Laminar liquid–liquid dispersion in the SMX static mixer

Highlights

• Superficial velocity and continuous phase viscosity are major effects on mean droplet diameter.

• Mean droplet diameter decreased with increasing surfactant concentration.

• Droplet size distributions were measured for above process parameters.

• Primary droplet diameter is related to the surface area to void volume ratio of the mixer elements.

• Model for mean droplet diameter based on drop breakup work and interfacial tension.

Abstract

The liquid–liquid dispersion of two immiscible viscous fluids was studied in an SMX static mixer in the laminar flow regime. The dispersed and continuous liquid phases were silicone oils and aqueous solutions of high fructose corn syrup, respectively. Several different phase viscosities were used and the effect of interfacial tension was examined by adding different concentrations of sodium dodecyl sulphate in the aqueous phase. Flow rates of the two phases were varied, and the effect of the volume fraction (holdup) of dispersed phase was explored for a few cases. The droplets were photographed with backlighting and the images were analysed using the Hough transform method. The drop size distributions for each set of conditions were typically obtained on the basis of about 200 images. Mean drop size was expressed as the mass mean diameter D₄₃.

It was found that the “tail” at the higher end of the droplet size distribution decreased with increasing superficial velocity and continuous phase viscosities and the same effect was seen in the values of D₄₃. It was also found that D₄₃ decreased with lowering of the interfacial tension. The effect of the dispersed phase viscosity was significant only at non-zero surfactant concentrations. The holdup was found to have a minimal effect on D₄₃.

A two-stage breakup model has been developed relating D₄₃ to the capillary number. The model uses the concept that primary drops are formed near the entry to the mixer, with a size determined by the spacing between the cross bars in the element. They are then further broken up by a hydrodynamic mechanism based on an energy balance between the energy input due to the viscous flow, and the surface energy increase due to the breakup of the primary drops. This model provides an approximate basis for correlating the data on D₄₃.

Introduction

Motionless mixers or static mixers have been in use since the 1970s (Thakur et al., 2003). They are found in a wide array of industries including grain processing, pharmaceuticals and cosmetics, petrochemicals, refining, and specialty chemicals. They are used in continuous processes in both distributive and dispersive mixing applications.

In general static mixers are more energy efficient than continuous stirred tanks with rotating impellers and their use is favoured for systems that require relatively short residence times and plug flow conditions, for example in the blending or dispersing of fluids that are sensitive to high shear. They are also a more cost effective option for high pressure services. These benefits are realized because of the static mixer's mechanical simplicity and compactness.

A typical static mixer contains a series of mechanical inserts, chosen to suit a particular application and to optimize the mixing performance. These inserts can be broadly categorized according to twisted-ribbon, plate and structured geometries. The twisted-ribbon type is ideal for mixing of low viscosity fluids (such as gas–liquid dispersions) under turbulent conditions. Plate type mixers are also used for applications in the turbulent flow regime, as these designs create vortices. Structured packings have more complex geometry and are often placed such that each cartridge is oriented 90° relative to its neighbours. The most versatile in this category are the SMX and SMXL types (Sulzer Chemtech USA, Inc., Tulsa, Oklahoma) which have geometries with cross bars angled at 45° and 30° for SMX and SMXL, respectively. The SMX packing, which is studied in this work, is said to be the best design choice for plug flow in tubular reactors and for blending and dispersing high viscosity fluids in the laminar flow regime (Paul et al., 2004, p. 428).

In order to scale up static mixers reliably in liquid–liquid dispersion applications, it is necessary to develop correlations or fundamental models to predict key characteristics such as pressure drop, mean droplet size and size distributions. The latter two characteristics depend on the fluid behaviour of multiple phases, which is affected by the two liquid phase viscosities and interfacial tension. Such correlations and basic insights also help to optimize the packing geometry for better performance. In liquid–liquid dispersions with SMX packing for example, there is a strong industrial motivation to eliminate the occurrence of oversized droplets in order to produce a more uniform droplet size distribution.

Much numerical and experimental work has been done in the area of droplet breakup since the early contribution by Grace (1982). For example, Rauline et al. (1998) have done numerical investigations to characterize elongational flow in various static mixers. Liu (2005) has done numerical and experimental studies to study flow fields inside an SMX mixer. He focused on single drop breakup in the laminar regime (Liu et al., 2005). Direct investigations of droplet size distribution in SMX mixers have been done by Legrand et al. (2001), Rama Rao et al. (2007), Fradette et al. (2007), Theron et al. (2010) and Das et al. (2005). Legrand et al. (2001) studied droplet dispersion in the turbulent regime and have based their correlations on the classical Kolmogorov theory, whereas Fradette et al. (2007) studied dispersion in the laminar regime. In all these studies, a major limiting factor was the measurement of droplet size distribution. In most cases, droplet size measurement was done using the micro encapsulation technique where the droplets were hardened at the surface by means of interfacial polymerization. Rama Rao et al. (2007) and Fradette et al. (2007) used image/video capture and then manually counted and measured the droplets to obtain a distribution. In the latter case the detailed measurements seriously limited the amount of data that could be acquired. These limitations can be reduced by automated data collection and analysis which can help experimenters to conduct more runs under different conditions, and come up with better correlations.

Therefore this work has two research objectives. The first is the capture of the droplet size distribution based on the application of computer vision algorithms for automated measurement. The second objective is the collection of substantial droplet size distribution data with the SMX elements in the laminar regime under varying viscosity ratios, holdups and most importantly under varying interfacial tension. This data will be used to develop a model for correlating the droplet size distribution with the variables involved.