Measurement of Slip Velocity and Lift Coefficient for Laterally Focused Particles in an Inertial Flow through a Spiral Microfluidic Channel

Microfluidic channels with a spiral geometry are extensively researched for their use in particle focusing, separation and identification. Instead of using electrophoresis, magnetophoresis, etc., spiral channel takes advantage of the Inertial Lift Force along with the Viscous Drag to achieve size based separation of particles. Inertial microfluidic channel can have high throughput and are much safer to use for live cell separation and other physiological fluids processing. A particle flowing freely in a spiral microchannel at low Reynolds number inertial flow, attains lateral equilibrium due to balance of Inertial Lift force and the viscous Dean Drag. The inertial lift forces are primarily due to the wall effect and the shear gradient of the fluid flow profile. Much theoretical research has been done in this field to explain the lateral migration of a particle in an inertial fluid flow. Notable contributions were made by Saffman (1965), Ho and Leal (1974) and later Vasseur and Cox (1976) in explaining the lift force on a particle theoretically. All these and many other theoretical models developed in the last few decades discuss Lift force being dependent on the particle slip velocity. Additionally many models including the one developed by Saffman predicts a linear dependence of Lift force on the slip velocity of particle. But it seems that the microfluidic community has ignored this dependence with the result that several hypotheses and models exist in which the slip velocity is nonexistent. The measurement of slip velocities for particles has never been done in the field of microfluidics. The current study aims to do so and bridge the gap in understanding the Lift force responsible for the lateral migration of particles. The focused particle’s velocity when it passes through the outer arm of the spiral microfluidic device is measured experimentally followed by a computational study (using COMSOL Multiphysics) to obtain the undisturbed fluid flow velocity through the spiral arm. To calculate the slip velocity, identification of focusing positions in the horizontal and vertical plane of the channel is necessary. Identification in horizontal plane is easy by simply observing the channel under microscope. To identify the vertical focusing positions, a high speed camera (Photron SA-4) coupled with a Nikon microscope and a 50x objective lens (depth of focus = 0.9 um) is used. The narrow depth of focus of objective lens coupled with the precise movement of microfluidic device in the vertical plane is used to identify the height of focused particles from the channel bottom. A focus-measure of all the acquired images is calculated (using a Matlab script which calculates the global variance of an image as a focus-measure) followed by its statistical distribution to obtain the particle’s vertical location within an error of ±5 um. Velocity of the particles for all the focused positions is now calculated using a Matlab script which detects the particles from the acquired images and traces it across successive frames. At the focused position, particle is in equilibrium due to a balance of Dean Drag and the Inertial Lift force. Velocity components of Dean Flow are obtained from the computational study, followed by calculation of Dean Drag acting on the focused particles. The Lift force acting on the particle is now known and equating it with the slip velocity of particles, numerical values of Lift coefficient are obtained for the first time. These Lift coefficients are obtained for various focusing positions in the vertical plane of channel for two sets of Reynolds number

Spectral/hp element methods for plane Newtonian extrudate swell

Spectral/hp element methods and an arbitrary Lagrangian-Eulerian (ALE) moving-boundary technique are used to investigate planar Newtonian extrudate swell. Newtonian extrudate swell arises when viscous liquids exit long die slits. The problem is characterised by a stress singularity at the end of the slit which is inherently difficult to capture and strongly influences the predicted swelling of the fluid. The impact of inertia (0 <Re < 100) and slip along the die wall on the free surface profile and the velocity and pressure values in the domain and around the singularity are investigated. The high order method is shown to provide high resolution of the steep pressure profile at the singularity. The swelling ratio and exit pressure loss are compared with existing results in the literature and the ability of high-order methods to capture these values using significantly fewer degrees of freedom is demonstrated

Pressure-driven flow of suspensions: simulation and theory

Dynamic simulations of the pressure-driven flow in a channel of a non-Brownian suspension at zero Reynolds number were conducted using Stokesian Dynamics. The simulations are for a monolayer of identical particles as a function of the dimensionless channel width and the bulk particle concentration. Starting from a homogeneous dispersion, the particles gradually migrate towards the centre of the channel, resulting in an homogeneous concentration profile and a blunting of the particle velocity profile. The time for achieving steady state scales as (H/a)3a/[left angle bracket]u[right angle bracket], where H is the channel width, a the radii of the particles, and [left angle bracket]u[right angle bracket] the average suspension velocity in the channel. The concentration and velocity profiles determined from the simulations are in qualitative agreement with experiment. A model for suspension flow has been proposed in which macroscopic mass, momentum and energy balances are constructed and solved simultaneously. It is shown that the requirement that the suspension pressure be constant in directions perpendicular to the mean motion leads to particle migration and concentration variations in inhomogeneous flow. The concept of the suspension ‘temperature’ – a measure of the particle velocity fluctuations – is introduced in order to provide a nonlocal description of suspension behaviour. The results of this model for channel flow are in good agreement with the simulations

Revisiting the 1954 Suspension Experiments of R. A.Bagnold

In 1954 R. A. Bagnold published his seminal findings on the rheological properties of a liquid-solid suspension. Although this work has been cited extensively over the last fifty years, there has not been a critical review of the experiments. The purpose of this study is to examine the work and to suggest an alternative reason for the experimental findings. The concentric cylinder rheometer was designed to measure simultaneously the shear and normal forces for a wide range of solid concentrations, fluid viscosities and shear rates. As presented by Bagnold, the analysis and experiments demonstrated that the shear and normal forces depended linearly on the shear rate in the 'macroviscous' regime; as the grain-to-grain interactions increased in the 'grain-inertia' regime, the stresses depended on the square of the shear rate and were independent of the fluid viscosity. These results, however, appear to be dictated by the design of the experimental facility. In Bagnold's experiments, the height (h) of the rheometer was relatively short compared to the spacing (t) between the rotating outer and stationary inner cylinder (h/t=4.6). Since the top and bottom end plates rotated with the outer cylinder, the flow contained two axisymmetric counter-rotating cells in which flow moved outward along the end plates and inward through the central region of the annulus. At higher Reynolds numbers, these cells contributed significantly to the measured torque, as demonstrated by comparing Bagnold's pure-fluid measurements with studies on laminar-to-turbulent transitions that pre-date the 1954 study. By accounting for the torque along the end walls, Bagnold's shear stress measurements can be estimated by modelling the liquid-solid mixture as a Newtonian fluid with a corrected viscosity that depends on the solids concentration. An analysis of the normal stress measurements was problematic because the gross measurements were not reported and could not be obtained

Recent advances in the simulation of particle-laden flows

A substantial number of algorithms exists for the simulation of moving particles suspended in fluids. However, finding the best method to address a particular physical problem is often highly non-trivial and depends on the properties of the particles and the involved fluid(s) together. In this report we provide a short overview on a number of existing simulation methods and provide two state of the art examples in more detail. In both cases, the particles are described using a Discrete Element Method (DEM). The DEM solver is usually coupled to a fluid-solver, which can be classified as grid-based or mesh-free (one example for each is given). Fluid solvers feature different resolutions relative to the particle size and separation. First, a multicomponent lattice Boltzmann algorithm (mesh-based and with rather fine resolution) is presented to study the behavior of particle stabilized fluid interfaces and second, a Smoothed Particle Hydrodynamics implementation (mesh-free, meso-scale resolution, similar to the particle size) is introduced to highlight a new player in the field, which is expected to be particularly suited for flows including free surfaces.Comment: 16 pages, 4 figure

CFD analysis of industrial multi-staged stirred vessels

This paper presents tools for analysis of CFD results adapted for flows in multi-stage stirred vessels through out two industrial cases. Those tanks fitted with double-flow impellers are used first to cool down highly viscous resins and subsequently for indirect emulsification. Since the simulation of these processes in their whole complexity would be unrealistic, it considers single-phase flows without heat transfer. The result analysis in order to prove that the mixing and the circulation are effective is not usual; in these cases, the circulation and impeller numbers are not adapted. The average axial flow numbers are relevant of the circulation in the whole tank and of the connection between the flows produced by the propellers in the given configuration. The velocity profiles give relevant results, but are not sufficient whereas the particle tracking validates that the propellers do not work together in one case and do work together in a second one