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Large-scale human mesenchymal stem cell expansion calls for a bioreaction system, that provides a sufficient growth surface. An alternative to static cultivations systems like cell factories are disposable stirred tank reactors. Here, microcarriers provide the required growth surface, but these make it difficult to achieve a complete homogenization in the bioreactor, while avoiding shear stress. To gain insight into this process, we investigated the impact of different power inputs (0.02–2.6 W m −3 ) on the mixing time (t m ). Whereas t m was inversely proportional to agitation in a one-phase-system, aeration resulted in a constant mixing time at 30–70 rpm. A high microcarrier concentration (30 g L −1 ) and low stirrer speed (30 rpm) in the liquid-solid system caused a 50-fold increase in t m and the formation of a discrete non-mixed upper zone. The effect of the microcarrier concentration on t m became negligible at higher stirrer speeds. In the three-phase system, microcarrier settling was prevented by aeration and a minimal specific power input of 0.6 W m −3 was sufficient for complete homogenization. We confirmed that a low power input during stem cell expansion leads to inhomogeneity, which has not been investigated in the three-phase system up to date. [ABSTRACT FROM AUTHOR]

Computational fluid dynamics (CFD) simulations were performed to predict the floating particles suspension in a baffled tank stirred by a standard Rushton turbine. An Eulerian multiphase model and a standard k- ε turbulence model with mixture properties were used in the CFD simulation. The impeller rotation was solved using a moving reference frame method. Flow pattern, power number and solid holdup distribution were obtained and compared with the results in literature. The effects of operating condition on floating particles suspension characteristics were studied. It indicated that the influences of impeller speed and solid loading on particle suspension varied with particle sizes. For small particles, the impeller speed and solid loading have no obvious effects on solid holdup distribution and suspension quality. For large particles, particle suspension quality becomes better first, and then keeps almost unchanged with enhancing of the impeller speed. Suspension quality is better for higher solid loading of large particles. Within the scope of the present study, solid loading has no great effect on suspension quality. Suspension quality becomes worse with increasing of the particle size. Large particles are easy to accumulate in the centres of the liquid free surface and the upper circular loop, and the vicinity of the shaft. [ABSTRACT FROM AUTHOR]

In this article, two novel numerical methods have been developed for simulating fluid/porous particle interactions in three-dimensional (3D) Stokes flow. The Brinkman-Debye-Bueche model is adopted for the fluid flow inside the porous particle, being coupled with the Stokes equations for the fluid flow outside the particle. The rotating motion of a porous ball and the interaction of two porous balls in bounded shear flows have been studied by these two new methods. The numerical results show that the porous particle permeability has a strong effect on the interaction of two porous balls. [ABSTRACT FROM AUTHOR]

[Display omitted] • A scheme was proposed to realize the harmless motion and accumulation of particles. • The particle suspension was effectively suppression, improving product quality and production efficiency. • The research can provide a basis of field productions concerning control technologies of particles. Particle suspension in a turbulent flow can seriously affect the performance of manufactured products in many industrial processes in which the motion of particles cannot be modeled using the numerical method because of the enormous number of particles. Therefore, in this study, a full-scale computational fluid dynamics (CFD) simulation and a 1/5 scaled-down water model experiment were employed to investigate the flow pattern and dynamic behavior of particles in a continuously stirred vessel system. Based on the understanding of the suspension mechanism of settling particles, a particle-suppression device was designed to realize the harmless movement and deposition of particles. The results showed that the flow guidance and division mechanisms of the particle-suppression device led to the inhibition of particle suspensions. In addition, the optimal parameter combination for the device from the water model experiment combined with the orthogonal experimental design, resulted in a 98.3% reduction in the concentration of suspended particles. The suspension of particles was effectively suppressed, which improves product quality and production efficiency. Reliable results can be achieved by combining CFD simulations and water model experiments. [ABSTRACT FROM AUTHOR]

Slot coating is used in the manufacturing of functional films, which rely on specific particle microstructure to achieve the desired performance. Final structure on the coated film is strongly dependent on the suspension flow during the deposition of the coating liquid and on the subsequent drying process. Fundamental understanding on how particles are distributed in the coated layer enables optimization of the process and quality of the produced films. The complex coating flow leads to shear-induced particle migration and non-uniform particle distribution. We study slot coating flow of non-colloidal suspensions by solving the mass and momentum conservation equations coupled with a particle transport equation using the Galerkin/Finite element method. The results show that particle distribution in the coating bead and in the coated layer is non-uniform and is strongly dependent on the imposed flow rate (wet thickness). © 2016 American Institute of Chemical Engineers AIChE J, 63: 1122-1131, 2017 [ABSTRACT FROM AUTHOR]

This study examines the use of a lattice Boltzmann method framework to study heat transfer behaviours within particle suspensions. This has been done through the use of an adapted interface condition to attempt to resolve the required continuity of temperature and flux at the boundary between the solid and fluid phases. The proposed method is tested against analytical solutions for layered media in both a 1D bar and a radial layout. These tests showed that the model was able to generate results with first order convergence towards the analytical outcomes. The model was then used to examine the behaviour of two moving particles travelling along a channel to illustrate its potential for resolving complex suspension flows. [ABSTRACT FROM AUTHOR]

In this paper, we explore the mechanics and the turbulent structure of two-phase (fluid-solid particle) flow system, for the first time, by considering the dynamic equilibrium coupled with suspended solid particle concentration, fluid flow and energetics of the two-phase flow system. The continuity, momentum and turbulent kinetic energy (TKE) equations of the fluid and the solid phases are treated separately to derive a generalized relationship of the two-phase flow system aided by suitable closure relationships. The results obtained from the numerical solution of resulting equations show that the particle concentration and the TKE diminish with an increase in the Rouse number, while the horizontal velocity component increases. On the other hand, the TKE flux, diffusion and production rates increase with an increase in the Rouse number, while the TKE dissipation rate decreases. In the vicinity of the reference level (that is, the hypothetical level from which the particles come in suspension), the Kolmogorov number increases with an increase in the Rouse number. However, as the vertical distance increases, this behaviour becomes reverse. A close observation of the turbulent length scales reveals that the Prandtl'smixing length decreases with an increase in the Rouse number, but the Taylor microscale and the Kolmogorov length scale increase. [ABSTRACT FROM AUTHOR]

Large-scale human mesenchymal stem cell expansion calls for a bioreaction system, that provides a sufficient growth surface. An alternative to static cultivations systems like cell factories are disposable stirred tank reactors. Here, microcarriers provide the required growth surface, but these make it difficult to achieve a complete homogenization in the bioreactor, while avoiding shear stress. To gain insight into this process, we investigated the impact of different power inputs (0.02–2.6 W m −3 ) on the mixing time (t m ). Whereas t m was inversely proportional to agitation in a one-phase-system, aeration resulted in a constant mixing time at 30–70 rpm. A high microcarrier concentration (30 g L −1 ) and low stirrer speed (30 rpm) in the liquid-solid system caused a 50-fold increase in t m and the formation of a discrete non-mixed upper zone. The effect of the microcarrier concentration on t m became negligible at higher stirrer speeds. In the three-phase system, microcarrier settling was prevented by aeration and a minimal specific power input of 0.6 W m −3 was sufficient for complete homogenization. We confirmed that a low power input during stem cell expansion leads to inhomogeneity, which has not been investigated in the three-phase system up to date. [ABSTRACT FROM AUTHOR]

Nearly all tubes and pores used to transport solids in fluids, such as arteries and filters, are subject to clogging. The length scales and geometries of these tubes are well defined. In spite of this knowledge, the collective clogging behavior of multiple tubes has not yet been connected to their shapes and sizes. We investigate the clogging behavior of ten parallel tubes, which we model with ten parallel tapered microchannels using poly(styrene) beads to induce clogging events. The clogging behavior depends on the channel geometry as well as the shear stress particles are subjected to. Although our microchannels model filters, our results can be applied to the clogging behavior of a broad range of applications such as the clogging in arteries, inkjets, or xylem in trees. [ABSTRACT FROM AUTHOR]

Multiphase displacement in porous media can be adjusted by micro/nanoparticle suspensions, which is widespread in many scientific and industrial contexts. Direct visualization of suspension flow dynamics and corresponding multiphase patterns is crucial to understanding displacement mechanisms and eventually optimizing these processes in geological, biological, chemical, and other engineering systems. However, suspension flow inside the opaque realistic porous media makes direct observation challenging. The advances in microfluidic experiments have provided us with alternative methods to observe suspension influence on the interface and multiphase flow behaviors at high temporal and spatial resolutions. Macroscale processes are controlled by microscale interfacial behaviors, which are affected by multiple physical factors, such as particle adsorption, capillarity, and hydrodynamics. These properties exerted on the suspension flow in porous media may lead to interesting interfacial phenomena and new displacement consequences. As an underpinning science, understanding and controlling the suspension transport process from interface to flow patterns in porous media is critical for a lower operating cost to improve resource production while reducing harmful emissions and other environmental impacts. This review summarizes the basic properties of different micro/nanoparticle suspensions and the state-of-the-art microfluidic techniques for displacement research activities in porous media. Various suspension transport behaviors and displacement mechanisms explored by microfluidic experiments are comprehensively reviewed. This review is expected to boost both experimental and theoretical understanding of suspension transport and interfacial interaction processes in porous media. It also brings forward the challenges and opportunities for future research in controlling complex fluid flow in porous media for diverse applications. [Display omitted] • A comprehensive review of progress on microfluidic experiments for micro/nanoparticles suspension-related multiphase displacement mechanism. • The microscopic particle kinetics and the basic properties of different micro/nanoparticle suspensions are summarized. • The state-of-the-art microfluidic techniques for displacement research activities in porous media are reviewed. • Various suspension transport behaviors and corresponding displacement mechanisms in porous media are summarized and discussed. [ABSTRACT FROM AUTHOR]

Biological tissues are characterised by spatially distributed gradients, intricately linked with functions. It is widely accepted that ideal tissue engineered scaffolds should exhibit similar functional gradients to promote successful tissue regeneration. Focusing on bone, in previous work we proposed simple methods to obtain osteochondral functionally graded scaffolds (FGSs), starting from homogeneous suspensions of hydroxyapatite (HA) particles in gelatin solutions. With the main aim of developing an automated device to fabricate FGSs, this work is focused on designing a stirred tank to obtain homogeneous HA–gelatin suspensions. The HA particles transport within the gelatin solution was investigated through computational fluid dynamics (CFD) modelling. First, the steady-state flow field was solved for the continuous phase only. Then, it was used as a starting point for solving the multi-phase transient simulation. CFD results showed that the proposed tank geometry and setup allow for obtaining a homogeneous suspension of HA micro-particles within the gelatin solution. [ABSTRACT FROM AUTHOR]

The influence of particles on the dynamics and eventual rupture of stretching liquid bridges is demonstrated experimentally in a drop-forming case. To analyze the particle-scale basis for the influence of particles in this flow, a lattice Boltzmann algorithm for a three-phase system of liquid, gas, and solid particles, has been developed. This provides full coupling between particles and fluids, fluid interfacial forces, and possible entry of particles into the interface (i.e. full and partial wetting by the liquid are considered). This work details the numerical method and its validation, and presents results of the simulations and related experiments. Fully-wetting particles up to a solid volume fraction of ϕ = 0.3 monotonically increased the rupture length of liquid bridges, as seen in experiments; experimental results show that the increase continues to a maximum at ϕ ≈ 0.4 , a condition beyond the present numerical capability. Depending on the wettability and volume fraction of the particles in the liquid bridge, particles can alter the structure of the bridge at pinch-off, suppress satellite drops, or produce asymmetrical pendant/sessile suspension drops as a result of their discrete nature. Particles with a neutrally wetting contact angle ( θ = 90 ° ) can reside in the bulk or be immersed in the interface if fluid deformation brings them into contact with it, and capillary forces are found to bring the interfacial particles near the narrow region (or “throat”) of the bridge prior to rupture. Fully wetting particles ( θ ≈ 0 ° ) remained interior to the liquid bridge, leaving less space to escape the throat region. Neutrally wetting particles increased the rupture length and altered the pinch-off structure relative to the particle-free case, but less so than fully wetting particles. [ABSTRACT FROM AUTHOR]

We studied the interactions among three circular particles suspended in a power-law fluid undergoing confined shear flow in two dimensions. The calculations are based on our previously developed lattice Boltzmann direct-forcing/fictitious-domain method. Reynolds numbers 1 ⩽ Re ⩽ 20 and power-law indices 0.5 ⩽ n ⩽ 1.5 were considered. We roughly classified the particles’ motion into “returning” and “passing” behaviors. We found that the particles are more likely to pass for higher Reynolds numbers or lower power-law indices, given the same flow conditions. In particular, we investigated the dynamics of the particles in shear flows and find two peaks in the horizontal fluid (drag) force for large Reynolds number or small power-law index. The first peak serves to decelerate the particles, while the second does the opposite, and might be primarily responsible for the transition from the “returning” to the “passing” behavior. We also studied the effects of the Reynolds number and the power-law index on particle velocity and streamline patterns. [ABSTRACT FROM AUTHOR]

In this study, we treat the dirty (small) and the adsorbing (large) particles, which are both of approximately micron-order or smaller, as charged and oppositely charged spheres and investigate the behavior of these particles under the gravity field by means of Brownian dynamics simulations. We have here mainly discussed the dependence of the adsorption rate on the particle diameter ratio, the volumetric fraction of large particles, and the input amount of large particles. Large particles adsorb much more small particles, per large particle, but the total number of small particles adsorbed by the large particles more significantly increases for large particles with smaller diameter if the same input amount of adsorbing agents (large particles) is used. This is because large particles with small diameter more actively perform random motion and move more extensively to adsorb small particles, although the surface area of large particles increases with decreasing diameter, leading to more opportunity to contact small particles. Hence, it is seen that putting numerous adsorbing particles with smaller diameter into water is more effective for removing suspended substances or dirty particles. Even if the input amount of large particles is increased, an adsorption performance cannot significantly be improved because the number of inefficient large particles that do not contribute to the adsorption performance increases. From these results, we understand that an optimal input amount of adsorption agents, from a commercial point of view, should be determined by various factors in the application of the adsorption technique to actual situations. [ABSTRACT FROM AUTHOR]

The hydrodynamic stability analysis of viscous flow between rotating porous cylinder has been researched for a long time by many researchers. But little works have been carried out about the linear stability analysis of the two-phase suspension. When the radial flow is present, the linear hydrodynamic stability analysis of suspension has been carried out between rotating porous cylinder. We know that the continuous and Stokes equations cannot only solve the stability problem of the continuous fluid phase, but also solving the stability problem of the discontinuous particle phase. The stability equations from an eigenvalue problem that was solved by a numerical technique based on Wan's method. The results reveal that the radial Reynolds number have a great effect on the critical Taylor number in the suspension. In this paper, we also researched on how the critical Taylor number changes as the radius ratio η, the axial wave number k, the particle concentration and the circumferential direction wave number happen to change with the radial Reynolds number increasing range from -5 to 5. Thus, our research discovered the radial inflow and outflow have a stabilizing effect on the two-phase suspension and the circumferential direction wave number also has a stabilizing effect. [ABSTRACT FROM AUTHOR]

We develop a model for the rheology of a threephase suspension of bubbles and particles in a Newtonian liquid undergoing steady flow. We adopt an 'effective-medium' approach in which the bubbly liquid is treated as a continuous medium which suspends the particles. The resulting three-phase model combines separate two-phase models for bubble suspension rheology and particle suspension rheology, which are taken from the literature. The model is validated against new experimental data for three-phase suspensions of bubbles and spherical particles, collected in the low bubble capillary number regime. Good agreement is found across the experimental range of particle volume fraction (0 = ɸp ≲ 0.5) and bubble volume fraction (0 = ɸb ≲ 0.3). Consistent with model predictions, experimental results demonstrate that adding bubbles to a dilute particle suspension at low capillarity increases its viscosity, while adding bubbles to a concentrated particle suspension decreases its viscosity. The model accounts for particle anisometry and is easily extended to account for variable capillarity, but has not been experimentally validated for these cases. [ABSTRACT FROM AUTHOR]

The linear stability analysis is carried out for the suspension flow of spherical particles between a rotating inner cylinder and a stationary concentric outer cylinder. The mass conservation equation and Navier-Stokes equation are applied to the continuous fluid phase and the particle phase. Results of stability analysis show that the increase of wave number in the circumferential direction attenuates the effect of the axial wave number on the amplification factor. The ratio of particle density to fluid density increasing above 0.1 amplifies the flow instability, while it can be weakened with higher circumferential direction wave number. Effect of the critical Taylor number on the amplification factor is reduced by increasing the circumferential direction wave number. The flow stability is affected by the geometry of flow field (the radius ratio) at non-zero circumferential direction wave numbers. [ABSTRACT FROM AUTHOR]

In this study, steady and unsteady magneto-hydrodynamic (MHD) Couette flows between two parallel infinite plates have been studied through numerical Differential Quadrature Method (DQM) and analytical Differential Transformation Method (DTM), respectively. Coupled equations by taking the viscosity effect of the two phases for fixed and moving plates have been introduced. The precious contribution of the present study is introducing new, fast and efficient numerical and analytical methods in a two-phase MHD Couette fluid flow. Results are compared with those previously obtained by using Finite Difference Method (FDM). The velocity profiles of two phases are presented and a parametric study of physical parameters involved in the problem is conducted. As an outcome, when magnetic source is fixed relative to the moving plate, by increasing the Hartmann number, velocity profiles for both phases increased, but when it is fixed relative to the fluid an inverse treatment is observed. [ABSTRACT FROM AUTHOR]

A mathematical model is presented for the steady, two-dimensional magneto-convection heat transfer of a two-phase, electrically-conducting, particle-suspension in a channel containing a non-Darcian porous medium intercalated between two parallel plates, in the presence of a transverse magnetic field. The channel walls are assumed to be isothermal but at different temperatures. The governing equations for the one-dimensional steady flow are formulated following Marble (1970) and extended to include the influence of Darcian porous drag, Forcheimmer quadratic drag, buoyancy effects, Lorentz body force (hydromagnetic retardation force) and particle-phase viscous stresses. Special boundary conditions for the particle-phase wall conditions are implemented. The governing coupled, non-linear differential equations are reduced from an (x,y) coordinate system to a one-dimensional (y) coordinate system. A series of transformations is then employed to non-dimensionalize the model in terms of a single independent variable, η, yielding a quartet of coupled ordinary differential equations which are solved numerically using the finite element method, under appropriate transformed boundary conditions. The influence of for example Grashof free convection number (Gr), Hartmann hydromagnetic number (Ha), inverse Stokes number (Skm), Darcy number (Da), Forcheimmer number (Fs),particle loading parameter (PL), buoyancy parameter (B) on the fluid-phase velocity and particle-phase velocity are presented graphically. A number of special cases of the transformed model are also studied. The mathematical model finds applications in solar collector devices, electronic fabrication, jet nozzle flows, industrial materials processing transport phenomena, MHD energy generator systems etc. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we present the mass transfer during the buoyant CO2 bubble absorption in a particle suspension by the experimental and computational studies. In the experimental study, the transient evolution of a single bubble behavior is visualized for the CO2 absorption in Al2O3-nanofluids. In the computational study, the finite element approximated Navier–Stokes equations are employed integrating with a level set method for tracking the interface on the convective diffused mass transfer in a CO2 bubble with the multi-freely suspended non-Brownian Al2O3-particles. In both approached studies, the particle hydrodynamic effect to the bubble motion takes effect on increasing the mass transfer area followed by inducing the mass transfer enhancement (MTE) by a term of the larger mass transfer coefficient (MTC) at the gas–liquid phase. From computational study, this is also supported that the enhanced mass flux is highly influenced by the particle hydrodynamics on the bubble surface in a buoyant bubble. Consequently, it can lead to find an existence as one of possible mechanisms for MTE on a gas-absorption in a suspension. [Copyright &y& Elsevier]

In this work, we consider model fluids which are dispersions of clay particles in aqueous solutions of carboxymethyl cellulose. Their rheological properties are measured in both steady and oscillatory shear flows. We present the experimental results obtained for different polymer concentrations and for three different molecular weights of the polymer. The clay is a bentonite sample and the particle concentration is fixed to a value of 5 %. The mechanical properties of these materials is the result of a competition between different mechanisms: association-dissociation of aggregates of particles, adsorption of polymer on the particles and desorption of solvent molecules from the particles, bridging of the particles by long polymer chains.

Mixing suspensions is a very important hydraulic operation. The pitched six-blade turbine is a widely-used axial-flow impeller. This paper deals with effect relative impeller size and particle content on theefficiency of a pitched six-blade turbine at particle suspension. Two pitched six-blade turbines were used in model measurements of just suspension impeller speed. The ratios of the vessel to agitator diameter D/d were 3 and 4.5. The measurements were carried out in a dish-bottomed vessel 300 mm in diameter. The just suspension impeller speeds were measured using an electrochemical method, and were checked visually. A 2.5 % NaCl water solution was used as the liquid phase, and glass particles with four equivalent diameters between 0.18 and 0.89 mmand volumetric concentration from 2.5 % to 40% were usedasthesolid phase. The criterion values πs=Po√Fr'3(d/D)7 were calculated from the particle suspension and power consumption measurements. The dependencies of πs on particle content cv show that larger agitators are more efficient for higher particle content.

Abstract: Pollution of water is a matter of concern all over the earth. Particles are known to play an important role in the transportation of pollutants in this medium. In addition, the emergence of new materials such as NOAA (Nano-Objects, their Aggregates and their Agglomerates) emphasizes the need to develop adapted instruments for their detection. Surveillance of pollutants in particulate form in waste waters in industries involved in nanoparticle manufacturing and processing is a telling example of possible applications of such instrumental development. The LIBS (laser-induced breakdown spectroscopy) technique coupled with the liquid jet as sampling mode for suspensions was deemed as a potential candidate for on-line and real time monitoring. With the final aim in view to obtain the best detection limits, the interaction of nanosecond laser pulses with the liquid jet was examined. The evolution of the volume sampled by laser pulses was estimated as a function of the laser energy applying conditional analysis when analyzing a suspension of micrometric-sized particles of borosilicate glass. An estimation of the sampled depth was made. Along with the estimation of the sampled volume, the evolution of the SNR (signal to noise ratio) as a function of the laser energy was investigated as well. Eventually, the laser energy and the corresponding fluence optimizing both the sampling volume and the SNR were determined. The obtained results highlight intrinsic limitations of the liquid jet sampling mode when using 532nm nanosecond laser pulses with suspensions. [Copyright &y& Elsevier]

Abstract: This paper shows the effect of the hydrodynamic interactions between non-Brownian isotropic particles for mass transfer enhancement in a shear flow generated by sliding walls in two dimensions through the direct numerical simulations. The particles are considered as a separate phase, while suspending solvent is modeled using the Stokes equation of which inertial and buoyancy effect are neglected. In the numerical simulation, we employ the finite element method to discretize the spatial domain with an explicit time stepping method. Interface capturing method is used to identify the boundary between the particle and the fluid. Automated adaptive mesh refinement is employed to increase the resolution in the vicinity of the particle boundaries as well as the interface between the solute and solvent. We investigate the effect of the particle hydrodynamics on mass transfer when the solute transports into the solvent and compare the mass transfer enhancements as a function of area fraction of multi-non-Brownian particles contributed. It is found that the mass transfer is enhanced by 3.6% in 1.0% area fraction which is a critical particle area fraction for the present flow conditions. [Copyright &y& Elsevier]

Abstract: Numerical simulations of the interaction between two non-Brownian isotropic particles in a shear flow confined between two sliding plates in two and three dimensions are presented. The suspending fluid is modelled using the Oldroyd-B constitutive equation and so incorporates the effects of viscoelasticity and first normal stress difference, but not shear-thinning. The particles are treated as a separate phase within the simulation with automated adaptive mesh refinement used to increase the resolution near the particle boundaries. The finite element method is used to discretise the spatial domain with a discontinuous Galerkin approximation for polymer stress and is implemented using the deal.II object oriented library. We identify three distinct types of interaction in two-dimensional systems: pass, return and tumble. We also show that the interactions between two spheres in a three-dimensional shear flow is qualitatively similar to the interaction between two circular particles, for particles in the same vorticity plane. For oblique interactions we find a further type of behaviour, similar to the Jeffery orbits of rigid rods. [Copyright &y& Elsevier]

Abstract: Ultrasound particle sizing is attracting an increasing attention from academic research and industrial applications as it offers non-invasive, suitable for highly turbid and concentrated nanoparticle suspensions and potentially no sample dilution needed features. The main challenge to this technique is thought to be its capability of dealing with high concentration. Most ultrasound particle sizing techniques employ ECAH (Epstein, Carhart, Allegra and Hawley) theory based models for the inversion of ultrasound spectra to particle size distribution (PSD). However, this theory is based on “single particle scattering”, namely a single particle immersed in an infinite medium, it is therefore only valid when ultrasound attenuation and particle concentration are linearly related. With the increase of particle concentration, due to the interactions between particles, the relation between attenuation and concentration may become nonlinear for solid–liquid suspensions. This paper demonstrates a method using population balance (PB) modelling to deal with the high concentration PSD problem for silica suspensions. It concludes that with a de-aggregation model, it is possible to convert attenuation inverted PSDs (ECAH model based inversion) at high concentrations into the PSD that is thought to be the correct PSD at a critical low concentration by a PB simulation. [ABSTRACT FROM AUTHOR]