Turbulent Liquid-liquid Dispersions Research Articles

Effect of surfactants and interfacial rheology on equilibrium drop size in turbulent liquid-liquid dispersions

Surfactants are often required to stabilize liquid-liquid dispersions produced by high shear mixers. Due to the high power input, drops are deformed rapidly in the dispersion zone so the dynamic interfacial properties governed by the surfactant adsorption rate can have a significant impact on the resulting drop size. The objective of this work is to develop a fundamental link between surfactant adsorption dynamics, interfacial properties, and turbulent emulsification processes. To ensure constant bulk surfactant concentration during dispersion, equilibrium drop size for dilute dispersions produced by a batch rotor-stator mixer were studied. Silicone oils of various viscosity were dispersed in aqueous nonionic surfactant solutions. Drop size distributions (DSD) were measured via a video microscopy/automated image analysis technique. Equilibrium interfacial tension was measured via a pendant drop technique, as a function of surfactant concentration. The dynamic surface tension was similarly measured. The data were fit to the Langmuir adsorption isotherm and the long-times approximation to the Ward – Tordai equation and the adsorption parameters and surfactant diffusivities so obtained were employed, with an estimate of the drop deformation timescale, to estimate the surface dilational modulus (Esd) or Marangoni stress acting on the drop’ surface due to interfacial tension gradients. Trends observed in the measured equilibrium mean drop size and DSD are explained in terms of the interfacial and rheological properties. Below the CMC, Esd peaks and the drop size increases with bulk surfactant concentration, despite a decrease in equilibrium interfacial tension. Above the CMC, Marangoni stresses are small but the presence of the surfactant still modifies the rheology of the interface, increasing the effective viscosity of the drops. A comprehensive set of mechanistic models for drop size in turbulent flows, based on Kolmogorov-Hinze theory, was developed and modified to partially account for the effect of surfactants via an appropriately defined effective viscosity. The approach allows integration of surfactant phenomena into widely accepted correlations for drop size in surfactant free systems.

Enhancement of turbulent liquid-liquid dispersions in a round-bottom stirred tank equipped by a flexible impeller

Stirred tanks have been widely used for liquid-liquid mixing in the chemical industry. In the present work, the influences of flexible impeller on the hydrodynamic characteristics and droplet size distribution of oil in water dispersions were investigated using experimental and numerical approaches. The one-way Fluid Structural Interaction (FSI) analysis was carried out to model the geometry of the flexible impeller used in CFD simulations. Computational fluid dynamics (CFD) was coupled with the population balance model (PBM) to simulate the liquid-liquid dispersion process in the stirred tank. The numerical model was validated by the experimental results. Compared with the rigid impeller, the flexible impeller generates a more uniform distribution of turbulent kinetic energy and turbulent dissipate rate in the stirred tank. Compared with the case of rigid impeller, the region indicating the trailing vortices behind the impeller blades was significantly reduced by the flexible impeller. It was found the flexible impeller with a smaller elastic modulus can result in narrower droplet size distributions in turbulent dispersion process. Its peak value of the number fraction frequency was in the range of 244-308μm while that was 308-388μm for the case of rigid impeller. It was found that most of the dispersed phase droplets occur in the turbulent inertial subrange regime. Related correlations between the Sauter mean diameter and local turbulent field were also obtained. The shape factor accounting for the effects of the impeller shape on the Sauter mean diameter was found to be dependent on the material property of the impeller blades, such as the Poisson's ratio and elastic modulus.

Using the full turbulence spectrum for describing droplet coalescence and breakage in industrial liquid-liquid systems: Experiments and modeling

A generalized model for breakage and coalescence kernels valid for the entire spectrum of turbulence is proposed and validated. Most of the available kernels in the literature indeed assume that in a turbulent liquid-liquid dispersion, the dispersed droplets have dimension in the inertial subrange, and are affected by eddies with size in the same subrange. These kernels are based on the Kolmogorov second-order structure function, which is valid only in the inertial subrange. However, in most industrially encountered situations, many droplets may have a size in the dissipation range, where the Kolmogorov second-order structure function does not apply. Therefore, a more general description of the energy transferred between these droplets and the turbulent eddies is needed to properly model breakage and coalescence events.In this work, the Coulaloglou and Tavlarides (1977) breakage and coalescence kernels have been modified through the implementation of the second-order structure function proposed by Davidson (2004), along with the Pope (2000) energy spectrum. Turbulent liquid-liquid dispersion experiments at high continuous phase viscosity are performed to test and validate the model. The generalized model is able to predict the experimental Sauter mean diameters at different viscosities, turbulent conditions and dispersed-phase volume fraction without any adjustment of the kernel parameters.

The Influence of Internal Intermittency, Large Scale Inhomogeneity, and Impeller Type on Drop Size Distribution in Turbulent Liquid-Liquid Dispersions.

The influence of the impeller type on drop size distribution (DSD) in turbulent liquid-liquid dispersion is considered in this paper. The effects of the application of two impellers, high power number, high shear impeller (six blade Rushton turbine, RT) and three blade low power number, and a high efficiency impeller (HE3) are compared. Large-scale and fine-scale inhomogeneity are taken into account. The flow field and the properties of the turbulence (energy dissipation rate and integral scale of turbulence) in the agitated vessel are determined using the k-ε model. The intermittency of turbulence is taken into account in droplet breakage and coalescence models by using multifractal formalism. The solution of the population balance equation for lean dispersions (when the only breakage takes place) with a dispersed phase of low viscosity (pure system or system containing surfactant), as well as high viscosity, show that at the same power input per unit mass HE3 impeller produces much smaller droplets. In the case of fast coalescence (low dispersed phase viscosity, no surfactant), the model predicts similar droplets generated by both impellers. In the case of a dispersed phase of high viscosity, when the mobility of the drop surface is reduced, HE3 produces slightly smaller droplets.

Inter-phase mass transfer in turbulent liquid-liquid dispersions: A comparative analysis of models

A comparative evaluation of eight models used to predict the dispersed phase mass transfer coefficient was undertaken using recent drop size and mass transfer data obtained under well known and controlled hydrodynamic conditions encountered in screen-type static mixers. A wide range of experimental conditions were covered ( ɛ = 1.5–117 W/kg, ϕ = 0.1–0.47) thereby allowing for proper assessment of the strength and weaknesses of each model. All models failed to properly predict the experimental results over a wide range of design and operating conditions with the exception of those that contain a system-specific adjustable fitting parameter. Although these models yielded reasonably acceptable order-of-magnitude predictions, they could not accurately account for the variations in the different parameters investigated. This shows that proper understanding of the various factors affecting the dispersed phase mass transfer coefficient is still incomplete and highlights the need for phenomenological models that can account for the various physicochemical and hydrodynamic conditions on the dispersed-phase mass transfer coefficient.

Stochastic Simulation of Particulate Dynamic Breakup.

Based on the analysis of dynamic breakup process of particles in particulate systems, a direct stochastic simulation method is proposed in this paper, which is applicable for general population balances with particle breakup. The detailed algorithm is presented. There are two important steps in algorithm: 1. to determine whether a particle breaks up, using the breakup frequency function; 2. to determine the volume of daughter particles for one breakup, using the probability distribution function of daughter particles after the breakup of a mother particle. A calculation example of turbulent liquid-liquid dispersion is given to predict the development of particle size distribution. The calculation results are in very good agreement with the analytical solution from Das (1996).

Coalescence of drops in stirred dispersion. A white noise model for coalescence

Coalescence between two droplets in a turbulent liquid-liquid dispersion is generally viewed as a consequence of forces exerted on the drop-pair squeezing out the intervening continuous phase to a critical thickness. A new synthesis is proposed herein which models the film drainage as a stochastic process driven by a suitably idealized random process for the fluctuating force. While the true test of the model lies in detailed parameter estimations with measurement of drop-size distributions in coalescing dispersions, experimental measurements on average coalescence frequencies lend preliminary support to the model.