Dilute Suspension Of Particles Research Articles

Dynamic settling of particles in shear flows of shear-thinning fluids

Dynamic settling is the phenomenon whereby a relatively dense particle settles through a sheared flow of a non-Newtonian fluid at a speed that depends on the shear rate of the background flow. This means that due to the nonlinear rheology, the settling velocity may vary spatially and temporally as the background shear rate of the suspending fluid varies, an effect which does not occur in Newtonian fluids. In this contribution, the consequences of this dependency are explored for a dilute suspension of particles released uniformly from a source in a sustained and externally-driven flow of shear-thinning fluid. It is shown theoretically that the concentration field does not remain uniform, but evolves downstream, allowing calculation of the runout length, settling times and distribution of the deposited particles. Flows with a velocity maximum are demonstrated to affect the concentration field very strongly as they develop a ‘kinematic barrier’ over which settling times are considerably lengthened. Flows with bi-disperse suspensions are shown to produce deposits that vary non-monotonically in thickness and composition with distance downstream, an effect which is solely due to dynamic settling. Finally flows of viscoplastic fluids which exhibit yielded and unyielded regions may accentuate the role and effects of the kinematic barrier to settling.

High-frequency effective viscosity of a dilute suspension of particles in Poiseuille flow between parallel walls

It is shown that the formal expression for the effective viscosity of a dilute suspension of arbitrary-shaped particles in Poiseuille flow contains a novel quadrupole term, besides the expected stresslet. This term becomes important for a very confined geometry. For a high-frequency flow field (in the sense used in Feuillebois et al. (J. Fluid Mech., vol. 764, 2015, pp. 133–147), the suspension rheology is Newtonian at first order in volume fraction. The effective viscosity is calculated for suspensions of $N$-bead rods and of prolate spheroids with the same length, volume and aspect ratio (up to 6), entrained by the Poiseuille flow between two infinite parallel flat hard walls. The numerical computations, based on solving the Stokes equations, indicate that the quadrupole term gives a significant positive contribution to the intrinsic viscosity $[{\it\mu}]$ if the distance between the walls is less than ten times the particle width, or less. It is found that the intrinsic viscosity in bounded Poiseuille flow is generally smaller than the corresponding value in unbounded flow, except for extremely narrow gaps when it becomes larger because of lubrication effects. The intrinsic viscosity is at a minimum for a gap between walls of the order of 1.5–2 particle width. For spheroids, the intrinsic viscosity is generally smaller than for chains of beads with the same aspect ratio, but when normalized by its value in the bulk, the results are qualitatively the same. Therefore, a rigid chain of beads can serve as a simple model of an orthotropic particle with a more complicated shape. The important conclusion is that the intrinsic viscosity in shear flow is larger than in the Poiseuille flow between two walls, and the difference is significant even for relatively wide channels, e.g. three times wider than the particle length. For such confined geometries, the hydrodynamic interactions with the walls are significant and should be taken into account.

Microfluidic rheology of active particle suspensions: Kinetic theory.

We analyze the effective rheology of a dilute suspension of self-propelled slender particles confined between two infinite parallel plates and subject to a pressure-driven flow. We use a continuum kinetic model to describe the configuration of the particles in the system, in which the disturbance flows induced by the swimmers are taken into account, and use it to calculate estimates of the suspension viscosity for a range of channel widths and flow strengths typical of microfluidic experiments. Our results are in agreement with previous bulk models, and in particular, demonstrate that the effect of activity is strongest at low flow rates, where pushers tend to decrease the suspension viscosity whereas pullers enhance it. In stronger flows, dissipative stresses overcome the effects of activity leading to increased viscosities followed by shear-thinning. The effects of confinement and number density are also analyzed, and our results confirm the apparent transition to superfluidity reported in recent experiments on pusher suspensions at intermediate densities. We also derive an approximate analytical expression for the effective viscosity in the limit of weak flows and wide channels, and demonstrate good agreement between theory and numerical calculations.

Validating dilute settling suspensions numerical data through MRI, UVP and EIT measurements

The measurement of fluid dynamic quantities are of great interest both for extending the range of validity of current correlations to be used in equipment design and for verification of fundamental hydrodynamic models. Studies where comparisons are made between imaging techniques serve to provide confidence on the validity of each technique for the study of multiphase flow systems. The advantage of cross-validation is that it can help establish the limitations of each technique and the necessary steps towards improvement. A small amount of comparative studies are found in the literature and none of them reports the study of settling particles suspension flow using simultaneously Ultrasonic Velocity Profiling (UVP), Magnetic Resonance Imaging (MRI) and Electrical Impedance Tomography (EIT), at least not to the best of the authors knowledge. In the present paper the authors report efforts made on the characterization of dilute suspensions of glass particles in turbulent flow, with increasing flow velocities and particles concentrations, in a pilot rig at a laboratorial scale, using both MRI, EIT and UVP: direct comparisons of EIT, MRI and UVP measurements acquired and mixture model numerical simulations are presented and the level of agreement explored.

Experimental investigation of heat transfer enhancement and viscosity change of hBN nanofluids

Hexagonal boron nitride (hBN) is a highly stable dielectric ceramic material that exhibits versatile properties such as, exceptionally high thermal conductivity and good chemical inertness. Due to its layered hexagonal crystal structure, hBN is the softest form among the other polymorphs of BN. Preparation, stability and thermophysical properties of hBN containing DI water, ethylene glycol (EG) and EG–DI water mixture (by volume 50%) based nanofluids are investigated. For this purpose a series of well dispersed, stable nanofluids, containing hBN nanoparticles with a mean diameter of 70nm, are produced with a two-step method, relying on ultrasonication and use of surface active materials such as sodium dodecyl sulfate (SDS) and polyvinyl pyrrolidone (PVP). The effect of these surfactants on the base fluids’ thermophysical properties is measured. The stability is evaluated by quantitative methods such as, time dependent zeta potential, and thermal conductivity measurements. Morphological characterization of nanofluids is completed by qualitative methods such as, SEM (Scanning Electron Microscopy) and TEM (Transmission Electron Microscopy). The thermal conductivity enhancement of nanofluids, with particle volume concentration varying between 0.03% and 3%, is investigated experimentally in accordance with their increase in viscosity. It is observed that the hBN nanofluids have remarkably higher thermal conductivity values than their corresponding base fluids, depending on the volume concentration of dispersed nanoparticles. Moreover, water based hBN nanofluids with relatively dilute particle suspensions, exhibits significant increase in thermal conductivity with respect to the viscosity increase.

Simultaneous characterization of rotational and translational diffusion of optically anisotropic particles by optical microscopy

We probe the roto-translational Brownian motion of optically anisotropic particles suspended in water with a simple and straightforward optical microscopy experiment that does not require positional or rotational particle tracking. We acquire a movie of the suspension placed between two polarizing elements and we extract the translational diffusion coefficient DT and the rotational diffusion coefficient DR from the analysis of the temporal correlation properties of the spatial Fourier modes of the intensity fluctuations in the movie. Our method is successfully tested with a dilute suspension of birefringent spherical colloidal particles obtained by polymerizing an emulsion of droplets of liquid crystal in a nematic phase, whose roto-translational dynamics is found to be well described by theory. The simplicity of our approach makes our method a viable alternative to particle tracking and depolarized dynamic light scattering.

Lagrangian particle modelling of spherical nanoparticle dispersion and deposition in confined flows

Particle diffusional losses in confined flows such as pipes are important for identification of erosion or accretion build-up. Its applications are varied and prominent in industrial and biomedical applications where essentially, tubular geometries transport fluid-particle flows. Computational modelling of dilute suspensions of ultrafine and nano-scale particles dispersing in a fluid often use the Lagrangian particle tracking approach. The Euler Implicit scheme in FLUENT v16 was evaluated for tracking such particles through a standard pipe geometry. It was found that the particles’ Brownian dispersion was dependent on the computational mesh, and the integration time step for a given particle size. For the pipe geometry well established analytical solutions for particle deposition efficiency are available to directly compare the simulated results. For irregular geometries (such as human respiratory anatomy) there are no analytical solutions and experimental deposition data is scarce and an alternative method is required to verify the simulation setup. In this case the computational models were set with zero velocity and the nanoparticles released from rest. The particle motion was then initiated purely by Brownian motion. The root mean square displacement was used to compare the time step size selector (either by the Length Scale Factor, LS, or the Step Length Factor SLF approach in FLUENT; and a fixed time step using an in-house code ‘PARTICLE’). This provides a modelling verification framework to determine the most appropriate time step selection that reproduces the particle Brownian dispersion behaviour correctly.

Flow Behavior and Distribution of Embolus-Model Particles at the Terminal Bifurcation of the Human Internal Carotid Artery

To investigate the possible role of fluid mechanical factors in thromboembolism that occurs at a high rate in the human middle cerebral artery (MCA). Isolated transparent cerebral arterial trees containing the terminal bifurcation of the internal carotid artery (ICA), where the ICA bifurcated into the MCA and the anterior cerebral artery, were prepared from human cadavers. The flow behavior and distribution of embolus-model polystyrene particles in dilute suspensions at the bifurcation were studied in detail by means of flow visualization and high-speed cinemicrographic techniques. Large particles in suspensions flowing through the ICA migrated radially away from the vessel wall toward the axis of the ICA. It became more remarkable by increasing the flow rate in the ICA (Q0), flow rate ratio of Q1 to Q0 (MCA/ICA), and particle diameter. As a result, redistribution of particles flowing in the ICA occurred at the bifurcation. The particles >1 mm in diameter (≈1/4 of vessel diameter) selectively entered the MCA, even when the flow rate ratio of Q1 to Q0 was decreased to as low as 0.34. In contrast, the particles whose diameters were <0.3 mm (≈1/10 of vessel diameter) and that did not show radial migration entered the MCA at the same rate as the flow rate ratio of Q1 to Q0. Due to the flow-dependent migration of particles away from the vessel wall toward the axis of the ICA, large particles selectively enter the MCA to which the core flow of the ICA is generally directed. This might explain why the incidence of thromboembolism is higher in the MCA than in the anterior cerebral artery in humans.

Delaying Boundary Layer Separation in a Retarded Potential Flow

The phenomena of convective transport in the boundary layer flow carrying a dilute nanosize suspension of small particles past a stationary wedge is investigated in this communication. The nanofluid modeling is based on non-homogeneous nanoparticle concentration within the boundary layer along with variable thermophysical material properties. It is shown that for the present nanofluid modelling the self-similar solution also exists as it does for the pure fluid case. The self-similar solution is found to exist for the situation when the undisturbed potential flow is of the form \(u_e \left( x \right) =u_1 x^{m}\). A number of qualitatively distinct potential scenarios are predicted concerning the physics of flow and heat transfer. These include boundary layer separation; control or its delay, and heat transfer enhancement. In depth analysis of momentum transport across the boundary layer revealed interesting physics. Worth mentioning effect of nanoparticle is to (slightly) delay the boundary layer separation in the case of retarding potential flow. The values of m are calculated for which the separation starts and are found to depend upon the nanoparticle concentration. Heat transfer augmentation connected directly with the nanoparticle concentration is also an important conclusion of this study.

Simulations of the PDF functions for dilute colloidal suspensions of molecular particles flowing in mesopores with rough surface boundaries

Simulations have been carried out to analyze the dynamics of dilute colloidal suspensions of macromolecular particles in solutions flowing in pores, subject to hydrodynamic forces, Brownian motion and stochastic collisions at rough pore boundaries in a two-dimensional spatial frame. A theoretical model is developed and intensively analyzed for the treatment of the mechanical restitution of the particles due to dynamic collisions at these boundaries. In particular we are able to calculate the Probability distribution functions for the spatial positions and the orientations of rod-like particles inside the pores. The results are presented for different widths of pore channels referenced to the size of a rod-like particle. These simulations are general in the sense that they are developed for confining and open pore channels, rough at the nano scale. The simulations also permit calculating the nematic order parameters for colloidal suspensions; the model calculation is applied for dilute colloidal suspensions of carbon nano-tubes in an aqueous single-stranded DNA solution flowing inside pores. Our calculated nematic order results for dilute suspensions of particles of known lengths flowing inside porous systems should indicate, when coupled to birefringence and dichroism experimental results, the possibility to estimate the pore widths for these systems.

Modeling Dilute Gas–Solid Flows Using a Polykinetic Moment Method Approach

Modeling a dilute suspension of particles in a polykinetic Eulerian framework is described using the conditional quadrature method of moments (CQMOM). The particular regimes of interest are multiphase flows comprised of particles with diameters small compared to the smallest length scale of the turbulent carrier flow and particle material densities much larger than that of the fluid. These regimes correspond to moderate granular Knudsen number and large particle Stokes numbers in which interparticle collisions and/or particle trajectory crossing (PTC) can be significant. The probability density function (PDF) of the particle velocity space is discretized with a two-point quadrature, the minimum resolution required to capture PTC which is common to these flows. Both two-dimensional (2D) test cases (designed to assess numerical procedures) and a three-dimensional (3D) fully developed particle-laden turbulent channel flow were implemented for collisionless particles. The driving gas-phase carrier flow is computed using direct numerical simulation of the incompressible Navier–Stokes (N–S) equations and one-way coupled to the particle phase via the drag force. Visualizations and statistical descriptors demonstrate that CQMOM predicts physical features such as PTC, particle accumulation near the channel walls, and more uniform particle velocity profiles relative to the carrier flow. The improvements in modeling compared to monokinetic representations are highlighted.

Glassy Behavior of a Tin Dioxide Nanoparticle Suspension.

Dilute suspensions of charged colloidal particles with a short-range attraction and long-range repulsion can exhibit a variety of arrested states. In many applications using suspensions of charged nanoparticles, the optimization of the process requires the understanding of the mechanism underlying the stability and the rheological properties of the suspensions. In an attempt to clarify the solidification mechanism for dilute suspensions of tin dioxide (SnO2) nanoparticles, we present dynamic viscoelasticity, dynamic and static light scattering, and small-angle X-ray scattering experiments on a SnO2 nanoparticle suspension with a nanoparticle concentration of 25.0 wt % (volume fraction φ = 0.045). The behaviors of the observed dynamic and static structure factors reveal that the aging of SnO2 nanoparticles is Wigner glassy rather than gel-like.

Influence of Rotation on the Magnetization of Dilute Suspensions of Magnetic Particles

The influence of rotation on the magnetization of a suspension of spherical magnetic particles in a uniform magnetic field is investigated theoretically with taking into account the inertial effects. A rotation of a single spherical non-Brownian particle with an embedded magnetic moment under action of a rotational flow of the ambient liquid in an applied uniform magnetic field is considered. The system of equations is obtained that determines the rotation of the particle and the instant orientation of its magnetic dipole moment with taking into account both the inertia of the particles and that of the dispersion liquid of the suspension. The magnetization vector of a suspension of non-Brownian spherical magnetic particles is found for the suspension rotating in a uniform constant magnetic field and for that rotating in a sufficiently weak uniform alternating magnetic field. The system of equations is obtained for the function of distribution over the orientations of the magnetic dipole moments for a suspension of Brownian spherical magnetic particles rotating in a uniform magnetic field. The solution to this system of equations is obtained for a suspension rotating in a sufficiently weak alternating magnetic field. With the use of this solution, the magnetization vector of the suspension is found.

To the Theory of Hyperthermia Effect Induced by Magnetic Nanoparticles

In this paper, we present results of theoretical modeling of the rise of temperature for the unit of time in a dilute suspension of the fiber ferromagnetic particles under the action of the linearly polarized oscillating magnetic field. Two mechanisms of the heat production, namely the particle rotation in the liquid and its internal remagnetization are considered. We study effect of the particle shape, its magnetic properties and rheological properties of the carrier liquid on the rise of temperature for the unit of time by the particles.

Finite-length effects on dynamical behavior of rod-like particles in wall-bounded turbulent flow

Combined Particle Image Velocimetry (PIV) and Particle Tracking Velocimetry (PTV) measurements have been performed in dilute suspensions of rod-like particles in wall turbulence. PIV results for the turbulence field in the water table flow apparatus compared favorably with data from Direct Numerical Simulations (DNS) of channel flow turbulence and the universality of near-wall turbulence justified comparisons with DNS of fiber-laden channel flow. In order to examine any shape effects on the dynamical behavior of elongated particles in wall-bounded turbulent flow, fibers with three different lengths but the same diameter were used. In the logarithmic part of the wall-layer, the translational fiber velocity was practically unaffected by the fiber length l. In the buffer layer, however, the fiber dynamics turned out to be severely constrained by the distance z to the wall. The short fibers accumulated preferentially in low-speed areas and adhered to the local fluid speed. The longer fibers (l/z>1) exhibited a bi-modal probability distribution for the fiber velocity, which reflected an almost equal likelihood for a long fiber to reside in an ejection or in a sweep. It was also observed that in the buffer region, high-speed long fibers were almost randomly oriented whereas for all size cases the slowly moving fibers preferentially oriented in the streamwise direction. These phenomena have not been observed in DNS studies of fiber suspension flows and suggested l/z to be an essential parameter in a new generation of wall-collision models to be used in numerical studies.

Reaction of a Particle Suspension in a Rapidly‐Heated Oxidizing Gas

AbstractThe reaction of a suspension of solid particles in a rapidly‐heated oxidizing gas is relevant to metalized explosives and propellants, as well as to combustion of solid fuel‐particle suspensions in premixed‐gaseous‐fuel clouds encountered in accidents within the mining and process industries. A simplified model is considered, using a constant‐volume approximation, which assumes that non‐volatile particles react heterogeneously via a one‐step surface reaction. The resulting unified particle reaction rate includes both kinetic and diffusive reaction resistances. It is shown that the onset of the chemical reaction in a rapidly heated particulate suspension may occur by two different physical mechanisms. The first mechanism, realized in a dilute suspension of particles, is defined by the ignition of a single particle, i.e., by the critical phenomenon associated with the rapid transition from a kinetically‐ to diffusively‐limited reaction regime. The second mechanism dominates the reaction onset in a dense particulate suspension and occurs in a similar manner to the reaction onset in a rapidly‐heated homogeneous gas mixture, where the highly‐activated reaction occurs in an explosion‐like manner after some time delay and preheating. Unlike the single particle ignition phenomenon, the second mechanism lacks criticality and is not limited to particles above a certain size. The interplay between these two reaction‐onset mechanisms leads to a nontrivial dependence of the total reaction time on the particle size and solid‐fuel concentration within the suspension.

Stress and strain amplification in a dilute suspension of spherical particles based on a Bird–Carreau model

A numerical study of a dilute suspension based on a non-Newtonian matrix fluid and rigid spherical particles was performed. In particular, an elongational flow of a Bird–Carreau fluid around a sphere was simulated and numerical homogenization has been used to obtain the effective viscosity of the dilute suspension ηhom for different applied rates of deformation and different thinning exponents. In the Newtonian regime the well-known Einstein result for the viscosity of dilute suspension is obtained: ηhom=(1+[η]φ)η with the intrinsic viscosity [η]=2.5. Here φ is the volume fraction of particles and η is the viscosity of the matrix fluid. However in the transition region from Newtonian to non-Newtonian behavior lower values of the intrinsic viscosity [η] are obtained, which depend on both the applied rate of deformation and the thinning exponent. In the power-law regime of the Bird–Carreau model, i.e. at high deformation rates, it is found that the intrinsic viscosity [η] depends only on the thinning exponent. Utilizing the simulation results a modification of the Bird–Carreau model for dilute suspensions with a non-Newtonian matrix fluid is proposed.

Rheological properties of a dilute suspension of self-propelled particles

With a detailed microscopic model for a self-propelled swimmer, we derive the rheological properties of a dilute suspension of such particles at small Peclet number. It is shown that, in addition to Einstein's like contribution to the effective viscosity, that is proportional to the volume fraction of the swimmers, a contribution due to the activity of self-propelled particles influences the viscosity. As a result of the activity of swimmers, the effective viscosity would be lower (higher) than the viscosity of the suspending medium when the particles are pusher (puller). Such activity-dependent contribution will also result a non-Newtonian behavior of the suspension in the form of normal stress differences.

On the effective viscosity of a dilute suspension of rigid spherical particles

The problem of the motion of a spherical bubble of arbitrary size with a specified velocity in a dilute suspension of solid spherical particles is considered in the Stokes approximation for a carrying continuous medium. An expression is obtained for the drag of the bubble in the first approximation in the volume concentration of the dispersed phase. Using the results obtained an expression is derived for the effective viscosity of the suspension, “as seen” by the spherical bubble as it moves through the dispersed medium. It is shown that the coefficient for the volume concentration in the formula for the effective viscosity of the suspension depends on the ratio of the dimensions of the dispersed particles and of the bubble. In the limit, when this ratio approaches zero, the coefficient obtained is identical with Einstein's result for the effective viscosity of the suspension. However, this coefficient may differ considerably from Einstein's result for “non-point” dispersed particles. By comparing this result with the similar result obtained earlier for the case of the motion of a rigid sphere in a viscous suspension it is shown that the coefficient for the volume concentration in the formula for the effective viscosity of the suspension depends not only on the size of the body, but also on the form of the boundary conditions on its surface.

The rheology of three-phase suspensions at low bubble capillary number.

We develop a model for the rheology of a three-phase 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 () and bubble volume fraction (). 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.