Analytical solutions for the profile of two-dimensional droplets with finite-length precursor films.

By means of the lubrication approximation we obtain the full family of static bidimensional profiles of a liquid resting on a substrate under partial-wetting conditions imposed by a disjoining-conjoining pressure. We show that for a set of quite general disjoining-conjoining pressure potentials, the free surface can adopt only five nontrivial static patterns; in particular, we find solutions when the height goes to zero which describe satisfactorily the complete free surface for a finite amount of fluid deposited on a substrate. To test the extension of the applicability of our solutions, we compare them with those obtained when the lubrication approximations are not employed and under conditions where the lubrication hypothesis are not strictly valid, and also with axisymmetric solutions. For a given disjoining-conjoining potential, we report a new analytical solution that accounts for all the five possible solutions.

Final state of a perturbed liquid film inside a container under the effect of solid-liquid molecular forces and gravity.

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.

Closed-form expression for the profile of partially wetting two-dimensional droplets under gravity.

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.

Molecular kinetics modeling in hemodialysis: on-line molecular monitoring and spectral analysis.

The knowledge of the underlying molecular kinetics is a key point for the development of a dialysis treatment as well as for patient monitoring. In this work, we propose a kinetic inference method that is general enough to be used on different molecular types measured in the spent dialysate. It estimates the number and significance of the compartments involved in the overall process of dialysis by means of a spectral deconvolution technique, characterizing therefore the kinetic behavior of the patient. The method was applied to 52 patients to reveal the underlying kinetics from dialysate time-concentration profiles of urea, which has a well-known molecular kinetic. Three types of behaviors were found: one-compartmental (exponential decay Tau = 180 +/- 61.64 minutes), bicompartmental (Tau1 = 24.96 +/- 19.33 minutes, Tau2 = 222.32 +/- 76.59 minutes), and tricompartmental (Tau1 = 23.03 +/- 14.21 minutes; Tau2 = 85.75 +/- 27.48 minutes; and Tau3 = 337 +/- 85.52 minutes). In patients with bicompartmental kinetics, the Tau2 was related to the level of dialysis dose. The study concluded that spectral deconvolution technique can be considered a powerful tool for molecular kinetics inference that could be integrated in on-line molecular analysis devices. Furthermore, the method could be used in the analysis of poorly understood molecules as well as in new hemodialysis target biomarkers.

Thin film of non-Newtonian fluid on an incline.

The slow flow of thin liquid films on solid surfaces is an important phenomenon in nature and in industrial processes, and an intensive effort has been made to investigate it. It is well known that the contact line of currents on an inclined surface may become unstable and then a pattern of "fingers" develops that affects the quality of the coatings. This instability has been intensively studied due to its relevance for the technology of various industrial processes. So far the theoretical and numerical research has been focused on Newtonian fluids, notwithstanding that often in the real situations as well as in the experiments, the rheology of the involved liquid is non-Newtonian. Using the lubrication approximation, we derive the governing equations for a current of a power law non-Newtonian fluid on an inclined plane under the action of gravity and the viscous stresses. We show that surface tension effects can be included in the theory by a slight modification of the governing equations, that can then be used as a starting point to investigate the influence of rheology on the fingering instability and other phenomena of interest. We consider the one-dimensional case and we present three families of traveling wave solutions: two running downwards and the other upwards.