Inertial microfluidics has been attracting considerable interest in recent years due to immensely promising applications in cell biology. Despite the intense attention, the primary focus has been on development of inertial microfluidic devices with less emphasis paid to elucidation of the inertial focusing mechanics. The incomplete understanding, and sometimes confusing experimental results that indicate a different number of focusing positions in square or rectangular microchannels under similar flow conditions, have led to poor guidelines and difficulties in design of inertial microfluidic systems. In this work, we describe and experimentally validate a two-stage model inertial focusing in microchannels. Our analysis and experimental results show that not only the well-accepted shear-induced and wall-induced lift forces act on particles within flow causing equilibration near microchannel sidewalls, but the rotation-induced lift force influences the position of these equilibria. In addition, for the first time, we experimentally measure lift coefficients, which previously could only be obtained from numerical simulations. More importantly, insights offered by our two-stage model of inertial focusing are broadly applicable to cross-sectional geometries beyond rectangular. With elucidation of the equilibration mechanism, we envision better guidelines for the inertial microfluidics community, ultimately leading to improved performance and broader acceptance of the inertial microfluidic devices in a wide range of applications, from filtration to cell separations.

Fundamentals of inertial focusing in microchannels

Gas-solid flows in nature and industrial applications are characterized by multiscale and nonlinear interactions that manifest as rich flow physics and pose unique modeling challenges. In this article, we review particle-resolved direct numerical simulation (PR-DNS) of the microscale governing equations for understanding gas-solid flow physics and obtaining quantitative information for model development. A clear connection between a microscale realization and meso/macroscale representation is necessary for PR-DNS to be used effectively for model development at the meso- and macroscale. Furthermore, the design of PR-DNS must address the computational challenges of parameterizing models in a high-dimensional parameter space and obtaining accurate statistics of flow properties from a finite number of realizations at acceptable grid resolution. This review also summarizes selected recent insights into the physics of momentum, kinetic energy, and heat transfer in gas-solid flows obtained from PR-DNS. Promising future applications of PR-DNS include the study of the effect of number fluctuations on hydrodynamics, instabilities in gas-solid flow, and wall-bounded flows.

Particle-Resolved Direct Numerical Simulation for Gas-Solid Flow Model Development

Numerical simulations are extensively used to investigate the motion of suspended particles in a fluid and their influence on the dynamics of the overall flow. Contexts range from the rheology of concentrated suspensions in a viscous fluid to the dynamics of particle-laden turbulent flows. This review summarizes several current approaches to the numerical simulation of rigid particles suspended in a flow, pointing out both common features and differences, along with their primary range of application. The focus is on non-Brownian systems for which thermal fluctuations do not play a role, whereas interparticle forces may result in particle self-assembly. Applications may include the motion of a few isolated particles with complex shape or the collective dynamics of many suspended particles.

Simulation Methods for Particulate Flows and Concentrated Suspensions

Progress in particle resuspension from rough surfaces by turbulent flows

Predicting the morphodynamics of sedimentary landscapes due to fluvial and aeolian flows requires answering the following questions: is the flow strong enough to initiate sediment transport, is the flow strong enough to sustain sediment transport once initiated, and how much sediment is transported by the flow in the saturated state (i.e., what is the transport capacity)? In the geomorphological and related literature, the widespread consensus has been that the initiation, cessation, and capacity of fluvial transport, and the initiation of aeolian transport, are controlled by fluid entrainment of bed sediment caused by flow forces overcoming local resisting forces, whereas aeolian transport cessation and capacity are controlled by impact entrainment caused by the impacts of transported particles with the bed. Here the physics of sediment transport initiation, cessation, and capacity is reviewed with emphasis on recent consensus‐challenging developments in sediment transport experiments, two‐phase flow modeling, and the incorporation of granular physics' concepts. Highlighted are the similarities between dense granular flows and sediment transport, such as a superslow granular motion known as creeping (which occurs for arbitrarily weak driving flows) and system‐spanning force networks that resist bed sediment entrainment; the roles of the magnitude and duration of turbulent fluctuation events in fluid entrainment; the traditionally overlooked role of particle‐bed impacts in triggering entrainment events in fluvial transport; and the common physical underpinning of transport thresholds across aeolian and fluvial environments. This sheds a new light on the well‐known Shields diagram, where measurements of fluid‐entrainment thresholds could actually correspond to entrainment‐independent cessation thresholds.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/2019RG000679

The Physics of Sediment Transport Initiation, Cessation, and Entrainment Across Aeolian and Fluvial Environments

Numerical calculations are carried out for the natural convection induced by temperature difference between a cold outer square cylinder and a hot inner circular cylinder. A two-dimensional solution for unsteady natural convection is obtained, using the immersed boundary method (IBM) to model an inner circular cylinder based on finite volume method, for different Rayleigh numbers varying over the range of . The study goes further to investigate the effect of an inner cylinder location on the heat transfer and fluid flow. The location of inner circular cylinder is changed vertically along the center-line of square enclosure. The number, size and formation of cell strongly depend on Rayleigh number and the position of inner circular cylinder. The changes in heat transfer quantities have been presented.

A Numerical Study of Natural Convection in a Square Enclosure with a Circular Cylinder at Different Vertical Locations

Recent research (Zeng, PhD thesis, 2007; Zeng et al., Phys. Fluids, vol. 21, 2009, art. no. 033302) has shown that both the shear- and wall-induced lift contributions on a particle sharply increase as the gap between the wall and the particle is decreased. Explicit expressions that are valid over a range of finite Re were obtained for the drag and lift forces in the limiting cases of a stationary particle in wall-bounded linear flow and of a particle translating parallel to a wall in a quiescent ambient. Here we consider the more general case of a translating and rotating particle in a wall-bounded linear shear flow where shear, translational and rotational effects superpose. We have considered a modest Reynolds number range of 1–100. Direct numerical simulations using immersed boundary method were performed to systematically figure out the characteristics of hydrodynamic forces on a finite-sized particle moving while almost in contact with a wall. We present composite correlation for the hydrodynamic forces which are in agreement with all the available low-Reynolds-number theories.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/D280B528C9C0F18738055F0CE8C918FD/S0022112010001382a.pdf/div-class-title-drag-and-lift-forces-on-a-spherical-particle-moving-on-a-wall-in-a-shear-flow-at-finite-span-class-italic-re-span-div.pdf

Drag and lift forces on a spherical particle moving on a wall in a shear flow at finite Re

A simple work-based criterion for the onset of downstream migration of a particle sitting on a rough bed in a turbulent flow is developed in the present work. The criterion is motivated by the fact that the geometric pocket formed by other bed particles within which the mobile particle is sitting can be viewed as a potential well and the gravitational and frictional mechanisms impose an energy barrier for the particle to fully escape the pocket and initiate irreversible downstream migration. The energy barrier is clearly a statistical quantity, as it depends on the shape, size, and other details of the mobile particle and the geometry of the pocket. The energy barrier imposes a threshold value for the hydrodynamic work that must be done on the particle in order to initiate downstream migration. The simple work-based criterion developed here is related to the critical force and critical impulse criteria that have been advanced in the past. The fluctuating nature of the effective hydrodynamic force that works towards dislodging the particle out of the pocket and migrating it downstream is explored with data from a direct numerical simulation of turbulent channel flow and the probabilities of instances when the force, impulse, and work-based criteria for particle motion are satisfied and computed. The work-based criterion for particle migration is used to obtain an expression for the bed load transport that can be applied on an instantaneous basis at any local region of the bed. The average nondimensional bed load transport rate, or Einstein number, computed based on the present work-based model is shown to compare well with existing experimental data and empirical models. In particular, at low mobility regime, the present model is able to naturally recover the well-accepted rapid increase in bed load transport as 16th power of average bed shear stress and at high mobility regime the present model captures the slower increase in bed load transport with increasing average bed shear stress.

Work-based criterion for particle motion and implication for turbulent bed-load transport

Up until recently direct numerical simulation (DNS) studies involving round turbulent jets have focused on first and second order statistics and vortical behavior near the source of the jet. The third order statistics necessary to compute the turbulent kinetic energy and Reynolds stress transport equations have been examined using LES studies. However, further examination with DNS is important as, on the subgrid scale, LES uses models for Reynolds stress. In this study a DNS of a turbulent free jet with a Reynolds number equal to ReJ = 2000 is computed using a second order accurate, time splitting finite volume scheme. First, second, and third order statistics are compared with previous experimental and numerical studies. All terms of the turbulent kinetic energy balance are calculated directly. The results are compared to experimental studies such as those of Hussein et al. [“Velocity measurements in a high-Reynolds-number, momentum-conserving, axisymmetric, turbulent jet,” J. Fluid Mech. 258, 31–75 (199...

A direct numerical simulation study of higher order statistics in a turbulent round jet

[1] The main objectives of the present study are to obtain improved models of hydrodynamic forces and torque on a particle sitting on a bed and to use these models for the investigation of incipient motion and resuspension of particles. The improved models for force and torque are obtained from numerical simulations of a particle sitting on a bed with a turbulent flow of logarithmic mean velocity profile approaching the particle. Since the mean turbulent velocity profile can depart from the logarithmic profile in case of macroscale rough beds or flow down steep slopes, we have also considered forces and torque on a particle due to both linear and uniform mean flow profiles. The computed drag and lift coefficients and the predicted critical shear stress for incipient particle motion and resuspension are compared against available experimental results. The improved force and torque models are also used to evaluate the effect of turbulent velocity fluctuations on the critical shear stress for incipient motion and resuspension. The present results are of direct relevance to cases where the particle is mostly exposed to the ambient flow. In cases where the particle protrusion is small and is submerged mostly within a pocket of other particles, the above formulation can be used with a redefined area of exposure and flow velocity seen by the particle. However, the drag, lift, and torque coefficients and the resisting forces will be influenced by the partial exposure and the details of pocket geometry, which require further investigation.

https://agupubs.onlinelibrary.wiley.com/doi/epdf/10.1029/2011JF002208

Hyungoo Lee

Papers

A Numerical Study of Natural Convection in a Square Enclosure with a Circular Cylinder at Different Vertical Locations

Drag and lift forces on a spherical particle moving on a wall in a shear flow at finite Re

Work-based criterion for particle motion and implication for turbulent bed-load transport

A direct numerical simulation study of higher order statistics in a turbulent round jet

Critical shear stress for incipient motion of a particle on a rough bed