A new approach for computation of drop terminal velocity in stagnant medium

A new approach for solving the drop motion problem in a continuous medium is presented in this work. The classical curve of the terminal velocity was divided into two parts, named “A” left side and “B” right side. Such a division was done with respect to drop of minimal size with a maximal terminal velocity. In a first step, we focus on the large drops moving in air (part B), in which some approximation schemes can be used by taking advantage of the region's properties. An expression of the terminal velocity is derived using an analytic approach to the study of the motion of large liquid drops falling in air. Our formula agrees well with experiments for drops falling in air of part B. However, for drops of the part A, large differences are observed. In an attempt to deal with this shortcoming, our formula was extended to liquid drops falling in air in both parts. The equation is also tested on drops moving in water. We observe that it is only applicable to the drops of the part A. As far as the part B liquid drops in water are concerned, an analogy between the surface waves of an infinite medium and the free fall of drops is made and a more generalized formula is proposed. Good agreement was found between the present model and experimental data from the literature. An extension of the expression for air and water to other continuous media is attempted.