Dilute Suspension Of Particles Research Articles

Energy costs of the sponge pump

Sponges pump large volumes of water to obtain nutrition from a dilute suspension of food particles and dissolved organic matter. Our review of the literature shows pumping power ranging from 0.85% up to 28% of the total metabolic respiration rate Rtot, where the pumping power (Pp = pumping rate × pump pressure) is the energy per unit time transferred to the water flow. Some published values of pumping costs are high while others are low due to incorrect estimates of some pressure losses in the aquiferous system of sponges. However, as improved descriptions of detailed structures and function, especially of the filter apparatus of the choanocytes, have become available, our corrected values for pressure losses show the respiration-specific pumping costs of Pp/Rtot = 1.3 to 22%. The stated pumping cost is based on the minimal (theoretical) pump power delivered to the water, which excludes a mechanical efficiency of pump action and a metabolic efficiency that expresses the fraction of total metabolism that is devoted to driving the pump action, considerations that should be included in future studies.

Ideal Collision Rate of Symmetric Hexapods in a Simple Shear Flow.

An ideal collision rate (ICR) is defined as the average rate of contact between two particles that translate and rotate with the imposed fluid flow in the absence of interparticle interactions. ICR in a simple shear flow provides an estimate of the collision rate in a flowing dilute particle suspension, and its value is known only for traditional convex shapes such as spheres and cylinders. In this work, we compute the ICR for a family of symmetric hexapods (shown in Figure 1) that are particles composed of three orthogonal cylinders with coinciding centers (forming six arms) with at least two cylinders having the same length. We employed the finite-element method to obtain the rotational dynamics of hexapods and Monte Carlo simulations to calculate their ICR. Our results indicate that the ICR for hexapods is not directly proportional to the volume of the particle, in contrast to what is observed for convex shapes such as spheres and cylinders. For hexapods of the same size, the ICR could be similar for particles with order-of-magnitude differences in their volumes and it could also vary by an order of magnitude for particles with similar volumes. Specifically for hexapods termed branched fibers, which have one longer cylinder, the ICR changes by an order of magnitude even when the shorter cylinders are significantly smaller than the longer cylinder. This change is attributed to the increase in the tumbling frequency of the particle due to hydrodynamic forces acting on the shorter arms, in addition to the increased probability of collision afforded by them. Using asymptotic theory for high-aspect ratio cylinders, we showed that the tumbling period of hexapods was proportional to an algebraic power of the ratio of its arm lengths and has a weaker logarithm relationship with the aspect ratio of its arms. The collision cross-section provided the relative cross-streamline particle separations for the most likely binary collisions in the suspensions, and its value was sensitive to the arm lengths, as well. The collision rate of hexapods also could not be estimated within an order of magnitude from existing geometric models, such as the ICR of a circumscribing convex shape, ICR for one of the individual cylinders of the hexapod, or using the particle volume times the shear rate. Our work indicates that collision rate for non-convex particles in shear flows critically depends on the shape of the particle due to nontrivial changes in the particle's orientational dynamics, and the ICR calculation serves as a more reliable method for estimating their true collision rates in the suspension.

The effect of Navier slip on the rheology of a dilute two-dimensional suspension of plate-like particles

Through boundary integral simulations and asymptotic analysis, we investigate the effect of a finite Navier slip length on the rheological proprieties of a dilute two-dimensional suspension of plate-like particles in the creeping flow limit. Specifically, we study the effects of Navier slip, particle thickness and Péclet number on the effective shear viscosity and average normal stress difference of an isolated two-dimensional plate-like particle in an unbounded shear flow field. We find that Navier slip induces a significant reduction in the effective viscosity and increases the average normal stress difference. The effect of slip becomes more enhanced as the thickness of the particle decreases and as the Péclet number increases. Remarkably, the analysis suggests that it is theoretically possible for a dilute suspension of slip plate-like particles at high Péclet numbers to have a shear viscosity smaller than that of the suspending fluid.

Effects of dilute coal char particle suspensions on propagating methane detonation wave

Effects of dilute coal char particle suspensions on propagating methane detonation wave

Sub-diffusion flow velocimetry with number fluctuation optical coherence tomography.

We have implemented number fluctuation dynamic light scattering optical coherence tomography (OCT) for measuring extremely slow, sub-diffusion flows of dilute particle suspensions using the second-order autocovariance function. Our method has a lower minimum measurable velocity than conventional correlation-based OCT or phase-resolved Doppler OCT, as the velocity estimation is not affected by the particle diffusion. Similar to non-dilute correlation-based OCT, our technique works for any Doppler angle. With our analysis we can quantitatively determine the concentration of particles under flow. Finally, we demonstrate 2D sub-diffusion flow imaging with a scanning OCT system at high rate by performing number fluctuation correlation analysis on subsequent B-scans.

Particle orientation distribution in a rotating, dilute suspension of rod-shaped particles

We consider a theoretical model for the settling of rod-shaped particles of a dilute, initially homogeneous, suspension in rapid rotation. The particle Reynolds number and the particle Taylor number of the detailed flow around the particles are assumed small, representing a relevant limit for an industrial centrifugal separation process. By applying a statistical approach using the Fokker–Planck equation, and neglecting particle–particle interactions, we obtain an explicit, analytical solution for the time dependent, spatially uniform particle orientation distribution function. Not only does the volume fraction in the bulk of the suspension decrease with time due to the divergent centrifugal field, as similarly described in the literature for suspensions of spherical particles, the orientation of the rod particles also changes with time from an initially uniform distribution to one where the particles tend to align with a plane perpendicular to the axis of rotation. The corresponding particle trajectories, as also influenced by first-order effects from the Coriolis acceleration and gyroscopic effects, are obtained numerically for different initial particle orientation angles.

Confined active matter in external fields.

We analyze a dilute suspension of active particles confined between walls and subjected to fields that can modulate particle speed as well as orientation. Generally, the particle distribution is different in the bulk compared to near the walls. In the bulk, particles tend to accumulate in the regions of low speed, but in the presence of an orienting field normal to the walls, particles rotate to align with the field and accumulate in the field direction. At the walls, particles tend to accumulate pointing into the walls and thereby exert pressure on walls. But the presence of strong orienting fields can cause the particles to reorient away from the walls, and hence shows a possible mechanism for preventing contamination of surfaces. The pressure at the walls depends on the wall separation and the field strengths. This work demonstrates how multiple fields with different functionalities can be used to control active matter under confinement.

Embedded 3D printing of dilute particle suspensions into dense complex tissue fibers using shear thinning xanthan baths.

In order to fabricate functional organoids and microtissues, a high cell density is generally required. As such, the placement of cell suspensions in molds or microwells to allow for cell concentration by sedimentation is the current standard for the production of organoids and microtissues. Even though molds offer some level of control over the shape of the resulting microtissue, this control is limited as microtissues tend to compact towards a sphere after sedimentation of the cells. 3D bioprinting on the other hand offers complete control over the shape of the resulting structure. Even though the printing of dense cell suspensions in the ink has been reported, extruding dense cellular suspensions is challenging and generally results in high shear stresses on the cells and a poor shape fidelity of the print. As such, additional materials such as hydrogels are added in the bioink to limit shear stresses, and to improve shape fidelity and resolution. The maximum cell concentration that can be incorporated in a hydrogel-based ink before the ink's rheological properties are compromised, is significantly lower than the concentration in a tissue equivalent. Additionally, the hydrogel components often interfere with cellular self-assembly processes. To circumvent these limitations, we report a simple and inexpensive xanthan bath based embedded printing method to 3D print dense functional linear tissues using dilute particle suspensions consisting of cells, spheroids, hydrogel beads, or combinations thereof. Using this method, we demonstrated the self-organization of functional cardiac tissue fibers with a layer of epicardial cells surrounding a body of cardiomyocytes.

Nonequilibrium dynamical structure factor of a dilute suspension of active particles in a viscoelastic fluid.

In this work we investigate the dynamics of the number-density fluctuations of a dilute suspension of active particles in a linear viscoelastic fluid. We propose a model for the frequency-dependent diffusion coefficient of the active particles which captures the effect of rotational diffusion on the persistence of their self-propelled motion and the viscoelasticity of the medium. Using fluctuating hydrodynamics, the linearized equationsfor the active suspension are derived, from which we calculate its dynamic structure factor and the corresponding intermediate scattering function. For a Maxwell-type rheological model, we find an intricate dependence of these functions on the parameters that characterize the viscoelasticity of the solvent and the activity of the particles, which can significantly deviate from those of an inert suspension of passive particles and of an active suspension in a Newtonian solvent. In particular, in some regions of the parameter space we uncover the emergence of oscillations in the intermediate scattering function at certain wave numbers which represent the hallmark of the nonequilibrium particle activity in the dynamical structure of the suspension and also encode the viscoelastic properties of the medium.

Inertial focusing of a dilute suspension in pipe flow

The dynamics of rigid particle suspensions in a wall-bounded laminar flow present several nontrivial and intriguing features, including particle ordering, lateral transport, and the appearance of stable, preferential locations like the Segré–Silberberg annulus. The formation of more than one annulus is a particularly puzzling phenomenon that is still not fully explained. Here, we present numerical simulation results of a dilute suspension of particles in (periodic) pipe flow based on the lattice Boltzmann and the discrete element methods. Our simulations provide access to the full radial position history of the particles while traveling downstream. This allows to accurately quantify the transient and steady states. We observe the formation of the secondary, inner annulus and show that its position invariably shifts toward the Segré–Silberberg one if the channel is sufficiently long, proving that it is, in fact, a transient feature for Reynolds numbers (Re) up to 600. We quantify the variation of the channel focusing length (Ls/2R) with Re. Interestingly and unlike the theoretical prediction for a point-like particle, we observe that Ls/2R increases with Re for both the single particle and the suspension.

Collision efficiency of non-Brownian spheres in a simple shear flow – the role of non-continuum hydrodynamic interactions

We study the collisions in a gaseous medium of a dilute bidisperse suspension of non-Brownian spherical particles sedimenting along the flow axis of a simple shear flow. Continuum lubrication forces prevent particles from coming into contact in a finite time, thus collisions can occur only due to attractive interactions such as the van der Waals force. However, in a low-pressure medium, the lubrication forces are weaker than their continuum counterparts and allow particle pairs to collide, even without any attractive forces. The Knudsen number, defined as the ratio of the mean free path of the medium to the mean radius of the interacting spheres, captures the significance of non-continuum interactions. We use uniformly valid hydrodynamic mobility functions, reflecting non-continuum lubrication at small separations and full continuum hydrodynamic interactions at moderate to larger separations. Due to the nature of the pair trajectory topology, the collision efficiency vanishes at a critical Knudsen number when simple shear flow alone drives the dynamics. Thus we perform collision calculations where particles experience the combined effects of van der Waals attraction and non-continuum hydrodynamics; van der Waals interactions enable collisions below the critical Knudsen number. Next, we calculate the collision efficiency for coupled differential sedimentation and simple shear driven motion in the presence of van der Waals interaction and non-continuum hydrodynamics. Finally, we explore the role of small particle inertia on relative trajectories and collision efficiencies in a non-continuum gas subject to a simple shear flow, ignoring the van der Waals force and gravity.

Shape dynamics and rheology of dilute suspensions of elastic and viscoelastic particles

This paper examines the shape dynamics of deformable elastic and viscoelastic particles in an ambient Newtonian fluid subjected to simple shear. The particles are allowed to undergo large deformation, with the elastic stress determined using the neo-Hookean constitutive relation. We first present a method to determine the shape dynamics of initially ellipsoidal particles that is an extension of the method of Roscoe (J. Fluid Mech., vol. 28, issue 2, 1967, pp. 273–293), originally used to determine the shape at steady state of an initially spherical particle. We show that our method recovers earlier results for the in-plane trembling and tumbling dynamics of initially prolate spheroids in simple shear flow, obtained by a different approach. We then examine the in-plane dynamics of oblate spheroids and triaxial ellipsoids in simple shear flow, and show that they too, like prolate spheroids, exhibit time-periodic tumbling or trembling dynamics, depending on the initial aspect ratios of the particle and the elastic capillary number $G \equiv \mu \dot {\gamma }/\eta$ , where $\mu$ is the viscosity of the fluid, $\eta$ is the elastic shear modulus of the particle and $\dot {\gamma }$ is the shear rate. In addition, we find a novel state wherein the particle extends indefinitely in time and asymptotically aligns with the flow axis. We demarcate all the dynamical regimes in the parameter space comprising $G$ and the initial particle aspect ratios. When the particles are viscoelastic, damped oscillatory dynamics is observed for initially spherical particles, and the tumbling–trembling boundary is altered for initially prolate spheroids so as to favour tumbling.

Unjamming and emergent nonreciprocity in active ploughing through a compressible viscoelastic fluid

A dilute suspension of active Brownian particles in a dense compressible viscoelastic fluid, forms a natural setting to study the emergence of nonreciprocity during a dynamical phase transition. At these densities, the transport of active particles is strongly influenced by the passive medium and shows a dynamical jamming transition as a function of activity and medium density. In the process, the compressible medium is actively churned up – for low activity, the active particle gets self-trapped in a cavity of its own making, while for large activity, the active particle ploughs through the medium, either accompanied by a moving anisotropic wake, or leaving a porous trail. A hydrodynamic approach makes it evident that the active particle generates a long-range density wake which breaks fore-aft symmetry, consistent with the simulations. Accounting for the back-reaction of the compressible medium leads to (i) dynamical jamming of the active particle, and (ii) a dynamical non-reciprocal attraction between two active particles moving along the same direction, with the trailing particle catching up with the leading one in finite time. We emphasize that these nonreciprocal effects appear only when the active particles are moving and so manifest in the vicinity of the jamming-unjamming transition.

Collective dynamics and rheology of confined phoretic suspensions

Similarly to their biological counterparts, suspensions of chemically active autophoretic swimmers exhibit a non-trivial dynamics involving self-organisation processes as a result of inter-particle interactions. Using a kinetic model for a dilute suspension of autochemotactic Janus particles, we analyse the effect of a confined pressure-driven flow on these collective behaviours and the impact of chemotactic aggregation on the effective viscosity of the active fluid. Four dynamic regimes are identified when increasing the strength of the imposed pressure-driven flow, each associated with a different collective behaviour resulting from the competition of flow- and chemically induced reorientation of the swimmers together with the constraints of confinement. Interestingly, we observe that the effect of the pusher (respectively puller) hydrodynamic signature, which is known to reduce (respectively increase) the effective viscosity of a sheared suspension, is inverted upon the emergence of autochemotactic aggregation. Our results provide new insights into the role of the collective dynamics in complex environments, which are relevant to synthetic as well as biological systems.

Data-driven closure model for the drag coefficient of the creeping flow past a translating sphere in a shear-thinning viscoelastic fluid

A drag force closure model for particle-laden viscoelastic fluid flows is the key to describing the ensemble-averaged behavior of the mixture. The effects of fluid rheological properties on the flow dynamics of a spherical particle in viscoelastic fluids in the creeping flow regime are parameterized using the Giesekus rheological model. Direct numerical simulations are performed within a large range of Deborah number(0−10).The drag force of a sphere in unbounded Giesekus fluids decreases monotonically with the increase of Deborah number. The negative wake may occur when the viscosity ratio is larger than 0.6 in Giesekus fluids but is absent in Oldroyd-B fluids in all conditions. An explicit closure model for the drag coefficient of a sphere in Giesekus fluids is established using the backpropagation artificial neural network. The drag closure model provides a method for explicitly formulating the momentum exchange model for dilute suspensions of solid particles in shear-thinning viscoelastic fluids.

Hydrodynamic simulations of sedimenting dilute particle suspensions under repulsive DLVO interactions

We present guidelines to estimate the effect of electrostatic repulsion in sedimenting dilute particle suspensions. Our results are based on combined Langevin dynamics and lattice Boltzmann simulations for a range of particle radii, Debye lengths and particle concentrations. They show a simple relationship between the slope K of the concentration-dependent sedimentation velocity and the range χ of the electrostatic repulsion normalized by the average particle-particle distance. When χ → 0, the particles are too far away from each other to interact electrostatically and K = 6.55 as predicted by the theory of Batchelor. As χ increases, K likewise increases as if the particle radius increased in proportion to χ up to a maximum around χ = 0.4. Over the range χ = 0.4-1, K relaxes exponentially to a concentration-dependent constant consistent with known results for ordered particle distributions. Meanwhile the radial distribution function transitions from a disordered gas-like to a liquid-like form. Power law fits to the concentration-dependent sedimentation velocity similarly yield a simple master curve for the exponent as a function of χ, with a step-like transition from 1 to 1/3 centered around χ = 0.6.

Infiltration and resuspension of dilute particle suspensions in micro cavity flow

Sedimentation of particle suspensions in a channel flow into a cavity is analysed numerically using a lattice Boltzmann method coupled with a discrete element method. The work focuses on the entrapment of particles inside a confined cavity and the particle dynamics after entrapment. A close examination of the particle motions reveals three distinct dynamic behaviours: i) resuspension, ii) circulation in the central vortex and iii) deposition to the rear edge of the cavity. The effects of fluid inertia, particle density and cavity size on the infiltration and resuspension behaviours are systematically investigated. The results show that decreasing the Reynolds number, and increasing the length and depth of the cavity all lead to an increase in the trap efficiency. Three distinctive regimes with respect to the trap efficiency were then identified by deriving an empirical dimensionless trap number Tp: a resuspension regime when Tp < 1, a continuous circulating regime when 1 ≤ Tp ≤ 2.5, and a fully trapped regime when Tp > 2.5.

Latex agglutination analysis by novel ultrasound scattering techniques

The latex agglutination test is employed to visualize antigen–antibody reactions through the aggregation of antibody-coated particles in the presence of an antigen. In the present study, we developed an ultrasound scattering technique to detect latex agglutination in an optically turbid media. However, the ultrasonic technique had less sensitivity to the dilute particle suspension than the optical techniques because of its wavelength. Therefore, we applied a time-correlation approach to detect small amounts of these aggregates using a sophisticated noise correction algorithm in the frequency domain. The lowest concentration of avidin used to detect aggregations of the biotin-coated particle using the ultrasound scattering technique was found to be 0.625 μg/ml. Furthermore, since the density differences between the particle and liquid were larger for silica suspensions than for polystyrene (PS) suspensions, a larger signal was proposed to be expected from silica suspensions. Nevertheless, it was found that latex agglutinations with the PS particle were more sensitive than those with the silica particles. The dynamic ultrasound scattering analysis along the sedimentation direction also supported the presence of strongly scattered intensity components of the PS aggregates, which is proposed to be due to the resonance scattering from PS spherical particles. Therefore, this technique can be employed to enhance scattering signals from particles for application in the agglutination test using ultrasound.

Inertial effects in dusty Rayleigh–Taylor turbulence

We investigate the dynamics of a dilute suspension of small, heavy particles superposed on a reservoir of still, pure fluid. The study is performed by means of numerical simulations of the Saffman model for a dilute particle suspension (Saffman, J. Fluid Mech., vol. 13, issue 1, 1962, pp. 120–128). In the presence of gravity forces, the interface between the two phases is unstable and evolves in a turbulent mixing layer which broadens in time. In the case of negligible particle inertia, the particle-laden phase behaves as a denser fluid, and the dynamics of the system recovers to that of the incompressible Rayleigh–Taylor set-up. Conversely, particles with large inertia affect the evolution of turbulent flow, delaying the development of turbulent mixing and breaking the up–down symmetry within the mixing layer. The inertial dynamics also leads to particle clustering, characterised by regions with higher particle density than the initial uniform density, and by the increase of the local Atwood number.

Characteristics of settling of dilute suspension of particles with different density at high Reynolds numbers

Dilute suspension of particles with same density and size develops clusters when settle at high Reynolds number (≥ 250). It is due to particles entrapment in the wakes produced by upstream particles. In this work, this phenomenon is studied for suspension having particles with different densities by numerical simulations. The particle-fluid interactions are modelled using immersed boundary method and inter-particle collisions are modelled using discrete element method. In simulations, settling Reynolds number is always kept above 250 and the suspension solid volume fraction is nearly 0.1 percent. Two particle density ratios (i.e. density of heavy particles to lighter particles) equal to 4:1 and 2:1 and particles with same density are studied. For each density ratio, the percentage volume fraction of each particle density is nearly varied from 0.8 to 0.2. Settling characteristics such as microstructures of settling particle, average settling velocity and velocity fluctuations of settling particles are studied. Simulations show that for different density particles settling characteristics of suspension is largely dominated by heavy particles. At the end of paper, the underlying physics is explained for the anomalies observed in simulation.