Nonlinear flow of couple stress fluid layer over an inclined plate

Abstract

The issue of stability of a thin couple-stress liquid layer flows on an inclined plane was inspected. The thin-film approximation was employed to obtain a Benney-like differential equation, that described the time record of the interface profile The linear transition state and reduction ratio of maximum classical (Newtonian) growth-rate were discussed. The complete evolution equation was solved numerically using the method of lines in order to support the novelty of the work. The linear stability could be enhanced by increasing the couple-stress coefficient and surface tension as well as reducing the inclination. However, the ordinary viscosity played an irregular role. The linear results predicted conditions (windows) in which the non-Newtonian film was more stable than its Newtonian counterpart. The nonlinear stimulation anticipated the existence of sock waves in certain situations. The appearance of instability through the linear subcritical region as well as irregular influences with respect to surface tension and couple-stress property was revealed. The nonlinear approach was more accurate in describing the stability issue than the linear one. Such results could be employed to attain the optimum statuses with regard to the film stability, and control the shock waves. They would not only enable accurate practical implementation in the design of inertial confinement fusion capsules and supernova explosions and implosions modeling, but also would allow for precise numerical simulation.