Nonlinear simulation and linear stability analysis of viscous fingering instability of viscoelastic liquids

2017 ◽  
Vol 29 (3) ◽  
pp. 033101 ◽  
Author(s):  
H. Shokri ◽  
M. H. Kayhani ◽  
M. Norouzi
Keyword(s):  
Stability Analysis ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Viscous Fingering ◽  
Nonlinear Simulation ◽  
Fingering Instability ◽  
Viscoelastic Liquids

scholarly journals Non-modal stability analysis of miscible viscous fingering with non-monotonic viscosity profiles

2018 ◽  
Vol 856 ◽  
pp. 552-579
Author(s):  
Tapan Kumar Hota ◽  
Manoranjan Mishra
Keyword(s):  
Stability Analysis ◽  
Viscous Fluid ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Physical Mechanism ◽  
Stable State ◽  
Viscous Fingering ◽  
Linear Perturbation ◽  
Optimal Perturbation ◽  
Nonlinear Simulations

A non-modal linear stability analysis (NMA) of the miscible viscous fingering in a porous medium is studied for a toy model of non-monotonic viscosity variation. The onset of instability and its physical mechanism are captured in terms of the singular values of the propagator matrix corresponding to the non-autonomous linear equations. We discuss two types of non-monotonic viscosity profiles, namely, with unfavourable (when a less viscous fluid displaces a high viscous fluid) and with favourable (when a more viscous fluid displaces a less viscous fluid) endpoint viscosities. A linear stability analysis yields instabilities for such viscosity variations. Using the optimal perturbation structure, we are able to show that an initially unconditional stable state becomes unstable corresponding to the most unstable initial disturbance. In addition, we also show that to understand the spatio-temporal evolution of the perturbations it is necessary to analyse the viscosity gradient with respect to the concentration and the location of the maximum concentration $c_{m}$. For the favourable endpoint viscosities, a weak transient instability is observed when the viscosity maximum moves close to the pure invading or defending fluid. This instability is attributed to an interplay between the sharp viscosity gradient and the favourable endpoint viscosity contrast. Further, the usefulness of the non-modal analysis demonstrating the physical mechanism of the quadruple structure of the perturbations from the optimal concentration disturbances is discussed. We demonstrate the dissimilarity between the quasi-steady-state approach and NMA in finding the correct perturbation structure and the onset, for both the favourable and unfavourable viscosity profiles. The correctness of the linear perturbation structure obtained from the non-modal stability analysis is validated through nonlinear simulations. We have found that the nonlinear simulations and NMA results are in good agreement. In summary, a non-monotonic variation of the viscosity of a miscible fluid pair is seen to have a larger influence on the onset of fingering instabilities than the corresponding Arrhenius type relationship.

scholarly journals Viscous Fingering of Thixotropic Fluids: a Linear Stability Analysis

2015 ◽  
Vol 43 (2) ◽  
pp. 31-38 ◽  
Author(s):  
Behnam Ebrahimi ◽  
Kayvan Sadeghy ◽  
Mohammad-Ali Akhavan Bahabadi
Keyword(s):  
Stability Analysis ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Viscous Fingering
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