An analytical solution for the profile and volume of a small drop or bubble symmetrical about a vertical axis

Abstract

A solution for the profile of a small drop or bubble symmetrical about a vertical axis and at rest in a second fluid is obtained as a first-order perturbation of a circle. At the end of the drop opposite the apex, the perturbation approach breaks down and a matching zero-gravity solution is used. The results agree with numerical solutions and indicate that the pendant-drop profile of maximum volume fitting a given small vertical tube intersects the exit plane at very nearly 90°. This enables the maximum volume to be determined accurately from a force balance.

Forces on a boiling bubble in a developing boundary layer, in microgravity with g-jitter and in terrestrial conditions

“…Fluids 24, 082104 (2012) liquid has successfully been predicted in the above Newtonian approach with analytical means with the neglect of inertia. 5 In this case, possible bubble shapes depend on the ratio of capillary to gravity forces. Detachment occurs in axisymmetric pool boiling if no possible shapes for a given bubble volume and a given foot radius exist.…”

“…Detachment occurs in axisymmetric pool boiling if no possible shapes for a given bubble volume and a given foot radius exist. 5 Bubble detachment in pool boiling has also been investigated by direct numerical simulation. 6 The present study is based on an alternative to the above-mentioned Newtonian treatment of bubble dynamics.…”

Some problems in nucleate flow boiling

“…If, additionally, the bubble shape is axisymmetric and the fluid is quiescent, only gravity and surface tension determine the bubble shape. The bubble shape can then be computed, see for example the analytical solution of Chesters [11]. These circumstances may serve as a reference for any measurement method, in particular when the contact angle is difficult to be measured.…”

“…With arbitrary deformation, more parameters than h are necessary to describe growth and detachment. In [11], a representation with Legendre polynomials is used. Here, a similar representation, but with the center point at distance h from the wall, is used.…”

Analytical Calculation of Falling Droplets from Cylindrical Capillaries

“…Other approaches are offered by Chesters [3], Eggers & Dupont [4] or Clanet & Lasheras [5]. They present much more extensive algorithms for the calculation of the shape of hanging and falling droplets using differential equations.…”