CFD simulation of aggregation and breakage processes in laminar Taylor-Couette flow

An experimental and computational investigation of the effects of local fluid shear rate on the aggregation and breakage of approximately 10 microm latex spheres suspended in an aqueous solution undergoing laminar Taylor-Couette flow was carried out according to the following program. First, computational fluid dynamics (CFD) simulations were performed and the flow field predictions were validated with data from particle image velocimetry experiments. Subsequently, the quadrature method of moments (QMOM) was implemented into the CFD code to obtain predictions for mean particle size that account for the effects of local shear rate on the aggregation and breakage. These predictions were then compared with experimental data for latex sphere aggregates (using an in situ optical imaging method) and with predictions using spatial average shear rates. The mean particle size evolution predicted by CFD and QMOM using appropriate kinetic expressions that incorporate information concerning the particle morphology (fractal dimension) and the local fluid viscous effects on aggregation collision efficiency match well with the experimental data.     

Analysis of the aggregation-fragmentation population balance equation with application to coagulation

Coagulation of small particles in agitated suspensions is governed by aggregation and breakage. These two processes control the time evolution of the cluster mass distribution (CMD) which is described through a population balance equation (PBE). In this work, a PBE model that includes an aggregation rate function, which is a superposition of Brownian and flow induced aggregation, and a power law breakage rate function is investigated. Both rate functions are formulated assuming the clusters are fractals. Further, two modes of breakage are considered: in the fragmentation mode a particles splits into w2 fragments of equal size, and in the erosion mode a particle splits into two fragments of different size. The scaling theory of the aggregation-breakage PBE is revised which leads to the result that under the negligence of Brownian aggregation the steady state CMD is self-similar with respect to a non-dimensional breakage coefficient theta. The self-similarity is confirmed by solving the PBE numerically. The self-similar CMD is found to deviate significantly from a log-normal distribution, and in the case of erosion it exhibits traces of multimodality. The model is compared to experimental data for the coagulation of a polystyrene latex. It is revealed that the model is not flexible enough to describe coagulation over an extended range of operation conditions with a unique set of parameters. In particular, it cannot predict the correct behavior for both a variation in the solid volume fraction of the suspension and in the agitation rate (shear rate).     

Analysis of droplet behavior in a de-oiling hydrocyclone

A mechanical separation process in a de-oiling hydrocyclone is described in which disperse oil droplets are separated from a continuous water phase. This separation process is influenced by droplet breakage and coalescence. Based on experimental data and simulation results in a stirred tank, a modified breakage model, which can be applied to droplet breakage in the de-oiling hydrocyclone, is developed. Then, a simulation model is developed coupling the numerical solution of the flow field in the hydrocyclone based on computational fluid dynamics (CFD) with population balances. The homogenous discrete method and the inhomogeneous discrete method are applied for solving the population balance model (PBM). The investigations show that the numerical results obtained by the simulation model coupled with the modified PBM using the inhomogeneous discrete method are in good accordance with experimental data under a high flow rate. According to this simulation model, the effect of three different inlet designs on the separation efficiency of the de-oiling hydrocyclone has been discussed. The results indicate that the separation efficiency of the de-oiling hydrocyclone can be improved with an appropriate inlet design.     

Population balance modeling of aggregation and breakage in turbulent Taylor-Couette flow

An experimental and computational study of aggregation and breakage processes for fully destabilized polystyrene latex particles under turbulent-flow conditions in a Taylor-Couette apparatus is presented. To monitor the aggregation and breakage processes, an in situ optical imaging technique was used. Consequently, a computational study using a population balance model was carried out to test the various parameters in the aggregation and breakage models. Very good agreement was found between the time evolution of the cluster size distribution (CSD) calculated with the model and that obtained from experiment. In order to correctly model the left-hand side of the CSD (small clusters), it was necessary to use a highly unsymmetric fragment-distribution function for breakage. As another test of the model, measurements with different solid volume fractions were performed. Within the range of the solid volume fractions considered here, the steady-state CSD was not significantly affected. In order to correctly capture the right-hand side of the CSD (large aggregates) at the higher solid volume fraction, a modified aggregation rate prefactor was used in the population balance model.     

Computational Analysis of Mixing and Scale-Up in Emulsion Polymerization Reactors

Summary: A hybrid multi-zonal/computational fluid dynamics (CFD) framework is currently being developed to aid in the scale-up of high solid content latex production and processing. Poly3D, a commercial laminar CFD code tailored to modelling the mixing of non-Newtonian fluids, has been coupled to a population balance model via a customized interface. CFD is used to generate flow fields inside a series of reactors; this information is then transferred to a multi-zone population balance model to assess the impact of non-homogenous mixing on the evolution of the latex particle size distribution (PSD) when concentrated latex suspension is altered via the addition of a coagulant. The rheological properties of high solid content latexes are sensitive to changes in the PSD, so the flow field is periodically updated if significant changes in the rheological properties of the latex are detected in any of the zones. The details of the models comprising the framework are presented and the utility of the framework is demonstrated.     

Quadrature method of moments for aggregation-breakage processes

Investigation of particulate systems often requires the solution of a population balance, which is a continuity statement written in terms of the number density function. In turn, the number density function is defined in terms of an internal coordinate (e.g., particle length, particle volume) and it generates integral and derivative terms. Different methods exist for numerically solving the population balance equation. For many processes of industrial significance, due to the strong coupling between particle interactions and fluid dynamics, the population balance must be solved as part of a computational fluid dynamics (CFD) simulation. Such an approach requires the addition of a large number of scalars and the associated transport equations. This increases the CPU time required for the simulation, and thus it is clear that it is very important to use as few scalars as possible. In this work the quadrature method of moments (QMOM) is used. The QMOM has already been validated for crystal growth and aggregation; here the method is extended to include breakage. QMOM performance is tested for 10 different cases in which the competition between aggregation and breakage leads to asymptotic solutions.     

Characterization of the Engineering Flow in a Miniaturised Bioreactor by Computational Fluid Dynamics

Three approaches based on computational fluid dynamics(CFD) techniques have been assessed for their ability to describe the engineering flow environment in a miniaturized mechanically agitated bioreactor. The three approaches tested were the source-sink(SS), the multiple reference frames (MRF) and the sliding grids(SG). In all the cases, the predictions of the velocity components agree with reported experimental data. However, the analysis of the results of the turbulent intensities predicted by the three approaches indicates the MRF and the SG techniques under predicted turbulent intensities are comparable to both experimental measurements and the SS method. The predicted power number and pumping number based on the SS ap-proach are closer to typical reported experimental values compared to those obtained from the MRF and SG methods.     

Prediction of emulsion particle sizes using a computational fluid dynamics approach

For many food products emulsification processes play an important role. Examples are ice cream, spreads, sauces, etc. As is well known, droplet break-up and coalescence phenomena are the local processes underlying the control of particle size in an emulsion process. Quite a number of studies have generated scaling laws which can be easily applied and which are useful in the design of a process. However, the prediction of particle sizes in an inhomogeneous flow, where the flow velocity is changing spatially in strength and direction and with time, is not yet well established. For one-phase flows computational fluid dynamics (CFD) methodologies are in use to predict details on the flow with quite some success. This methodology has been extended to capture the dispersed phase in an efficient way. The essence is that break-up and coalescence processes determine source terms in a transport equation for the moments of the particle size distribution, while velocity vectors as obtained in the one-phase CFD simulation determine the convective term. This method allows particle size prediction in any equipment. The approach is illustrated for the particle size evolution of an oil-in-water emulsion, for a phase-separated biopolymeric mixture (a so-called water-in-water emulsion) and for the escape of the included oil droplets from a double emulsion of the type oil-in-water-in-oil. In all cases experimental results are compared with simulation results, which match very well. This shows the strength of the method.     

Shear Flow of Aggregated Nanosuspensions–Fundamentals and Model Formulation

Theoretical aspects of shear flows of aggregated nanosuspensions are presented and applied to formulate appropriate models. Technological context of this work is related to formulation of stable suspensions of nanoparticles of specific rheological properties by breaking‐up nanoparticle clusters in high shear devices. Accordingly the population balance modeling is applied with kinetics including effects of aggregation, breakage and restructuring of aggregates; effects of suspension rheology on the flow are included as well. Rheological model includes the effect of clustering of primary nanoparticles. Population balances are solved using QMOM that is linked to the CFD code. Results of numerical simulations are presented for laminar and turbulent flows.     

Experimental and modeling study of breakage and restructuring of open and dense colloidal aggregates

In this work we present experimental and simulation analysis of the breakage and restructuring of colloidal aggregates in dilute conditions under shear. In order to cover a broad range of hydrodynamic and interparticle forces, aggregates composed of primary particles with two sizes, d(p) = 90 and 810 nm, were generated. Moreover, to understand the dependence of breakage and restructuring on the cluster structure, aggregates grown under stagnant and turbulent conditions, having substantially different initial internal structures with fractal dimension d(f) equal to 1.7 and 2.7, respectively, were used. The aggregates were broken by exposing them to a well-defined elongational flow produced in a nozzle positioned between two syringes. To investigate the evolution of aggregate size and morphology, respectively, the mean radius of gyration, , and d(f) were monitored during the breakup process using light scattering and confocal laser scanning microscopy. It was found that the evolution of aggregates' fractal dimension during breakage is solely controlled by their initial structure and is independent of the primary particles size. Similarly, the scaling of the steady-state vs the applied hydrodynamic stress is independent of primary particle size, however, depends on the history of aggregate structure. To quantitatively explain these observations, the breakage process was modeled using stokesian dynamics simulations incorporating DLVO and contact interactions among particles. The required flow-field for these simulations was obtained from computational fluid dynamics. The complex flow pattern was simplified by considering a characteristic stream line passing through the zone with the highest hydrodynamic stress inside the nozzle, this being the most critical flow condition experienced by the clusters. As the flow-field along this streamline was found to be neither pure simple shear nor pure extensional flow, the real flow was approximated as an elongational flow followed by a simple shear flow, with a stepwise transition between them. Using this approach, very good agreement between the measured and simulated aggregate size values and structure evolution was obtained. The results of this study show that the process of cluster breakup is very complex and strongly depends on the initial aggregate structure and flow-field conditions.     

Study on laminar viscosity and zero shear viscosity of latex systems

The flowing nature and rheological properties of polymethyl methacrylate latex systems in a coaxial cylinder viscometer were studied on the basis of laminar shear flow model and rheological experimental data. The physical meaning of laminar viscosity (eta(i,j)) and zero shear viscosity (eta(0)) were described. We assumed that laminar shear flows depended on position and shear time, so microrheological parameters were the function of position and shear time. eta(i,j) was the viscosity of any shear sheet i between two neighboring laminar shear flows at time t; j was denoted as j=t/Deltat; and Deltat was the interacting time of two particles or two laminar shear flows. tau(i,j) and gamma(i,j) were shear stress and shear rate of any shear sheet i at j moment. According to Newton regulation tau(i,j)=eta(i,j)gamma(i,j), apparent viscosity eta(a) should be a statistically mean value of j shear sheets laminar viscosity at j moment, i.e., eta(a)= summation operator(i=j)eta(i,j)gamma(i,j)/ summation operator(i=j)gamma(i,j). eta(0) was defined as shear viscosity between a laminar shear flow and a still fluid surface, i.e., eta(0)=(tau(i,j)/gamma(i,j))(j-i-->0). These new ideas described above may be helpful in the study of the micromechanisms of latex particle systems and worthy of more research.     

Simulation of aggregating particles in complex flows by the lattice kinetic Monte Carlo method

We develop and validate an efficient lattice kinetic Monte Carlo (LKMC) method for simulating particle aggregation in laminar flows with spatially varying shear rate, such as parabolic flow or flows with standing vortices. A contact time model was developed to describe the particle-particle collision efficiency as a function of the local shear rate, G, and approach angle, θ. This model effectively accounts for the hydrodynamic interactions between approaching particles, which is not explicitly considered in the LKMC framework. For imperfect collisions, the derived collision efficiency [?=1 - ∫(0)(π/2) sinθ exp(-2cotθΓ(agg)/G)dθ] was found to depend only on Γ(agg)∕G, where Γ(agg) is the specified aggregation rate. For aggregating platelets in tube flow, Γ(agg)=0.683 s(-1) predicts the experimentally measured ε across a physiological range (G = 40-1000 s(-1)) and is consistent with α(2b)β(3)-fibrinogen bond dynamics. Aggregation in parabolic flow resulted in the largest aggregates forming near the wall where shear rate and residence time were maximal, however intermediate regions between the wall and the center exhibited the highest aggregation rate due to depletion of reactants nearest the wall. Then, motivated by stenotic or valvular flows, we employed the LKMC simulation developed here for baffled geometries that exhibit regions of squeezing flow and standing recirculation zones. In these calculations, the largest aggregates were formed within the vortices (maximal residence time), while squeezing flow regions corresponded to zones of highest aggregation rate.     

Rheometry-PIV of shear-thickening wormlike micelles

The shear-thickening behavior of an equimolar semidilute aqueous solution of 40 mM/L cetylpyridinium chloride and sodium salicylate was studied in this work by using a combined method of rheometry and particle image velocimetry (PIV). Experiments were conducted at 27.5 degrees C with Couette, vane-bob, and capillary rheometers in order to explore a wide shear stress range as well as the effect of boundary conditions and time of flow on the creation and destruction of shear-induced structures (SIS). The use of the combined method of capillary rheometry with PIV allowed the detection of fast spatial and temporal variations in the flow kinematics, which are related to the shear-thickening behavior and the dynamics of the SIS but are not distinguished by pure rheometrical measurements. A rich-in-details flow curve was found for this solution, which includes five different regimes. Namely, at very low shear rates a Newtonian behavior was found, followed by a shear thinning one in the second regime. In the third, shear banding was observed, which served as a precursor of the SIS and shear-thickening. The fourth and fifth regimes in the flow curve were separated by a spurtlike behavior, and they clearly evidenced the existence of shear-thickening accompanied by stick-slip oscillations at the wall of the rheometer, which subsequently produced variations in the shear rate under shear stress controlled flow. Such a stick-slip phenomenon prevailed up to the highest shear stresses used in this work and was reflected in asymmetric velocity profiles with spatial and temporal variations linked to the dynamics of creation and breakage of the SIS. The presence of apparent slip at the wall of the rheometer provides an energy release mechanism which leads to breakage of the SIS, followed by their further reformation during the stick part of the cycles. In addition, PIV measurements allowed the detection of apparent slip at the wall, as well as mechanical failures in the bulk of the fluid, which suggests an extra contribution of the shear stress field to the SIS dynamics. Increasing the residence time of the fluid in the flow system enhanced the shear-thickening behavior. Finally, the flow kinematics is described in detail and the true flow curve is obtained, which only partially fits into the scheme of existing theoretical models for shear-thickening solutions.     

Implementation of Lees-Edwards periodic boundary conditions for direct numerical simulations of particle dispersions under shear flow

A general methodology is presented to perform direct numerical simulations of particle dispersions in a shear flow with Lees-Edwards periodic boundary conditions. The Navier-Stokes equation is solved in oblique coordinates to resolve the incompatibility of the fluid motions with the sheared geometry, and the force coupling between colloidal particles and the host fluid is imposed by using a smoothed profile method. The validity of the method is carefully examined by comparing the present numerical results with experimental viscosity data for particle dispersions in a wide range of volume fractions and shear rates including nonlinear shear-thinning regimes.     

Investigation of droplet size distribution for liquid-liquid emulsions in Taylor-Couette flows

In this paper, we investigate oil-in-water emulsions in a Taylor-Couette flow. A high-speed camera was employed to record the formation of those emulsions, and image processing was used to obtain the diameter of the droplets. No surfactants were added in order to study the pure effect of the fluid dynamical forces on the droplets. The results for three different oil-in-water emulsions show that the Sauter mean diameter considerably depends on the local shear rate and the material properties and that the droplet size distribution follows a log-normal distribution. We, therefore, propose to express the Sauter mean diameter normalized by Prandtl mixing length in terms of a correlation, which is based on the Kolmogorov turbulence theory. This correlation subsequently depends on the local shear rate and the material properties such as viscosity, density, and interfacial tension. The predictions of the correlation show fairly good agreement with the experimental measurement the Sauter mean diameter. Finally, comparing the predictions of the correlation to the data presented by Eskin et al. [Chem. Eng. Sci. 161 36–47; 2017] shows excellent agreement in the case, where the droplets are larger than the Kolmogorov length scale.     

Investigation of the Hydrate Plugging and Non-Plugging Properties of Oils

Three laboratories (Norwegian Institute of Science and Technology [NTNU], Institut Français du Pétrole [IFP], and the Colorado School of Mines [CSM]) determined hydrate plug formation characteristics in three oils, each in three conditions: (1) in their natural state, (2) with asphaltenes removed, and (3) with naturally occurring acids removed from the oil. The objective was to determine the major variables that affect hydrate plugging tendencies in oil-dominated systems, to enable the flow assurance engineer to qualitatively assess the tendency of an oil to plug with hydrates. In the past, it was indicated that chemical effects, for example, water-in-oil/hydrate-in-oil (emulsion/dispersion) stability, prevented hydrate plugs. For example, deasphalted oils provided low emulsion/dispersion stability and thus hydrate particles aggregated. In contrast pH 14-extracted oils were reported to remove stabilizing naphthenic acids, causing asphaltene precipitation on water/hydrate droplets, stabilizing the emulsion/dispersion to prevent aggregation and pluggage. This work suggests that in addition to chemistry, shear can enable plug-free operation in the hydrate region. High shear can prevent hydrate particle aggregation, while low shear encourages particle aggregation and plugging. As a result, flow assurance engineers may be able to forecast hydrate plug liability of an oil by a combination of chemistry and flow variables, such as: a) measurements of live oil emulsion stability, b) predictions of flow line shear, and c) knowledge of water cut. Plug formation qualitative trends are provided for the above three variables. Implications for flow assurance are given.     

Effect of depletion interactions on transport of colloidal particles in porous media

The influence of depletion interactions on the transport of micrometer-sized, negatively charged polystyrene latex particles through porous media was studied by analysis of particle breakthrough curves as a response to short-pulse particle injections to the inlet of a packed column of glass beads. The column outlet latex particle concentration profiles and the total amount of particles exiting the column were determined as a function of the concentration of small, silica nanoparticles in the solution and the bulk flow rate. Because of similar charges, the silica particles do not adsorb to either the latex particles or glass beads and thus induce an attractive depletion force between the latex particles and glass bead collectors. The total column outlet latex particle amount was calculated by integrating the measured breakthrough concentration curve and compared to the known amount of injected particles at the column inlet. It was found that the particle recovery was a decreasing function of the silica nanoparticle concentration and the carrier fluid residence time, and an increasing function of the velocity in the bed. In addition, removing the silica nanoparticles from the flowing solution caused a second outlet peak to appear, suggesting that some of the polystyrene particles were captured in secondary energy wells. The experimental data were interpreted using the predicted potential energy profile between a single particle and a glass bead, which was assumed to consist of electrostatic, van der Waals, and depletion components. The results indicate that secondary energy wells significantly affect particle transport behavior through porous media.