M.N. Coelho Pinheiro

Liquid phase mass transfer coefficients for bubbles growing in a pressure field: A simplified analysis

The rigorous mathematical treatment of the mass transfer process of a solute between a growing bubble and the surrounding liquid requires the resolution of a non-steady state diffusion equation with an expanding surface. In the present study a simplified analysis of this mass transfer process is presented in order to estimate the liquid phase mass transfer coefficients. In particular, the mass transfer process from/into a bubble rising through a liquid pool with a low pressure above the liquid free surface, is considered. The enhancement factors obtained with this simplified analysis to correct the liquid phase mass transfer coefficients are overestimated relatively to the predictions obtained with the detailed one but their variation with the bubble expansion rate is well predicted.

GAS HOLD-UP IN AERATED SLUGGING COLUMNS

Gas hold-up is one of the most important parameters characterizing the hydrodynamics of bubble columns. A study is presented about the gas hold-up in gas-liquid slugging columns. Expansion of liquid columns is measured for a wide range of superficial velocities of bubbling gas, and the data are compared with available theory. The experiments were performed with liquids of different kinematic viscosities, in columns of 22 mm, 32 mm and 52 mm internal diameters and the initial liquid heights were greater than 2.5 m. A discussion is presented based on the effects of the flow pattern in the wakes of the Taylor bubbles and on coalescence of bubbles. When the flow regimes in the liquid and in the wake are both turbulent or both laminar, the theory predicts the gas hold-up. When the flow in the wake is turbulent and in the main liquid is laminar, the experimental gas hold-up is higher than predictions. This disagreement is explained by the shape of the liquid velocity profile emerging from the wake and by the long length, between bubbles, needed to restore the laminar profile in the liquid.

A simple model to obtain mass transfer coefficients from a soluble solid to a flowing fluid in closed recirculating systems

Dissolution experiments of a solid in a flowing liquid are usually performed when correlations of mass transfer coefficients must be known for liquid-solid interfaces. Frequently, these experiments are carried out in a closed recirculation set-up where the liquid is pumped from a reservoir to a cell with the soluble solid and returns to the reservoir. In the present study, a model of the mass transfer considering the connecting tubes between reservoir and cell as a series of well-mixed tanks is proposed. Results obtained in experiments of dissolution of a planar surface of benzoic acid to a confined water jet that impinges onto the solid surface are used to apply the model developed. Sherwood numbers calculated for experiments performed with two different volumes of liquid in the reservoir are almost the same (discrepancy of 2 %) when the increase of solute concentration in the connecting tubes was taken in account. Q 2001 Elsevier Science Ltd

Stripping in a bubbling pool under vacuum-contribution of the interfacial tension to the pressure inside the bubbles

Abstract In a stripping process conducted under vacuum where the gas is dispersed in the liquid mixture as very small bubbles (microbubbles), the contribution of the interfacial tension to the pressure inside a bubble is significant. As a result, the bubble does not expand significantly approaching the liquid free surface, even if the pressure drop in the gas is considerable comparatively to the pressure outside the bubble. This behaviour certainly determines the mass transfer rate mainly in the upper portion of the bubbling pool. In the present study a simplified model of the mass transfer process is proposed for this situation. One important conclusion is obtained from the predictions for the system pentane / n-paraffins in operations conducted under a pressure of 300 N m−2: the amount of solute removed from the liquid is lower when microbubbles are injected in the liquid although the interfacial area per unit volume of gas is very high.