Bubble behavior in cylindrical and square vessels under centric mechanical stirring

Abstract

Water model experiments were carried out to investigate the bubble behavior in cylindrical and square vessels under centric mechanical stirring. The bubble behavior in the square vessel was investigated in detail by using a high-speed camera to record the transient images of the bubbles. An image analysis software was used to obtain the bubble diameter. The results showed that the centric mechanical stirring in the square vessel was suitable for breakage and dispersion of bubbles, but not suitable for that in the cylindrical vessel. Increasing the impeller blade length and impeller rotation speed was beneficial to disintegrate and disperse bubbles widely. The bubble diameter decreased with the increase in the Weber number and increased slightly with the increase in the modified Froude number. The dimensionless correlation equation of bubble diameter was obtained by the dimensional analysis method.

Appendix

Dimensionless form of Calderbank equation is given below.

Under the conditions that the stirring power is completely dissipated using baffles, it can be expressed by

$$ P \propto \rho n^{3} l^{5} $$

(A1)

If the geometric similarity hold, the bath volume V is taken as

$$ V \propto L^{3} \propto l^{3} $$

(A2)

Then,

$$ {P \mathord{\left/ {\vphantom {P V}} \right. \kern-\nulldelimiterspace} V} \propto \rho n^{3} l^{2} $$

(A3)

Ignoring the last term in Eq. (1), the Calderbank equation can be arranged as follows:

$$ {{d_{\rm B} } \mathord{\left/ {\vphantom {{d_{B} } l}} \right. \kern-\nulldelimiterspace} l} \propto \varepsilon^{0.5} We^{{ - {3 \mathord{\left/ {\vphantom {3 5}} \right. \kern-\nulldelimiterspace} 5}}} $$

(A4)

Thus, the power of the Weber number of Eq. (1) or Eq. (A4) (− 3/5) is similar to that of Eq. (6) (− 0.5). It is to be noted that the average diameter of droplets dispersed in liquid under mechanical stirring is proportional to We^−3/5 [25].