Professor, UCSB (currently at UNCPBA, argentina)
Control of the displacement of small volumes for mixing, reaction and separation of liquid species.
Here we present the thermocapillary migration of droplets of partially wetting liquids on a non-uniform heated substrate. The model includes the effect of a non-zero contact angle introduced through a disjoining–conjoining pressure term. Instead of assuming a fixed shape for the droplet, as in previous works, here we allow the droplet to change its profile with time. We identify and describe three different regimes of behaviour. For small contact angles, the droplet spreads into a long film profile with a capillary ridge near the leading edge, a behaviour that resembles the experiments on Marangoni films reported by Ludviksson & Lightfoot (Am. Inst. Chem. Eng. J., vol. 17, 1971, pp. 1166). For large contact angles, the droplet moves as a single entity, weakly distorted from its static shape. This regime is the usual one reported in experiments on thermocapillary migration of droplets. We also show some intriguing morphologies that appear in the transition between these two regimes. The occurrence of these three regimes and their dependence on various parameters is analysed.
Abstract: We present a new analytical solution for the static shape of a two-dimensional droplet in equilibrium with a surrounding thin film on a solid substrate. The modeling includes the effects of capillarity and disjoining-conjoining pressure accounting for intermolecular forces between the solid and the liquid. We derive new analytical solutions for the shape of the droplet, the cross-sectional area, the half-width, and the maximum curvature and inflection points. We study the effects of the size of the droplet on the apparent contact angle. The shape of the droplet in the contact line region is compared with profiles obtained by employing approximations suggested in the literature, and the observed differences are discussed. Finally, we present the time evolution to the steady state to show how the whole profile, including the thin film, evolves to the corresponding stationary configuration.
Pub.: 14 May '09, Pinned: 07 Jun '17
Abstract: Analytical solutions for the shape of both hanging and sitting droplets under the effects of gravity and surface tension are presented. The modeling also includes the action of molecular forces arising between the liquid and the substrate, which are responsible for the formation of a stable nanometric film in the region close to the droplet contact line. The shape of the droplet is completely described by an analytical solution that also accounts for the pancake-shaped droplets as a limiting case. We find expressions that relate microscopic and nanoscopic aspects, such as the strengths of the molecular forces and the thickness of the nanometric film, to macroscopic quantities, such as the cross-sectional area and the width of the droplet. We study the effect of gravity on the contact angle and find that for small droplets the contact angle follows a power law with the droplet's size. For sitting droplets we find that the there is an upper limit for the value of the gravity.
Pub.: 12 Dec '12, Pinned: 07 Jun '17
Abstract: We investigate theoretically the possible final stationary configurations that can be reached by a laterally confined uniform liquid film inside a container. The liquid is under the action of gravity, surface tension, and the molecular interaction with the solid substrate. We study the case when the container is in an upright position as well as when it is turned upside down. The governing parameters of the problem are the initial thickness of the film, the size of the recipient that contains the liquid, and a dimensionless number that quantifies the relative strength of gravity with respect to the molecular interaction. The uniform film is always a possible final state and depending on the value of the parameters, up to three different additional final states may exist, each one consisting in a droplet surrounded by a thin film. We derive analytical expressions for the energy of these possible final configurations and from these we analyze which state is indeed reached. A uniform thin film may show three different behaviors after a perturbation: The system recovers its initial shape after any perturbation, the fluid evolves towards a drop (if more than one is possible, it tends toward that with the thinnest precursor film) for any perturbation, or the system ends as a uniform film or a drop depending on the details of the perturbation.
Pub.: 16 May '14, Pinned: 07 Jun '17
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