cohesion model bubble/coalescence

Purpose

Implementing the bubble coalescence model from Lau et al..

Warning

This is an experimental feature. It may produce unexpected results, and its behaviour may change without announcement in a future version

Syntax

cohesion bubble/coalescence [other model_type/model_name pairs as described here ] settings keyword values

zero or more keyword/value pairs may be appended after the keyword settings (after all models are specified)

use_radius_max values = 'on' or 'off'
  on = once a bubble has reached a defined maximum radius growth is stopped
  off = no upper limit on bubble growth
use_vel_max values = 'on' or 'off'
  on = only if one of two bubbles velocity in contact is below a defined threshold they can coalesce
  off = no limit on bubble coalescence

Associated material properties

Global scalars 

surfaceTension ( $\sigma$ ): surface tension coefficient [force/length]
radiusBubbleMax ( $r_{max}$ ): maximum bubble radius [length]
velBubbleMax ( $v_{max}$ ): maximum contact velocity for bubble coalescence [length/time]

Description

This model implements bubble coalescence as described in Lau et al.. For coalescence to occur, the kinetic energy of the collision must exceed the surface energy for the bubble:

$E_{kin} > E_{surf} E_{surf} = \sigma \left(\frac{\pi}{6}\right)^{2/3} (d_1^2+d_2^2) E_{kin} = 0.5 \rho_{gas} v_{rel}^2 \frac{\pi}{6} \frac{d_1^3 d_2^3}{d_1^3+d_2^3}$

where $\sigma$ is the surface tension coefficient, $d_1$ and $d_2$ are the diameters of the colliding bubbles, $\rho_{gas}$ is the gas density, and $v_{rel}$ is the relative velocity between the bubbles.

When coalescence occurs (i.e., above criterion is satisfied), the merging of the bubbles is performed by continuously growing the larger of the two bubbles, and shrinking the smaller of the two bubbles, which is then finally deleted when it reached some threshold radius.

This model can be used as part of pair bubble.

Restrictions

None

Coarse-graining information:

Using coarsegraining in combination with this command might lead to different dynamics or system state and thus to inconsistencies.

Default

use_radius_max = off, use_vel_max = off

Literature

[1] Lau, Deen and Kuipers, Chemical Engineneering Science, 108, p 9 (2014).