The 'wimple' : rippled deformation of a fluid drop caused by hydrodynamic and surface forces during thin film drainage

It is well-known that hydrodynamic pressures in a thin draining liquid film can cause inversion of the curvature of a drop or bubble surface as it approaches another surface, creating a so-called “dimple”. Here it is shown that a more complicated rippled shape, dubbed a “wimple”, can be formed if a fluid drop that is already close to a solid wall is abruptly pushed further toward it. The wimple includes a central region in which the film remains thin, surrounded by a ring of greater film thickness that is bounded at the outer edge by a barrier rim where the film is thin. This shape later evolves into a conventional dimple bounded by the barrier rim, which then drains in the normal way. During the evolution from wimple to dimple, some of the fluid in the thicker part of the film ring flows toward the central region before eventually draining in the opposite direction. Although the drop is pressed toward the wall, the central part of the drop moves away from the wall before approaching it again. This is observed even when the inward push is too small to create a wimple.

The influence of surface forces on thin film drainage between a fluid drop and a flat solid

An experiment is described in which a mica surface is driven towards a mercury drop immersed in aqueous electrolyte. Under appropriate conditions, hydrodynamic pressure in the aqueous film creates a classical dimple in the mercury drop. The use of optical interferometry and video recording to monitor the shape of the drop and the thickness of the aqueous film with sub-nanometre resolution yields a high density of precise data showing the formation and evolution of the dimple as the film drains. Variation of electrical potential applied to the mercury phase allows control of the surface forces acting between the drop and the mica surface, so that the effect of surface forces on the film drainage process is highlighted. It is found that the film thickness at the centre of the dimple and the lateral extent of the dimple are not significantly affected by surface forces. On the other hand, the minimum film thickness at the edge of the dimple is sensitive even to weak surface forces. Since this minimum film thickness is a major determinant of the film drainage rate, it is shown that surface forces have an important effect on the overall drainage process.

Assessment of spatiotemporal varying relationships between rainfall, land cover and surface water area using geographically weighted regression

Traditional regression techniques such as ordinary least squares (OLS) are often unable to accurately model spatially varying data and may ignore or hide local variations in model coefficients. A relatively new technique, geographically weighted regression (GWR) has been shown to greatly improve model performance compared to OLS in terms of higher R 2 and lower corrected Akaike information criterion (AICC). GWR models have the potential to improve reliabilities of the identified relationships by reducing spatial autocorrelations and by accounting for local variations and spatial non-stationarity between dependent and independent variables. In this study, GWR was used to examine the relationship between land cover, rainfall and surface water habitat in 149 sub-catchments in a predominately agricultural region covering 2.6 million ha in southeast Australia. The application of the GWR models revealed that the relationships between land cover, rainfall and surface water habitat display significant spatial non-stationarity. GWR showed improvements over analogous OLS models in terms of higher R 2 and lower AICC. The increased explanatory power of GWR was confirmed by the results of an approximate likelihood ratio test, which showed statistically significant improvements over analogous OLS models. The models suggest that the amount of surface water area in the landscape is related to anthropogenic drainage practices enhancing runoff to facilitate intensive agriculture and increased plantation forestry. However, with some key variables not present in our analysis, the strength of this relationship could not be qualified. GWR techniques have the potential to serve as a useful tool for environmental research and management across a broad range of scales for the investigation of spatially varying relationships.

The drainage of thin liquid films between solid surfaces

We present measurements of the thickness as a function of time of liquid films as they are squeezed between molecularly smooth mica surfaces. Three Newtonian, nonpolar liquids have been studied: octamethylcyclotetrasiloxane, n-tetradecane, and n-hexadecane. The film thicknesses are determined with an accuracy of 0.2 nm as they drain from ∼1 μm to a few molecular layers. Results are in excellent agreement with the Reynolds theory of lubrication for film thicknesses above 50 nm. For thinner films the drainage is slower than the theoretical prediction, which can be accounted for by assuming that the liquid within about two molecular layers of each solid surface does not undergo shear. In very thin films the continuum Reynolds theory breaks down, as drainage occurs in a series of abrupt steps whose size matches the thickness of molecular layers in the liquid. The presence of trace amounts of water has a dramatic effect on the drainage of a nonpolar liquid between hydrophilic surfaces, causing film rupture which is not observed in the dry liquids.

Thin film drainage : hydrodynamic and disjoining pressures determined from experimental measurements of the shape of a fluid drop approaching a solid wall

Accurate measurements of the shape of a mercury drop separated from a smooth flat solid surface by a thin aqueous film reported recently by Connor and Horn (Faraday Discuss. 2003, 123, 193-206) have been analyzed to calculate the excess pressure in the film. The analysis is based on calculating the local curvature of the mercury/aqueous interface, and relating it via the Young-Laplace equation to the pressure drop across the interface, which is the difference between the aqueous film pressure and the known internal pressure of the mercury drop. For drop shapes measured under quiescent conditions, the only contribution to film pressure is the disjoining pressure arising from double-layer forces acting between the mercury and mica surfaces. Under dynamic conditions, hydrodynamic pressure is also present, and this is calculated by subtracting the disjoining pressure from the total film pressure. The data, which were measured to investigate the thin film drainage during approach of a fluid drop to a solid wall, show a classical dimpling of the mercury drop when it approaches the mica surface. Four data sets are available, corresponding to different magnitudes and signs of disjoining pressure, obtained by controlling the surface potential of the mercury. The analysis shows that total film pressure does not vary greatly during the evolution of the dimple formed during the thin film drainage process, nor between the different data sets. The hydrodynamic pressure appears to adjust to the different disjoining pressures in such a way that the total film pressure is maintained approximately constant within the dimpled region.