Non-neutrally Buoyant Particles Research Articles

Inertial migration of fine mineral particles in a curved microfluidic channel: Demystifying the role of non-neutrally buoyant particles

Fine mineral particles (FMPs) are ubiquitous in hazardous waste derived from metal mining, processing, and smelting. Inertial microfluidics has sparked tremendous attention due to its potential applications in separating neutral buoyant particles. However, it often fails when applied into non-neutral buoyant FMPs. The inertial migration and focusing tendencies of FMPs were still unknown. Herein, we present a modified microfluidic experiment platform to ensure the steady flow of FMPs in microfluidic systems. This platform avoids the deposition issue of FMPs by combined sample input and suspension system along with design of effective flow rate. FMPs of various particle diameter (2.2 μm, 6.8 μm and 10.2 μm, density of 6.29 g/cm3 or 3.2 g/cm3) were classified and compared to neutral buoyant particles (1.1 μm, 7 μm and 9.9 μm, density of 1.05 g/cm3) to investigate their differences in migration and focusing behaviors within a curved microfluidic channel (CR = 0.07). The migration dynamics of particles with multiple scale sizes may be divided into focusing, rough focusing, and non-focusing modes. Results revealed that a high density of FMPs had less effect on FMP migration and focusing behaviors in three modes. Nonetheless, the variability of FMP size and shape must be considered, as it will induce a shift in particle focusing position and, ultimately, might inhibit FMP separation in microfluidic channels. This work provides an experimental basis for the microfluidic behaviors of FMPs and might give advanced support for the possible application of microfluidic technology in mineral particle separation and sorting.

Hydrodynamic Boundary Layers at Solid Wall—A Tool for Separation of Fine Solids

A theoretical study is performed about the hydrodynamic interaction of fine species entrapped in the boundary layer (BL) at solid wall (plate). The key starting point is the analysis of the disturbance introduced by solid spheres in the background fluid flow. For a neutrally buoyant entity, the type of interaction is determined by the size of the spheres as compared to the thickness of the BL region. The result is granulometric separation of the solids inside the BL domain at the wall. The most important result in view of potential applications concerns the so-called small particles Rp < L/ReL5/4 (ReL is the Reynolds number of the background flow and Rp is the radius of the entrapped sphere). In the case of non-neutrally buoyant particles, gravity interferes with the separation effect. Important factor in this case is the relative density of the solid species as compared to this of the fluid. In view of further practical uses, particles within the range of Δρ/ρ < Fr2/ReL1/2 (Fr is Froude number and Δρ/ρ is the relative density of the entrapped solids) are systematically studied. The trajectories inside the BL region of the captured species are calculated. The obtained data show that there are preferred regions along the wall where the fine solids are detained. The results are important for the assessment of the general efficiency of entrapment and segregation of fine species in the vicinity of solid walls and have high potential for further design of industrial separation processes.

Inertial focusing of non-neutrally buoyant spherical particles in curved microfluidic ducts

Abstract

Numerical investigation of microfluidic sorting of microtissues

We characterize through simulation a microfluidic-based particle sorting approach instrumental in flow cytometry for quantifying microtissue features. The microtissues are represented herein as rigid spheres. The numerical solution employed draws on a Lagrangian–Lagrangian (LL), Smoothed Particle Hydrodynamics (SPH) approach for the simulation of the coupled fluid–rigid-body dynamics. The study sets out to first quantify the influence of the discretization resolution, numerical integration step size, and SPH marker spacing on the accuracy of the numerical solution. By considering the particle motion through the microfluidic device, we report particle surface stresses in the range of σ=[0.1,1.0]Pa; i.e., significantly lower than the critical value of 100Pa that would affect cell viability. Lift-off of non-neutrally buoyant particles in a rectangular channel flow at the target flow regime is investigated to gauge whether the particle shear stress is magnified as a result of dragging on the wall. Several channel designs are considered to assess the effect of channel shape on the performance of the particle sorting device. Moreover, it is shown that a deviation in flow rate does not influence the focusing of the particles at the channel outlet.

The effect of shape on the margination dynamics of non-neutrally buoyant particles in two-dimensional shear flows

The margination dynamics of microparticles with different shapes has been analyzed within a laminar flow mimicking the hydrodynamic conditions in the microcirculation. Silica spherical particles, quasi-hemispherical and discoidal silicon particles have been perfused in a parallel plate flow chamber. The effect of the shape and density on their margination propensity has been investigated at different physiologically relevant shear rates S. Simple scaling laws have been derived showing that the number n of marginating particles scales as S - 0.63 for the spheres; S - 0.85 for discoidal and S - 1 for quasi-hemispherical particles, regardless of their density and size. Within the range considered for the shear rate, discoidal particles marginate in a larger number compared to quasi-hemispherical and spherical particles. These results may be of interest in drug delivery and bio-imaging applications, where particles are expected to drift towards and interact with the walls of the blood vessels.

Viscous resuspension in a tube: The impact of secondary flows resulting from second normal stress differences

The viscous resuspension of non-neutrally buoyant particles has been modeled as a competition between the rate of shear-induced diffusion and sedimentation or as a balance between gradients in the particle stress and gravity. Typically, however, the rheology of the suspension has been modeled using a simple concentration-dependent Newtonian viscosity. In this paper, we demonstrate through theory and comparison with existing experimental results that the anisotropy of the total stress tensor must be included to accurately describe the resuspension process in a tube. At steady state, the isotropic model predicts a secondary current within the tube cross section that flows downwards at the center and upwards near the sidewalls, resulting in a concave upward interface between the clear suspending fluid and the particles [K. Zhang and A. Acrivos, Int. J. Multiphase Flow 20, 579 (1994)]. In contrast, with the inclusion of the known non-Newtonian suspension rheology, the secondary current profile is reversed: upwards near the center and downwards near the walls. This leads to a concave downward shape of the interface between the suspending fluid and the suspension and is in quantitative agreement with the experimental measurements of Altobelli et al. [J. Rheol. 35, 721 (1991)].

Particle dynamics and pattern formation in a rotating suspension

A rotating suspension of non-neutrally buoyant particles, confined by a horizontal cylinder, can be unstable to axial perturbations in concentration. A highly regular pattern of particle density and fluid flow then coexists in a non-equilibrium stationary state. The density profile along the cylinder axis is roughly sinusoidal, with a well-defined wavelength close to the cylinder diameter, and has a magnitude of approximately 30% of the average number density. We have used numerical simulations within the Stokes-flow approximation to investigate the mechanism underlying axial-band formation. Our results show that bands develop from an inhomogeneous particle distribution in the radial plane, which is itself driven by the competition between gravity and the viscous drag of the rotating fluid. We have discovered that the mean angular velocity of the particles is an order parameter which distinguishes between a low-frequency segregated phase and a high-frequency dispersed phase, where the particles fill the whole volume uniformly. The order parameter is a function of a single dimensionless frequency, with a characteristic length that is the mean interparticle separation. As the rotational frequency increases, the particle distribution becomes more homogeneous and the band structure disappears. Hydrodynamic diffusion stabilizes the suspension against centrifugal forces, allowing for a uniformly dispersed phase that can be used to grow three-dimensional cell cultures in an artificial microgravity environment.

Effect of settlement on dense slurry flow in a horizontal channel

A shear viscosity model for the underfill flow is proposed based on slug flow, which is appropriate in the case of neutrally buoyant particles. However, the filling particles used in practice are often heavier than the liquid carriers. The effect of non-neutrally buoyant particles is investigated in this work. The flow of dense slurry in which the filling particles are heavier than the liquid carrier is analyzed by considering the particle-particle and particle-wall interactions, which are derived from fluid film lubrication theory. The effect of settlement causes the flow behavior to depart from that of slug flow. Nevertheless, steady flow is still found possible, and, for a few representative packing patterns considered, somewhat modified flow patterns exist.

Experimental verification of fractional history effects on the viscous dynamics of small spherical particles

We investigate the low Reynolds, high-frequency particle response of non-neutrally buoyant particles suspended in a fluid. Gravity effects are suppressed by means of a very thin tether, whose effect on the horizontal movement of the particle is negligible due to the small amplitude, high-frequency nature of the forcing. The measured stationary responses of particles of different densities closely match the theoretical predictions for the full solution, including Basset history effects for both the amplitude ratio and the phase, and clearly differ from the solution where the history force is neglected.

Inertial migration of rigid spherical particles in Poiseuille flow

An experimental study of the migration of dilute suspensions of particles in Poiseuille flow at Reynolds numbers from the entrance, changes from one centred at the annulus predicted by the theory to one with the particles primarily on the inner annulus. The case of slightly non-neutrally buoyant particles was also investigated. A particle trajectory simulation based on asymptotic theory was performed to facilitate the comparison of theory and the experimental observations.

Axial segregation in a cylindrical centrifuge.

We propose a theory for axial segregation of suspensions of non-neutrally buoyant particles in a rotating cylinder. The cylinder is oriented in the horizontal plane, so that any axial forces must arise from interparticle interactions. We show that the hydrodynamic interaction between pairs of particles produces a relative motion in the axial direction, independent of the gravitational force. If the particles are denser than the suspending fluid, differential centrifuging between particles at different radial positions leads to an at-tractive interaction, inducing a rapid growth of axial density perturbations. We suggest that this mecha-nism can explain the origin of band formation in rotating suspensions of non-neutrally buoyant particles.