Temporal instability analysis of power-law fluid jets in quiescent air under symmetric (varicose) perturbations

Power-law fluids, such as paints, silica suspensions, and polymers, are frequently employed in industrial processes such as spray painting, agricultural spraying, and fuel injection, which disintegrate liquid sheets into smaller droplets. Their flow characteristics are distinct and intricate because of the absence of fixed viscosity. In contrast to Newtonian fluids, power-law fluid atomization is significantly influenced by the non-linear relationship between shear stress and shear rate. With an emphasis on the interaction of fluid rheology, sheet dynamics, and instability processes, this work explores the primary breakup of power-law liquid sheets. Using linear stability analysis, a theoretical attempt has been made to capture the primary breakup characteristics of these liquids in stagnant air under the influence of symmetric(varicose) mode of interfacial instability. Combining the continuity equation, linearised momentum equation, and the relevant boundary conditions, the dispersion relation for predicting the stability of the tested mode has been arrived. The stability variables namely the temporal growth rate, the breakup frequency, and the critical wave number were determined. On plotting the primary breakup variables in the dimensionless form, regression functions have attained a superior correlation coefficient for both shear-thinning and shear-thickening liquids.