Effect of boundary roughness on nonlinear saturation of Rayleigh-Taylor instability in couple-stress fluid

Vishwanath B Awati,Priya M Gouder,Krishna B Chavaraddi

doi:10.1515/nleng-2018-0031

Vishwanath B Awati, Priya M Gouder + Show 1 more

Open Access

https://doi.org/10.1515/nleng-2018-0031

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Journal: Nonlinear Engineering	Publication Date: Jan 28, 2019
Citations: 6	License type: CC BY 4.0

Affiliation: Rani Channamma University, Belagavi

Abstract

Abstract The boundary roughness effects on nonlinear saturation of Rayleigh-Taylor instability (RTI) in couple-stress fluid have been studied using numerical technique on the basis of stability of interface between two fluids of the system. The resulting fourth order ordinary nonlinear differential equation is solved using Adams-Bashforth predictor and Adams-Moulton corrector techniques numerically. The various surface roughness effects and surface tension effects on nonlinear saturation of RTI of two superposed couple-stress fluid and fluid saturated porous media are well investigated. At the interface, the surface tension acts and finally stability of the problem is discussed in detail.

Highlights

The growth rate of instability due to gravity associated with a dense layer overlying lighter layer, Rayleigh-Taylor instability (RTI) depends on constitutive law related to stress and strain rate
The boundary roughness e ects on nonlinear saturation of Rayleigh-Taylor instability (RTI) in couplestress uid have been studied using numerical technique on the basis of stability of interface between two uids of the system
The various surface roughness e ects and surface tension e ects on nonlinear saturation of RTI of two superposed couple-stress uid and uid saturated porous media are well investigated

Summary

Introduction

The growth rate of instability due to gravity associated with a dense layer overlying lighter layer, Rayleigh-Taylor instability (RTI) depends on constitutive law related to stress and strain rate. Rudraiah et al [6] analyzed the couple-stress uid e ects on the control of RTI at interface between dense uids accelerated by lighter uid and used the approximations to derive the growth rate of RTI Another important application of RTI is ow past a porous layer is the design of e ective porous wall insulation. We consider two-dimensional nonlinear saturation of RTI on two superposed couple-stress uid and uid saturated porous layer using slip condition proposed by Sa man [18] with the e ect of boundary roughness. ∂p ∂x is the pressure gradient, μ is the uid viscosity and ρ is the uid density of the uid

Slip condition

Couple-stress conditions:

Results and Discussion