Draining of generalized Newtonian films on short quasi-vertical substrates

PERALTA, J. M.; MEZA, B. E.; ZORRILLA, S. E.

Paraná

Congreso; XVI Reunión sobre Recientes Avances en Fı́sica de Fluidos y sus Aplicaciones (Fluidos 2021); 2021

Facultad de Ingenierı́a de la Universidad Nacional de Entre Rı́os

Free-draining flow is observed in many practical and industrial situations. It is considered as a stage of a batch dip-coating process (such as in the manufacture of coated ice creams and ?alfajores?). This system is a self-metered process, where a film of liquid is freely formed onto a substrate by a draining flow. In general, the flow is mostly affected by the rheology of the film, the geometry of the system, and the gravity and the surface phenomena (i.e., surface tension) acting on the film. The complete dip-coating process consists of immersing the substrate in the film-forming fluid, then removing it from the container to begin forming the film, and allowing the excess fluid to drain. Depending on the relative importance of the previously mentioned effects, this system can be analyzed near the film-forming liquid level (presence of a meniscus) for long substrates or near to the top edge of the substrate where the film begins for short ones. In the first case, the surface phenomena play an important role to generate a constant final thin film thickness. In the second case, a variable film thickness is observed where gravity and rheology are the most important effects. In the food industry, where fluids are usually generalized Newtonian and highly viscous in nature, and also the substrates are short in length (e.g., biscuits and ice creams), the second scenario is more commonly found. However, the complexity of these systems can sometimes require arduous mathematical analyses with usually no analytical solutions. This work is focused on obtaining an improved and extended general theoretical analysis of a two-dimensional film draining of a generalized Newtonian fluid on a short quasi-vertical plate, solving rigorous mass, momentum, and energy balances. Mathematical expressions have been obtained assuming a monophasic, isothermal, and non-evaporative system, where the most important forces are viscous and gravitational. A dimensional analysis and scaling were used to simplify the mathematical description, and a generalized Newtonian fluid (e.g., generalized Quemada, Carreau Yassuda, and generalized Ofoli et al.) was assumed as the film-forming material. A new quantity that governs the draining flow and film characteristics, called viscous dissipation, was proposed as part of the novel analytical expressions of the main variables obtained in this work (velocity profile, average velocity, flow rate, viscous dissipation, and local and average film thickness). As a result, this study expanded the ways of calculation and the interconnection between the main variables in a free-draining flow system in order to obtain the analytical solutions for a given generalized Newtonian model.