Experimental investigation on unsteady dynamic characteristics of shear-thinning power-law droplets

The unsteady deformation and motion of shear-thinning power-law droplets exist widely in various engineering fields. In this work, the deformation and motion of sodium carboxymethyl cellulose solution droplets subjected to continuous airflow are experimentally investigated, with an initial Weber number ranging from 1.1 to 13.2, an initial effective Ohnesorge number from 0.013 to 0.068, and an initial Reynolds number from 950 to 3250. First, a three-dimensional algorithm is developed to determine the centroid of deformed droplets. Combined with forward–backward filtering, this algorithm enables reliable calculation of the instantaneous velocity and drag coefficient of deformed droplets under experimental conditions. Second, the droplet deformation and drag coefficient exhibit synchronous periodic oscillations over time, with deformation peaks increasing with the Weber number (We) and decreasing with the effective Ohnesorge number, reaching the maximum deformation of 1.61. The classical deformation correlation developed for Newtonian droplets shows limited applicability to the present shear-thinning power-law droplets. A set of deformation prediction correlations is developed for the oscillation process of shear-thinning power-law droplets, showing good agreement with the present experimental data. Finally, the critical dimensionless relative acceleration triggering the unsteady effect is determined as −0.47. The unsteady drag coefficient increment exhibits a negative correlation with the dimensionless relative acceleration, peaking at 1.62. A predictive correlation for the unsteady drag coefficient increment is further developed to characterize the combined influence of droplet deformation and the unsteady effect over the tested Weber number range of 1 < We < 12.