Population balances combined with computational fluid dynamics : a modeling approach for dispersive mixing in a high pressure homogenizer

High pressure homogenization is at the heart of many emulsification processes in the food, personal care and pharmaceutical industry. The droplet size distribution is an important property for product quality and is aimed to be controlled in the process. Therefore a population balance model was built in order to predict the droplet size distribution subject to various hydrodynamic conditions found in a high pressure homogenizer. The hydrodynamics were simulated using Computational Fluid Dynamics and the turbulence was modeled with a RANS k–e model. The high energy zone in the high pressure homogenizer was divided into four compartments. The compartments had to be small enough to secure nearly homogeneous turbulent dissipation rates but large enough to hold a population of droplets. A population balance equation describing breakage and coalescence of oil droplets in turbulent flow was solved for every compartment. One set of parameters was found which could describe the development of the droplet size distribution in the high pressure homogenizer with varying pressure drop. An improvement of 65% was found compared to the same model containing just one compartment. The compartment approach may provide an alternative to direct coupling of CFD and population balances

Modeling of Complex Processes in Turbulent Flow of Unstable Emulsions of Immiscible Liquids

Turbulent flows of emulsions are associated with the processes of breakage, coalescence and sedimentation of droplets of dispersed liquid. Mechanisms of these physical phenomena that form the equilibrium composition of the droplets of dispersed phase are predetermined by the structure of turbulence. Spectrum of distribution of the dispersed droplets according to the size determines in turn the nature of the interaction with the continuous medium. Therefore, a hydrodynamic model for unstable emulsion (CFD) is completed by discrete population balance model (DPB). It reflects the state of the dispersed phase of the emulsion required to construct an adequate model for CFD. A joint application requires the coordination of the composition and structure of these models for formalizing of the complex interrelationships of physical phenomena in the continuous medium and the dispersed phase of the emulsion. The key advantages of such specification of the overall structure of the partial models of the CFD consist in that model includes only the mechanisms of breakup, coalescence and sedimentation of the droplets of the dispersed phase, which are really work in the given conditions. Using of a priori theoretical information in the form of mechanisms of basic physical phenomena (MBPP) is proposed, which is necessary for obtaining the desired particular solutions of applied problems on the basis of common CFD and DPB models

Investigation on liquid-liquid dispersion in stirred tanks through experimental approach and computational fluid dynamic (CFD)

Stirred tanks have a vital role in chemical engineering industries. Among the various applications of stirred tanks, mixing of two immiscible liquid phases is of interest in chemical processes. Mixing of two immiscible liquids in the stirred tank is an integral part of achieving a stable emulsion, which impacts the product quality. The design of the stirred tanks including but not limited to the geometry and dimensions of the vessel, the location, size, and the type of the impeller, fluid rheology, and the volume fraction of dispersed phase relies on comprehensive knowledge about the liquid-liquid mixing performance. One of the major factors affecting the stability of liquid-liquid dispersion is droplet size distribution (DSD) of dispersed phase. The study of DSD in liquid-liquid dispersions still relies on experimental data. The main objective of this study is to evaluate the effect of dispersed phase viscosity, volume fraction, and agitation speed on dilute liquid-liquid dispersions. Therefore, the liquid-liquid dispersion in stirred tank has been evaluated through electrical resistance tomography (ERT), focused beam reflectance measurement (FBRM), and computational fluid dynamics (CFD). ERT provides a non-intrusive online measurement to evaluate the mixing hydrodynamic of dispersion in the tank. FBRM technique is an online particle size measurement technique which evaluates the effect of mixing process on particle interactions and droplet size distribution. Using CFD coupled with population balance modeling (PBM) is the last step toward complete analysis of liquid-liquid dispersion process

Prediction of Emulsion Drop Size Distributions with Population Balance Equation Models to Enable Emulsified Product Design

Oil-in-water emulsions are ubiquitous dispersed phase systems with diverse applications in consumer products, processed foods, and the pharmaceutical industry. Emulsion formulation variables and process operating conditions both impact the drop size distribution, a key property that influences emulsion rheology, stability, texture, and appearance. A typical emulsified product requires the drop size distribution to be maintained within acceptable limits. Due to a lack of quantitative understanding, emulsified products are currently manufactured by combining a broad knowledge of previous product formulations with empirical scientific experimentation. An alternative to trial-and-error experimentation is to utilize a suitable mathematical model to predict the drop size distribution. The population balance equation (PBE) modeling framework particularly is well suited for this problem as size distribution dynamics can be captured using mechanistic functions for drop breakage and coalescence phenomena which occur during emulsification. This thesis presents a PBE modeling framework for high intensity emulsification processes including high pressure homogenizers and colloid mills. It is demonstrated that by incorporating coalescence phenomenon into PBE model with only breakage functions significantly improves model predictions of emulsion drop size distributions at high oil-to-surfactant ratios. To make the model more realistic, the effect of surface coverage of surfactant molecules is added to the coalescence function which improves the extensibility of the model over different surfactant types. To extend model predictability over a large range of surfactant and oil concentrations, a new drop breakage model is formulated; and to capture the change in emulsion viscosity due to changes in oil and surfactant concentrations, the PBE model is coupled with an experimentally fitted emulsion viscosity model. Furthermore, it is demonstrated that use of a dynamic surface coverage model over an equilibrium model, improves the predictions of drop size distribution in both “surfactant rich” and “surfactant limited” regimes. In this thesis, the PBE model is also utilized to optimally achieve target emulsion drop size distributions by controlling the number of homogenization passes and the pressure of each pass. The model predictions are successfully validated by performing homogenization experiments using the optimal formulation and homogenization variables. Apart from developing models for the high pressure homogenization, this thesis presents a new model for emulsification in colloid mill obtained by formulating new mechanistic breakage frequency and daughter drop distribution functions. The predictions of the new model are significantly better than predictions obtained using models with conventional daughter drop distribution functions

Applications of CFD Simulations on Chemical Processing Equipment Designs

The objective of this work is to achieve process intensification by seeking optimal equipment design with CFD investigations. In this work, two projects on chemical equipment design have been discussed. The first project is on design and optimization of fractal distributor in a novel ion-exchanger. Flow distributors are adopted extensively by chemical industry to distribute an incoming process stream uniformly to the downstream equipment. Currently, the performance of chemical equipment installed with conventional distributor is severely undermined due to poor flow distribution. For conventional distributors such as spray nozzle distributors, their design concept is based on maintaining very high pressure drop across the whole device with very little opening areas through orifices. Fractal distributors can achieve high outlet densities with low pressure drop due to their inherent self-similarity feature. To investigate the performance of fractal distributor, a novel ion-exchanger equipped with fractal distributor was proposed and manufactured. With comparison against conventional distributor, fractal distributor is proven to be able to offer much better flow distribution inside ion-exchanger by both CFD and experimental investigations. To seek optimal performance, the design space of fractal distributor has been explored with CFD studies. The influence of key design parameters such as channel aspect ratio was investigated and fractal distributor with “deep and narrow” channels were found to achieve superior performance. While conducting large scale design explorations, automation tools were developed to handle massive number of study cases. The second project focuses on design explorations of a novel oil-water separator. The flow pattern was investigated first with single phase studies. An improved design was proposed with draft tube diameter ratio of 0.6 and a larger twisting angle of impeller. The new impeller design was shown to have better separation efficiency from experiments. Later, the design has been studied with multiphase simulation with population balance model. With the challenge of lacking available kernels in low Reynolds number flow, a new coalesce kernel was proposed. The model offers as a comprehensive tool to understand flow pattern and phase separation process inside the device

Investigation of fluid dynamics and emulsification in Sonolator liquid whistles

The Sonolator liquid whistle is an industrial inline mixer used to create complex multiphase mixtures which form components of high value added liquid products. Despite its wide use, this device’s mechanism of operation is not well understood which has led to this combined experimental and computational study to elucidate key phenomena governing drop and jet break-up. The work has focused on single phase Particle Image Velocimetry (PIV) measurements of a model device to validate single phase Computational Fluid Dynamics (CFD) simulations to gain basic understanding of the flow fields which are responsible for the breakage behaviour, assuming dilute dispersions. Multiphase pilot plant experiments on a silicone oil-water-SLES emulsion have been used to characterise the droplet size reduction in a pilot scale Sonolator for both dilute and medium concentrations of the dispersed phase. An empirical model of droplet size was constructed based on pressure drop, dispersed phase viscosity and surfactant concentration. This empirical model was compared with the droplet breakage theories of Hinze, Walstra and Davies. Extra work mentioned in the appendices includes studies on cavitation in the Sonolator, with the cavitating flow conditions identified and the contribution to emulsification considered, and the usage of population balance methods to simulate droplet breakup in the environment indicated by CFD/PIV studies in order to investigate how the droplet size distributions measured in pilot plant studies came about

Design and fabrication of novel microfluidic systems for microsphere generation

In this thesis, a study of the rational design and fabrication of microfluidic systems for microsphere generation is presented. The required function of microfluidic systems is to produce microspheres with the following attributes: (i) the microsphere size being around one micron or less, (ii) the size uniformity (in particular coefficient of variation (CV)) being less than 5%, and (iii) the size range being adjustable as widely as possible. Micro-electro-mechanical system (MEMS) technology, largely referring to various micro-fabrication techniques in the context of this thesis, has been applied for decades to develop microfluidic systems that can fulfill the foregoing required function of microsphere generation; however, this goal has yet to be achieved. To change this situation was a motivation of the study presented in this thesis. The philosophy behind this study stands on combining an effective design theory and methodology called Axiomatic Design Theory (ADT) with advanced micro-fabrication techniques for the microfluidic systems development. Both theoretical developments and experimental validations were carried out in this study. Consequently, the study has led to the following conclusions: (i) Existing micro-fluidic systems are coupled designs according to ADT, which is responsible for a limited achievement of the required function; (ii) Existing micro-fabrication techniques, especially for pattern transfer, have difficulty in producing a typical feature of micro-fluidic systems - that is, a large overall size (~ mm) of the device but a small channel size (~nm); and (iii) Contemporary micro-fabrication techniques to the silicon-based microfluidic system may have reached a size limit for microspheres, i.e., ~1 micron. Through this study, the following contributions to the field of the microfluidic system technology have been made: (i) Producing three rational designs of microfluidic systems, device 1 (perforated silicon membrane), device 2 (integration of hydrodynamic flow focusing and crossflow principles), and device 3 (liquid chopper using a piezoelectric actuator), with each having a distinct advantage over the others and together having achieved the requirements, size uniformity (CV ≤ 5%) and size controllability (1-186 µm); (ii) Proposing a new pattern transfer technique which combines a photolithography process with a direct writing lithography process (e.g., focused ion beam process); (iii) Proposing a decoupled design principle for micro-fluidic systems, which is effective in improving microfluidic systems for microsphere generation and is likely applicable to microfluidic systems for other applications; and (iv) Developing the mathematical models for the foregoing three devices, which can be used to further optimize the design and the microsphere generation process