Session: 10.2.3 - Interfacial Phenomena and Flows III

Paper Number: 158078

158078 - Falling Water Droplet on Water Surface for Coalescence Cascade 

Abstract: 

The three laws of “Elevancy” were derived by combining the three laws of motion of Newtonian mechanics and Archimedes' principle of buoyancy. That is, according to Newton's third law of action/reaction, an object with mass ‘M’ falls freely on an equipotential surface and either collides, stagnates, or moves by inertia on that surface. Then, for an object to exist in that isosurface, it is supported by static, dynamic, and inertial buoyancy forces with corresponding reaction forces. For example, in the case of Newton's second law of motion, the moment a free-falling object begins to rest and remains in contact with the fluid, the corresponding buoyant force is created by the equivalent fluid volume of the falling object, which is derived as follows: The pressure generated from the kinetic energy of a falling object is distributed evenly throughout the fluid volume, resulting in a confined pressure. This pressure acts as a reaction force on the contact surface. This force can be defined as “dynamic buoyancy,” which is the reaction force on a freely falling object.

Additionally, the dimensionless Lee Number, which is an arbitrary multiple of the object's weight 'Mg', was introduced to determine whether a free-falling object will bounce, stay, or sink when it collides with the surface. Using the above new laws and dimensionless numbers, this study aims to theoretically approach a natural phenomenon known as coalescence cascade of water droplets freely falling on a water surface. The movement that occurs when a water droplet freely falls from a certain height and contacts the bulk water surface was divided into three types (bounce, stay, and sink) and a related analysis was performed. In particular, the three actions are defined as staying on the water when the Lee Number is a unit value (L_E = 1.0) and bouncing when the Lee Number is greater than the unit value (L_E > 1.0). Additionally, a Lee Number value less than 1 (L_E < 1.0) means that the water droplet sinks below the water surface. Meanwhile, when a free-falling water droplet touches the water surface, its residence time is calculated as a function of gravity. Additionally, Stay and Bounce behaviors are distinguished on the water surface, depending on the droplet's initial falling height. Finally, after free-falling water droplets combine with water in the bulk, the process of rising to the surface of the water and becoming daughter water droplets is determined by the law of conservation of mass for falling water droplets and the surface tension of water as the daughter water droplet formation energy. In connection with this study, the maximum diameter of water droplets (including morning dew and raindrops) was obtained at atmospheric temperature.

Presenting Author: Jong Lee Kongju National University

Presenting Author Biography: