Flow of two immiscible uniformly rotating micropolar and viscous fluid layers

The interfacial flow of two immiscible uniformly rotating micropolar and viscous fluid layers is investigated in this article. The top layer contains a micropolar fluid of having velocity components (u1,v1,w1), micro-rotation components (N1,N2,N3), density rho(1), viscosity mu(1) and pressure p(1) that is rotating with angular velocity omega(1). A viscous fluid layer exists in the lower region with velocity components (u(2),v(2),w(2)), density rho(2), viscosity mu(2) and pressure p(2) rotating with constant angular velocity omega(2). The flow similarity solutions exist under the constraint sigma(2)rho=1, where sigma=omega(2)/omega(1) (angular velocities ratio) and rho=rho(2)/rho(1) (densities ratio). The flow shows a co-rotating case for sigma>0 and a counter-rotating case for sigma<0. A strong numerical technique known as the Keller-box approach is utilized to obtain the solution of the resultant set of an ordinary differential equation. Similarity solutions can be found for 0 <=sigma <= 1 (co-rotating flows) but for sigma<0 (counter-rotating flows), the similarity solution occurs up to the certain critical value of sigma (i.e., sigma c(mu)<=sigma <= 1. Due to the coupling type of the flow near the liquid-liquid interface, the micro polarity parameter K-1 has an impact on both fluid's layer, even though the micropolar fluid exists just in the upper layer. The key objective of the current article is to analyze how these two different fluid layers will behave under the weak and strong concertation of microelements that can be fruitful in the engineering and scientific disciplines.

Automated summary

The article investigates the flow of two immiscible uniformly rotating micropolar and viscous fluid layers at the interface. It analyzes co-rotating and counter-rotating cases for different angular velocities ratios. The study utilizes a numerical technique called the Keller-box approach to obtain solutions for the ordinary differential equation.