Keywords : surfactant mode
European Journal of Molecular & Clinical Medicine,
2020, Volume 7, Issue 7, Pages 4317-4320
Linear stability analysis of two liquid layers with different viscosities flowing down on rigid surface in presence of insoluble surfactant at LL interface and in absence of shear stress at interfaces is studied. This problem is studied for two different viscosity ratio (μr = 0.4, 50) and has shown the effect of angle (θ) on the growth rate of LL perturbations and surfactant perturbations. Here, we find three interfacial modes like gas-liquid (GL), surfactant (or Marangoni) and liquid-liquid (LL) modes in which the effect of an angle (θ) on two modes (surfactant and LL) are studied. The effect of angle on the growth rate of surfactant mode for viscosity ratio μr = 0.4 is found unstable. It means the growth rate of unstable surfactant mode enhances exponentially with time. On the other hand, the growth rate of LL perturbations for high viscosity ratio (μr = 50) are decaying exponentially with time. It can be said that we can use or apply this research as per our requirement. It can be applied to produce either stable or unstable configurations. For solving linear governing equation, we used MATLAB for initial guesses and C coding for producing final results.