rise and deformation modeling of single droplet motion in yield stress fluids by using aspect ratio and dimensionless numbers

The motion of a single droplet rising in quiescent yield stress fluids was investigated experimentally. by using a high-speed camera to follow the rising droplet, the images of the recorded frames were digitized and analyzed using matlab, and the aspect ratio and terminal velocity of the droplets were obtained. the results show that the droplet aspect ratio decreases with the increase of dimensionless numbers such as eötvös number and tadaki number, and the droplet gradually changes from spherical to ellipsoidal. the larger the yield stress, the larger the bingham number, which limits the lateral stretching of the droplet, and the droplet shows a spherical shape. the experimental drag coefficient and aspect ratio were compared with correlations in literature, and the comparison showed that these correlations do not give fully satisfactory results in predicting the drag coefficient and aspect ratio of droplet rising in yield stress fluid, showing a big relative error. therefore, two new empirical correlations were proposed to predict the aspect ratio and the drag coefficient, respectively. it was found that the calculated results by the present correlation agree well with the experimental data.