ratios and contact angles; (ii) the filling factor for all tested liquids is an invariant, offering good prediction within the range of ~0.9-1.0. The distance of the wicking front versus square root of time relationship was well established throughout the whole considered wicking evolution time.