Session LC: Microfluidics Dynamics IX: Velocimetry

3-D 3-C Layered Micro-PIV

A method to estimate three-components of velocity in a micro-flow has been developed using a micron-resolution Particle Image Velocimetry (micro-PIV) technique (Meinhart et al. 1999) to resolve a number of velocity-vector fields spaced in the out-of-plane direction. A fourth-order accurate finite differencing algorithm is used to estimate the out-of-plane component of velocity at each point in the flow by solving the continuity equation. An experiment was completed to estimate flow around an adherent red blood cell. In that experiment, fourteen velocity-vector field layers each spaced 0.88 microns in the out-of-plane direction were resolved using the micro-PIV technique. A numerical simulation of flow around a rigid hemispherical protrusion (the size of the red cell) was used to estimate the accuracy of the post-processing algorithm to be within one percent. The numerical simulation was also compared to experimental results of flow around a red cell to show agreement. We will discuss the experimental results, accuracy, limitations, and applications of this method.   

PIV Measurements of Slug Flow in a Square Microchannel

Many ``lab on a chip'' flows contain packets of one fluid, e.g. water, surrounded by a non-mixing fluid, e.g. oil, flowing through microchannels. This flow regime is referred to as slug flow. Issues of current importance include determining the magnitudes of wall shear (drag) forces and the mixing characteristics associated with slug flows. Water in oil slug flow was studied by Micro-PIV in a square cross section micro-channel. The slug flows have Re$_{D} \cong $ 10, (D = channel hydraulic diameter), and Ca $\cong $1.4 x 10$^{-4}$. Aspect ratios, A, (A = L/D, where L = slug length) from 1.5 to 3.25 were studied. Measurements of the slug internal flow fields are presented. These show that the flows are qualitatively well described by solutions to the Biharmonic equation. Entry length like regions (and similar ``exit regions'') are observed at the leading (trailing) edge of the slugs over which the velocity profile varies from nearly uniform to a fully developed parabolic profile. These regions affect the wall shear (viscous drag) developed by slugs. In a co-ordinate frame traveling with the slug two counter rotating regions which resemble ``tank tracks'' rolling along the channel walls become apparent. Regions of high shear, which have important implications for mixing, are observed near the leading and trailing edge of the slug where these ``rolling tracks'' come together or separate.   

Particle Motion under Shear-Induced Migration in Square-PDMS Microchannels

An experimental study has been conducted to quantitatively characterize particle motion under shear-induced migration in square-PDMS microchannels by applying $\mu $-PTV technique. It is shown that particles are accumulated at the equilibrium position of 0.67$H$, with $H$ being a half width of the channel, which is analogous to what is observed in circular tube flow in macro scale. Since high shear rate can be induced due to the scale effect, particle migration occurs markedly even at low Reynolds number ranging from 4 to 57 while this phenomenon dose not typically occur at this range of the Reynolds number in macro scale. At \textit{Re} = 57, it is found that particles are nearly absent around the center of the channel, which is coincident with previous numerical result obtained for a square duct at \textit{Re} = 100. The outermost edge of particle cluster is in good agreement with previous study. It is rapidly converging to about $y/H$ = 0.7 at $L_{3}$ = 1, where $L_{3}$ = (0.5$d_{p}$/$H)^{3}(l$/$2H)$\textit{Re} is the reduced tube length, $d_{p}$ is the diameter of the spherical particle and $l$ is the measurement position from channel inlet. Since the thickness of particle-free layer is largest at $L_{3}$ = 1, it is indicated that plasma selectivity and total amount of plasma separated can be maximized at this value of $L_{3}$ when serum from the whole blood is separated into side channels in lab-on-a-chip systems, by minimizing the clogging of RBCs (Red Blood Cells). The present study is expected to give optimum factors for designing of microfluidic systems.   

Three-component velocity measurement in a micro-scale three-dimensional flow environment using correlation tracking.

A tentative study on a technique for measuring the full field (x,y,z,u,v,w) velocity distribution of the fluid flow at the micrometer scale using single high-speed camera, an epifluorescent microscope, a CW laser, and a piezo actuator. To investigate the three-dimensional (3D) flow structures on a microscopic scale flow, 3D scanning micro-particle image velocimetry was applied to the inclined micro round tube. A three-dimensional (3D) scanning micro-PIV technique having a micrometer scale spatial resolution is applied to an inclined micro round tube to develop the 3D-3C velocity measurement technique with a formerly known out of plane velocity component. In two time sequential micro or macro PIV images, if they are correlated and then they are deformed with respect to the half of the in-plane displacements they will become almost the same. In this study, we investigated the alteration of the correlation peak height in the time domain. Gradient of the cross-correlation is strongly related with the dept-wise velocity component. Correlation peak height alteration captured clearly in time sequential image assemblies. From these correlation gradients, extraction of depth-wise velocity component could seem to be straight forward.   

Two-Component Velocity Measurements of the Flow over a Backward Facing Step within a Microchannel using Molecular Tagging Velocimetry

Flow over a backward facing step at macro scales has been extensively studied in the past. The micro-scale counterpart of this flow has received less attention, however. In this work we investigate the flow over a micro step as a possible geometric configuration useful for enhanced chemical mixing and detection caused by a longer flow residence time within the recirculation zone. The geometry considered here consists of a microchannel with a gap height of 170 microns that expands to a gap height of 340 microns after a step. Measurements are based on molecular tagging velocimetry (MTV) using phosphorescent supramolecules as molecular tracers. Past applications of MTV in microflows have utilized line tagging for obtaining velocity data in primarily unidirectional flows, an approach this is not suitable for the flow studied here. We use tagging by a grid of intersecting laser lines to measure two components of the velocity field over a plane. Velocity fields before, at, and after the step will be presented for different flow rates, allowing the determination of the flow characteristics in the presence of a step.   

The Structure of Transitional Wall-Bounded Microscale Flows

Micro-PIV is used to study the structure of transitional wall- bounded flows at the microscale. High-resolution, instantaneous measurements of the velocity fields are obtained in the streamwise--wall-normal plane of a 536\,$\mu$m glass capillary over a broad Reynolds-number range ($1800<\mathrm{Re}<3500$). The mean velocity profiles show a deviation from laminar behavior at $\mathrm{Re}\sim 1900-2000$, with fully-developed turbulence occurring at $\mathrm{Re}\sim 3400-3500$. Examination of the instantaneous velocity fields for the transitional Reynolds numbers reveals the existence of isolated patches of turbulent flow that are interspersed within regions of flow displaying purely laminar behavior. These observations are similar to the observations of turbulent spots in macroscale transitional pipe flow. The progress of transition to turbulence is studied by comparing the instantaneous velocity profiles at all streamwise locations to the expected parabolic profile for laminar flow in order to estimate the fraction of the flow that displays laminar behavior. The ``laminar fraction'' of the flow as a function of the Reynolds number reveals a smooth transition to turbulence at the microscale. A similar trend is also noted in the energy distribution represented by the eigenvalue spectra of the POD modes.   

Statistical and Structural Features of Wall Turbulence at the Microscale

Measurements of instantaneous velocity fields are made using micro-PIV in the streamwise--wall-normal plane of a 536\,$\mu$m glass capillary at $\mathrm{Re}=4500$ to study the statistical and structural features of wall turbulence at the microscale. Single-point velocity statistics are found to agree well with established direct numerical simulations of turbulence in the same geometry at $\mathrm{Re}=5300$, thereby validating the efficacy of micro-PIV as an experimental technique for studying instantaneous and unsteady flow behavior at the microscale. The instantaneous micro-PIV velocity fields reveal multiple spanwise vortices that streamwise-align to form larger-scale interfaces inclined away from the wall at a shallow angle. These observations are consistent with the signatures of hairpin vortices and their alignment into hairpin vortex packets that are observed in instantaneous PIV realizations of macroscale wall turbulence. Further, the hairpin structures and their organization into larger-scale vortex packets are shown to be statistically-significant features of wall turbulence at the microscale using two-point velocity correlations and estimates of the conditionally-averaged velocity fields given a spanwise vortex core.   

Measurement and Simulation of Hindered Diffusion and the Implications for Near-Wall Velocimetry

The dynamics of hindered diffusion of near-wall colloidal particles is measured using Frustrated-Total Internal Reflection Fluorescent Microscopy and simulated using Brownian Dynamics.~ Particles can be experimentally tracked in three dimensions with an accuracy of 32 nm.~ The experimental and numerical results are in excellent agreement, and demonstrate the anisotropy of hindered diffusion, in good agreement to the classical theoretical results of Goldman and Brenner.~ The effect of shear on the diffusion dynamics is also explored, and it is found that the particle displacement distribution changes significantly as the Peclet number rises, reaching an equilibrium shear-dominated distribution for Pe $>$ 3.~ These results have significant implications for near wall velocimetry experiments in which an estimation of velocity is derived from the observed motion of tracer particles.~ We identify the errors that can arise due to Brownian motion, hindered diffusion and shear and discuss how these errors are affected by the various flow conditions as well as the time between adjacent observations of particles.   

Label-free and real-time imaging of microscale mixture concentration fields using Surface Plasmon Resonance (SPR) reflectance

A label-free visualization technique is presented based on surface plasmon resonance (SPR) reflectance sensing. The developed SPR imaging system is applied for the nonintrusive and real-time mapping of microscale mixture concentration fields. The key idea is that the SPR reflectance sensitively varies with the refractive index of the near-wall region of the test field contacting the thin metal (Au) layer. The Fresnel equation, based on Kretschmann's theory, correlates the SPR reflectance with the refractive index of the test medium and with the mixture concentration. An example application is presented for the case of ethanol penetrating into water contained in a micro-channel with a rectangular cross-section of 91-micrometer wide and 50-micrometer high. The measurement sensitivity, uncertainties and detection limitations of the implemented SPR imaging sensor are carefully examined for its potential as a nonintrusive means of microscale concentration field mapping.   

Diffusion-Induced Bias in Near-Wall Velocimetry

Brownian fluctuations of the colloidal tracers used in many microscale velocimetry techniques yield effects that are typically isotropic in the bulk. In contrast, near-wall Brownian diffusion is strongly influenced by the wall because of the no-flux condition and hindered diffusion. These effects bias any measurement sampled by the colloidal tracers, potentially leading to significant overestimation of near-wall velocities. A Fokker-Planck description of the Brownian motion is used to generate probability density functions of the distances normal to the wall sampled by matched particles present in the same window at both the start and end of a time interval. The importance of the resulting bias for experimental parameters is then quantified in terms of the size of the tracer particles, imaged region, and measurement interval. A method for rescaling near-wall velocity data is presented, and the implications for image velocimetry and slip length measurements are briefly discussed.   

Estimating the Slip Length using Single Quantum Dot (QD) Velocimetry

The motion of Quantum Dot (QD) nanoparticles is tracked within a few hundred nanometers of a surface using evanescent wave illumination. Water soluble quantum dots with a core diameter size of 6 nm and effective hydrodynamic diameter of 16 nm are used in this study. The local fluid velocity is inferred from tracking the QDs in a pressure-driven flow of an aqueous solution inside a 200 micron microchannel. An estimate of slip between the liquid and solid surface is obtained once the measured velocity is assigned to a `mean location' based on the QD distribution that is deduced from their intensity values. Several issues, including the high diffusivity of QDs and the non-uniform distribution of the dots near to the wall, affect the interpretation of the measurements and hence the slip estimates. The effects of these parameters are discussed and methods to correctly interpret the measurements are presented. The measured velocities and QD distributions along with slip estimates are presented for a flow in a quartz microchannel with a naturally hydrophilic surface.   

Slip Lengths on Hydrophobic and Hydrophilic Surfaces Measured by Quantum Dots

We report measurements of slip length obtained from tracking of individual quantum dots (QDs) within a few hundred nanometers of a surface using evanescent wave illumination. The measurements are obtained at different shear rates on a hydrophilic (quartz) and a hydrophobic (OTS-coated quartz) surface forming the wall of a rectangular microchannel nominally 300 micron in height. The shear rate is obtained independently by molecular tagging velocimetry (MTV) measurement of the in-situ velocity profile across the 300 micron height of the microchannel. Results indicate a larger slip length for the hydrophobic surface.