کمیسازی وقوع ناپایداری ویسکوز فینگرینگ جریان سیال در محیط متخلخل

Abstract

In this paper, nonlinear simulation of viscous fingering instability of miscible displacement involving nanofluid is investigated. Using vorticity and stream functions and the spectral method governing equations are obtained. Due to the fractality of fluid-fluid interface in instability phenomena, by using box counting method, its fractal dimension is calculated in different parameters such as deposition rate, mobility ratio and diffusion rates. The results show that increasing the deposition rate reduces the complexity of finger patterns and the diffusion rate of nanofluid has no effect on complexity of finger patterns while increasing the diffusion rate of displaced fluid has significant effect on patterns and makes it more complicated. The fractal analysis also shows that the effect of mobility ratio depends on the deposition rate. By considering deposition rate, although the mobility ratio has no effect on fractal dimension and effective time is constant and equal to 275, start time of instability is delayed by 25 units. It can be concluded that fractal analysis of viscous fingering phenomena can be considered as one of the instability characteristics.