Analysis of Hydrodynamics and Mass Transfer of Gas-Liquid and Liquid-Liquid Taylor Flows in Microchannels: Theoretical Approach and Experimental Proofs

Introduction

In the past decades micro and minireactors are actively investigated for their use instead of conventional devices as well as for new processes which are crucially increased due to smaller transversal sizes of the micro and minichannels (capillaries in other word). One understands under the micro channels usually the channels with hydraulic diameter roughly smaller than 1 mm (often 100–200 μm or even smaller, down to 10 μm). The mini channels have larger diameters, approximately up to 2 mm (see Background section for details). The advantages of micro and mini channels are:

• 1.

  Smaller diffusional path, e.g. for typical diffusivity in the liquid D = 10^–9 m²/s the characteristic time of diffusion could be assessed as t_dif ≈ d²/D, i.e. for d = 100 mm t_dif ≈ 10⁷ s = 2778 hours, for d = 10 mm t_dif ≈ 10⁵ s = 28 hours, for d = 1.0 mm t_dif ≈ 10³ s = 16.7 min, for d = 0.1 mm t_dif ≈ 10 s. Hence, the decrease of the channel diameter results in much shorter time necessary to perform mass transfer due to diffusion alone.

• 2.

  The flow in micro and minichannels is close to the plug flow due to absence of turbulent mixing, especially for so-called Taylor (or slug, or chain) flow (Figure 1), where the bubbles/droplets of dispersed phase have the length larger than diameter of the channel.

• 3.

  The smaller volume of micro and minireactors is easier to control due to less inertia of hydrodynamics, heat and mass transfer parameters.

• 4.

  For explosive chemicals produced in micro and minireactors there is no risk of explosion because of their diameter is smaller than the critical value of diameter.

• 5.

  Excellent mixing in each element of Taylor flow structure due to inner local vortices (so-called Taylor vortices), allowing to increase mass transfer several times compared to one-phase laminar flow.

Figure 1.

Schematic diagram used in formulating the continuity equation for the slug flow of a two-phase mixture

The application of micro and mini technologies can not only improve the quality of end products, reducing energy and resource consumption, but also increase the manufacturing mobility and the possibility of its rapid reset to produce other products. Micro- and minireactors can reduce the space occupied by the plant, making it safer and more environmental friendly.

Micro and minireactors are widely studied attracting significant interest of both researcher and industry. Nonetheless, many of published results have either experimental or numerical nature, and some theoretical approach is needed to provide more sophisticated understanding of phenomena and processes taking place in this promising type of chemical equipment.

Thus, the aim of this chapter is to build up a general view to the two-phase Taylor flows in capillaries which allows to describe mathematically the structure (length of the bubbles/droplets of dispersed phase - plugs and the droplets of continuous phase - slugs) and hydrodynamics of this flow, and further to have a key for heat and mass transfer description and optimization. Methods of multiphase fluid dynamics are used for this aim with some assumptions along. The proposed mathematical models allow to predict with quite high precision the hydrodynamics and mass transfer characteristics of two-phase Taylor flows and to improve design of industrial and lab scale devices.