Browsing by Author "Teixeira, Miguel"
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- The shape of two-dimensional liquid bridgesPublication . Teixeira, Paulo; Teixeira, MiguelWe have studied a single vertical, two-dimensional liquid bridge spanning the gap between two flat, horizontal solid substrates of given wettabilities. For this simple geometry, the Young–Laplace equation can be solved (quasi-)analytically to yield the equilibrium bridge shape under gravity. We establish the range of gap widths (as described by a Bond number Bo) for which the liquid bridge can exist, for given contact angles at the top and bottom substrates (θt c and θb c, respectively). In particular, we find that the absolute maximum span of a liquid bridge is four capillary lengths, for θb c = 180◦ and θt c = 0◦; whereas for θb c = 0◦ and θt c = 180◦ no bridge can form, for any substrate separation. We also obtain the minimum value of the cross-sectional area of such a liquid bridge, as well as the conditions for the existence and positions of any necks or bulges and inflection points on its surface. This generalises our earlier work in which the gap was assumed to be spanned by a liquid film of zero thickness connecting two menisci at the bottom and top substrates.
- When is a surface foam-phobic or foam-philic?Publication . Teixeira, Miguel; Arscott, Steve; Cox, Simon; Teixeira, PauloIt is commonly assumed that the liquid making up a sessile bubble completely wets the surface upon which the bubble lies. However, this need not be so, and the degree of wetting will determine how well a collection of bubbles - a foam - sticks to a surface. As a preliminary to this difficult problem, we study the shape of a single vertical soap film spanning the gap between two flat, horizontal solid substrates of given wettabilities. For this simple geometry, the Young-Laplace equation can be solved (quasi-) analytically to yield the equilibrium shapes, under gravity, of the two-dimensional Plateau borders along which the film contacts the substrates. We thus show that these Plateau borders, where most of a foam's liquid resides, can only exist if the values of the Bond number Bo and of the liquid contact angle yc lie within certain domains in (yc, Bo) space: under these conditions the substrate is foam-philic. For values outside these domains, the substrate cannot support a soap film and it is foam-phobic. In other words, on a substrate of a given wettability, only Plateau borders of a certain range of sizes can form. For given (yc, Bo), the top Plateau border can never have greater width or cross-sectional area than the bottom one. Moreover, the top Plateau border cannot exist in a steady state for contact angles above 901. Our conclusions are validated by comparison with both experimental and numerical (Surface Evolver) data. We conjecture that these results will hold, with slight modifications, for non-planar soap films and bubbles. Our results are also relevant to the motion of bubbles and foams in channels, where the friction force of the substrate on the Plateau borders plays an important role.
- When is a surface foam-phobic?Publication . Teixeira, Miguel; Arscott, Steve; Cox, Simon; Teixeira, Paulo• In confined foams there exist wall Plateau borders (PBs), or menisci, where the films meet the confining substrates. • What is the shape of a PB of a given size on a surface of a given wettability (i.e., contact angle θc)? Can that surface support a foam? • This is important for firefighting foams, containers for foamy foodstuffs, etc • We solve the Young-Laplace equation with gravity for a planar film spanning a gap between two horizontal, flat substrates, to predict the shape of the PBs. • Validate results by comparing with Surface Evolver and experimental data