THE DEPENDENCE OF THE SHAPE AND STABILITY OF CAPTIVE ROTATING DROPS ON MULTIPLE PARAMETERS

摘要: The dependence of the shape and stability rigidly rotating captive drops on multiple parameters is analysed by applying asymptotic computer-aided techniques from bifurcation theory to Young-Laplace equation which governs meniscus shape. In accordance with Brown Scriven, equilibrium shapes for volume a cylinder without gravity are grouped into families like symmetry that branch cylindrical at specific values rotation rate, measured rotational Bond number E. Here, evolution these changes in drop Y , length B gravitational G presented. Criteria laid out predicting this parameter-space they circumvent much extensive solution eigenproblems used previously. Asymptotic analysis describes slightly different ones shows some bifurcations cylinders wavy, axisymmetric menisci ruptured small or gravity. Near points least one singularly develops fold limit point. Numerical methods couple finite-element representation valid wide range computer-implemented tracking families. An algorithm presented calculates, two parameters, loci points; map four-dimensional parameter space (E, / ). numerical results compare well region where latter valid. exchange mode instability predicted numerically volumes smaller than cylinder.