Numerical study of interface tracking for the unsteady flow of two immiscible micropolar and Newtonian fluids through a horizontal channel with an unstable interface

Chandrawat, RK; Joshi, V; Beg, OA

Abstract

The dynamics of the interaction between immiscible fluids is relevant to numerous complex
flows in nature and industry, including lubrication and coating processes, oil extraction, physicochemical
separation techniques etc. In this article, the unsteady flow of two immiscible fluids i.e. an Eringen
micropolar and Newtonian liquid, is considered in a horizontal channel. Despite the no-slip and hyper-stick
boundary conditions at the channel wall, it is accepted that the fluid-fluid interface is unstable, and it travels
from one position to another, and may even be deformed; hence the single momentum equation in the
volume of fluid (VOF) method is combined with the continuum surface approach model to track the
interface. The immiscible fluids are considered to flow under three applied pressure gradients (constant,
decaying and periodic) and flow is analyzed under seamless shear stress over the entire interface. The
modified cubic b-spline differential quadrature method (MCB-DQM) is used to solve the modeled coupled
partial differential equations for the fluid interface evolution. The advection and tracking of the interface
with time, wave number, and amplitude are illustrated through graphs. It is observed that the presence of
micropolar parameters affects the interface with time. The novelty of the current study is that previous
studies (which considered smooth and unstable movement of the micropolar fluid, the steady stream of two
immiscible fluids and interface monitoring through different modes) are extended and generalized to
consider unsteady flow of two immiscible Eringen micropolar and Newtonian fluids with a moving interface
in a horizontal channel. For the decaying pressure gradient case, which requires more time to achieve the
steady state, the peak of the waves resemble those for the constant pressure gradient case. The interface becomes steady for a more extensive time when a constant pressure gradient is applied. The interface
becomes stable quickly with time as the micropolar parameter is decreased for the constant pressure
gradient case i.e. weaker micropolar fluids encourage faster stabilization of the interface. With periodic
pressure gradient, the interface takes more time to stabilize, and the crest of the waves is significantly
higher in amplitude compared to the constant and decaying pressure cases. The simulations demonstrate
the excellent ability of MCB-DQM to analyze complex interfacial immiscible flows.

Citation

Chandrawat, R., Joshi, V., & Beg, O. (2021). Numerical study of interface tracking for the unsteady flow of two immiscible micropolar and Newtonian fluids through a horizontal channel with an unstable interface. Journal of Nanofluids, 10(4), 552-563. https://doi.org/10.1166/jon.2021.1805

• Journal Article Type: Article
• Acceptance Date: Aug 3, 2021
• Publication Date: Dec 1, 2021
• Deposit Date: Aug 4, 2021
• Publicly Available Date: Nov 26, 2021
• Journal: Journal of Nanofluids
• Print ISSN: 2169-432X
• Electronic ISSN: 2169-4338
• Publisher: American Scientific Publishers
• Volume: 10
• Issue: 4
• Pages: 552-563
• DOI: https://doi.org/10.1166/jon.2021.1805
• Publisher URL: https://doi.org/10.1166/jon.2021.1805
• Related Public URLs: http://www.aspbs.com/jon.htm