Thin Liquid Films: From Theory to Applications

In particle engineering, spray drying is an essential technique that depends on producing sprays, ideally made of equal-sized droplets. Ultrasonic sprays appear to be the best option to achieve it, and Faraday waves are the background mechanism of ultrasonic atomization. The characterization of sprays in this atomization strategy is commonly related to the relation between characteristic drop sizes and the capillary length produced by the forcing frequency of wavy patterns on thin liquid films. However, although this atomization approach is practical when the intended outcome is to produce sprays with droplets of the same size, drop sizes are diverse in real applications. Therefore, adequate characterization of drop size is paramount to establishing the relations between empirical approaches proposed in the literature and the outcome of ultrasonic atomization in actual operating conditions. In this sense, this work explores new approaches to spray characterization applied to ultrasonic sprays produced with different solvents. The first two introduced are the role of redundancy in drop size measurements to avoid resolution limitation in the measurement technique and compare using regular versus variable bin widths when building the histograms of drop size. Another spray characterization tool is the Drop Size Diversity to understand the limitations of characterizing ultrasonic sprays solely based on representative diameters or moments of drop size distributions. The results of ultrasonic spray characterization obtained emphasize: the lack of universality in the relation between a characteristic diameter and the capillary length associated with Faraday waves; the variability on drop size induced by both liquid properties and flow rate on the atomization outcome, namely, lower capillary lengths produce smaller droplets but less efficiently; the higher sensibility of the polydispersion and heterogeneity degrees in Drop Size Diversity when using variable bin widths to build the histograms of drop size; the higher drop size diversity for lower flow rates expressed by the presence of multiple clusters of droplets with similar characteristics leading to multimodal drop size distributions; and the gamma and log-normal mathematical probability functions are the ones that best describe the organization of drop size data in ultrasonic sprays. Full article

Hydrocolloid-based films are a good alternative in the development of biodegradable films due to their properties, such as non-toxicity, functionality, and biodegradability, among others. In this work, films based on hydrocolloids (gellan gum, carrageenan, and guar gum) were formulated, evaluating their dynamic rheological behavior and creep and recovery. Maxwell’s classical and fractional rheological models were implemented to describe its viscoelastic behavior, using the Vortex Search Algorithm for the estimation of the parameters. The hydrocolloid-based films showed a viscoelastic behavior, where the behavior of the storage modulus $({\mathrm{G}}^{\prime })$ and loss modulus (${\mathrm{G}}^{″})$ indicated a greater elastic behavior (${\mathrm{G}}^{\prime }>{\mathrm{G}}^{″}$). The Maxwell fractional model with two spring-pots showed an optimal fit of the experimental data of storage modulus (${\mathrm{G}}^{\prime }$) and loss modulus (${\mathrm{G}}^{″})$ and a creep compliance (J) (${\mathrm{F}}_{\min }<0.1$ and ${\mathrm{R}}^2>0.98$). This shows that fractional models are an excellent alternative for describing the dynamic rheological behavior and creep recovery of films. These results show the importance of estimating parameters that allow for the dynamic rheological and creep behaviors of hydrocolloid-based films for applications in the design of active films because they allow us to understand their behavior from a rheological point of view, which can contribute to the design and improvement of products such as food coatings, food packaging, or other applications containing biopolymers. Full article

The present work explores the impact of rotation on the dynamics of a thin liquid layer deposited on a spheroid (bi-axial ellipsoid) rotating around its vertical axis. An evolution equation based on the lubrication approximation was derived, which takes into account the combined effects of the non-uniform curvature, capillarity, gravity, and rotation. This approximate model was solved numerically, and the results were compared favorably with solutions of the full Navier–Stokes equations. A key advantage of the lubrication approximation is the solution time, which was shown to be at least one order of magnitude shorter than for the full Navier–Stokes equations, revealing the prospect of controlling film dynamics for coating applications. The thin film dynamics were investigated for a wide range of geometric, kinematic, and material parameters. The model showed that, in contrast to the purely gravity-driven case, in which the fluid drains downwards and accumulates at the south pole, rotation leads to a migration of the maximum film thickness towards the equator, where the centrifugal force is the strongest. Full article

Nonlinear dynamics of patterns near the threshold of long-wave monotonic Marangoni instability of conductive state in a heated thin layer of liquid covered by insoluble surfactant is considered. Pattern selection between roll and square planforms is analyzed. The dependence of pattern stability on the heat transfer from the free surface of the liquid characterized by Biot number and the gravity described by Galileo number at different surfactant concentrations is studied. Using weakly nonlinear analysis, we derive a set of amplitude equations governing the large-scale roll distortions in the presence of the surface deformation and the surfactant redistribution. These equations are used for the linear analysis of modulational instability of stationary rolls. Full article

We provide a new framework for analyzing the flow of an axisymmetric liquid film flowing down a vertical fiber, applicable to fiber coating flows and those in similar geometries in heat exchangers, water treatment, and desalination processes. The problem considered is that of a viscous liquid film falling under the influence of gravity and surface tension on a solid cylindrical fiber. Our approach is different from existing ones in that we derive our mathematical model by using a control-volume approach to express the conservation of mass and axial momentum in simple and intuitively appealing forms, resulting in a pair of equations that are reminiscent of the Saint-Venant shallow-water equations. Two versions of the model are obtained, one assuming a plug-flow velocity profile with a linear drag force expression, and the other using the fully-developed laminar velocity profile for a locally uniform film to approximate the drag. These can, respectively, model high- and low-Reynolds number regimes of flow. Linear stability analyses and fully nonlinear numerical simulations are presented that show the emergence of traveling wave solutions representing chains of identical droplets falling down the fiber. Physical experiments with safflower oil on a fishing line are also undertaken and match the theoretical predictions from the laminar flow model well when machine learning methods are used to estimate the parameters. Full article

This paper analyses the two-dimensional unsteady and incompressible flow of a non-Newtonian hybrid nanofluid over a stretching surface. The nanofluid formulated in the present study is${\mathrm{TiO}}_2+\mathrm{Ag}+\mathrm{blood}$, and ${\mathrm{TiO}}_2+\mathrm{blood}$, where in this combination ${\mathrm{TiO}}_2+\mathrm{blood}$ is the base fluid and ${\mathrm{TiO}}_2+\mathrm{Ag}+\mathrm{blood}$ represents the hybrid nanofluid. The aim of the present research work is to improve the heat transfer ratio because the heat transfer ratio of the hybrid nanofluid is higher than that of the base fluid. The novelty of the recent work is the approximate analytical analysis of the magnetohydrodynamics mixed non-Newtonian hybrid nanofluid over a stretching surface. This type of combination, where ${\mathrm{TiO}}_2+\mathrm{blood}$ is the base fluid and ${\mathrm{TiO}}_2+\mathrm{Ag}+\mathrm{blood}$is the hybrid nanofluid, is studied for the first time in the literature. The fundamental partial differential equations are transformed to a set of nonlinear ordinary differential equations with the guide of some appropriate similarity transformations. The analytical approximate method, namely the optimal homotopy analysis method (OHAM), is used for the approximate analytical solution. The convergence of the OHAM for particular problems is also discussed. The impact of the magnetic parameter, dynamic viscosity parameter, stretching surface parameter and Prandtl number is interpreted through graphs. The skin friction coefficient and Nusselt number are explained in table form. The present work is found to be in very good agreement with those published earlier. Full article

The study focused on a theoretical study of natural convection in a van der Waals gas near a vertical plate. A novel simplified form of the van der Waals equation derived in the study enabled analytical modeling of fluid flow and heat transfer. Analytical solutions were obtained for the velocity and temperature profiles, as well as the Nusselt numbers. It was revealed that nonlinear effects considered by the van der Waals equation of state contribute to acceleration or deceleration of the flow. This caused respective enhancement or deterioration of heat transfer. Results for a van der Waals gas were compared with respective computations using an ideal gas model. Limits of the applicability of the simplified van der Waals equations were pinpointed. Full article