A robust numerical strategy for finding surface waves in flows of non-Newtonian liquids

Gravity-driven flows of liquid films are frequent in nature and industry, such as in landslides, lava flow, cooling of nuclear reactors, and coating processes. In many of these cases, the liquid is non-Newtonian and has particular characteristics. In this paper, we analyze numerically the temporal stability of films of non-Newtonian liquids falling by gravity, on the onset of instability. The liquid flows over an incline, where surface waves appear under certain conditions, and we do not fix a priori its rheological behavior. For that, we made used of the Carreau-Yasuda model without assigning specific values to its constants, and we compute general stability solutions. The numerical strategy is based on expansions of Chebyshev polynomials for discretizing the Orr-Sommerfeld equation and boundary conditions, and a Galerkin method for solving the generalized eigenvalue problem. In addition, an Inverse Iteration method was implemented to increase accuracy and improve computational time. The result is a robust and light numerical tool capable of finding the critical conditions for different types of fluids, which we use to analyze some key fluids. We show that the outputs of the general code match previous solutions obtained for specific computations. Besides increasing our knowledge on surface-wave instabilities in non-Newtonian liquids, our findings provide a new tool for obtaining comprehensive solutions on the onset of instability.Comment: This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0

Bidisperse micro fluidized beds: Effect of bed inclination on mixing

Micro fluidized beds are basically suspensions of solid particles by an ascending fluid in a mm-scale tube, with applications in chemical and pharmaceutical processes involving powders. Although in many applications beds are polydisperse, previous works considered only monodisperse beds aligned in the vertical direction. However, introducing an inclination with respect to gravity leads to different bed patterns and mixing levels, which can be beneficial for some applications. In this paper, we investigate experimentally the behavior of micro gas-solid beds consisting of bidisperse mixtures under different inclinations. In our experiments, mono and bidisperse beds are filmed with a high-speed camera and the images are processed for obtaining measurements at both the bed and grain scales. We show that the degree of segregation is larger for vertical beds, but mixing varies non-monotonically with inclination, with an optimal angle of 30$^{\circ}$--50$^{\circ}$ with respect to gravity. By computing the mean and fluctuation velocities of grains, we reveal that the mixing layer results from the competition between segregation by kinetic sieving and circulation promoted by the fluid flow. We also observe worse fluidization as the angle relative to gravity increases, accounting then for the non-monotonic behavior. Our results bring new insights into mixing and segregation in polydisperse beds, which can be explored for processing powders in industry.Comment: This article appeared in Phys. Fluids 36, 013303 (2024) and may be found at https://doi.org/10.1063/5.017915