Draining of generalized Newtonian films on short quasi-vertical substrates

PERALTA, JM; MEZA, BE; ZORRILLA, SE

Paraná

Congreso; Fluidos 2021, XVI Reunión sobre Recientes Avances en Física de Fluidos y sus Aplicaciones; 2021

Universidad Nacional de Entre Ríos

Free-drainingflow is observed in many practical and industrial situations. It is consideredas a stage of a batch dip-coating process (such as in the manufacture of coatedice creams and ?alfajores?). This system is a self-metered process, where afilm of liquid is freely formed onto a substrate by a draining flow. Ingeneral, the flow is mostly affected by the rheology of the film, the geometryof the system, and the gravity and the surface phenomena (i.e., surfacetension) acting on the film. The complete dip-coating process consists ofimmersing the substrate in the film-forming fluid, then removing it from thecontainer to begin forming the film, andallowing the excess fluid to drain. Depending on the relative importance of thepreviously mentioned effects, this system can be analyzed near the film-formingliquid level (presence of a meniscus) for long substrates or near to the topedge 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 filmthickness. In the second case, a variable film thickness is observed wheregravity 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 demands arduous mathematical analyseswith usually no analytical solutions. Thiswork focused on obtaining an improved and extended general theoretical analysisof a two-dimensional film draining of a generalized Newtonian fluid on a shortquasi-vertical plate, solving rigorous mass, momentum, and energy balances.Mathematicalexpressions have been obtained assuming a monophasic, isothermal, andnon-evaporative system, where the most important forces are viscous andgravitational. A dimensional analysis and scaling were used to simplify themathematical description, and a generalized Newtonian fluid (e.g., generalizedQuemada, Carreau Yassuda, and generalized Ofoliet al.) was assumed as the film-forming material. A new quantity that governsthe draining flow and film characteristics, called viscous dissipation, wasproposed as part of the novel analytical expressions of the main variablesobtained in this work (velocity profile, average velocity, flow rate, viscousdissipation, and local and average film thickness).Asa result, this study expanded the ways of calculation and the interconnectionbetween the main variables in a free-draining flow system in order to obtainthe analytical solutions for a given generalized Newtonian model.