Michael G. Olsen

Brownian motion and correlation in particle image velocimetry

In particle image velocimetry applications involving either low velocities or small seed particles, Brownian motion can be significant. This paper addresses the effects of Brownian motion. First, general equations describing cross-correlation particle image velocimetry are derived that include Brownian motion. When light-sheet illumination particle image velocimetry (PIV) is used Brownian motion diminishes the signal strength. A parameter describing this effect is introduced, and a weighting function describing the contribution to the measured velocity as a function of position is derived. The latter is unaffected by Brownian motion. Microscopic PIV Brownian motion also diminishes the signal strength. The weighting function for microscopic PIV is found to depend on Brownian motion, thus affecting an important experimental parameter, the depth of correlation. For both light-sheet illumination and microscopic PIV, a major consequence of Brownian motion is the spreading of the correlation signal peak. Because the magnitude of the spreading is dependent on temperature, PIV can, in principle, be used to simultaneously measure velocity and temperature. The location of the signal peak provides the velocity data, while the spreading of the peak yields temperature.

Passive mixing in microchannels: Fabrication and flow experiments

Abstract Obtaining rapid mixing in microfluidic systems is a problem that must continue to be addressed if microelectromechanical systems are to attain their full potential in commercial markets. We present the paradigm of “designing for chaos” as a general framework for enhancing mixing in microfluidic applications. Designing for chaos is based on a fundamental understanding of the kinematics underlying the mixing process, freeing the MEMS researcher to work with design guidelines instead of empirically determined physical configurations. We have applied this strategy in designing a passive in-line micromixer that relies on three degrees of freedom to create chaos. The mixer design was fabricated using a compression micromolding process to create three-dimensional flow channels in polydimethylsiloxane (PDMS). Computational and experimental analyses demonstrate the effectiveness of the resulting design in generating chaos in the flow and hence enhancing mixing.

Validation of an analytical solution for depth of correlation in microscopic particle image velocimetry

Because the entire flowfield is generally illuminated in microscopic particle image velocimetry (microPIV), determining the depth over which particles will contribute to the measured velocity is more difficult than in traditional, light-sheet PIV. This paper experimentally and computationally measures the influence that volume illumination, optical parameters, and particle size have on the depth of correlation for typical microPIV systems. First, it is demonstrated mathematically that the relative contribution to the measured velocity at a given distance from the object plane is proportional to the curvature of the local cross-correlation function at that distance. The depth of correlation is then determined in both the physical experiments and in computational simulations by directly measuring the relative contribution to the correlation function of particles located at a known separation from the object plane. These results are then compared with a previously derived analytical model that predicts the depth of correlation from the basic properties of the imaging system and seed particles used for the microPIV measurements. Excellent agreement was obtained between the analytical model and both computational and physical experiments, verifying the accuracy of the previously derived analytical model.

A microscale multi-inlet vortex nanoprecipitation reactor: Turbulence measurement and simulation

Microscale reactors capable of generating turbulent flow are used in Flash NanoPrecipitation, an approach to produce functional nanoparticles with unique optical, mechanical and chemical properties. Microreactor design and optimization could be greatly enhanced by developing reliable computational models of the nanoprecipitation process. A microscale multi-inlet vortex nanoprecipitation reactor was investigated using microscopic particle image velocimetry and computational fluid dynamics. Velocity data such as the mean velocity and turbulent kinetic energy displayed good agreement between experiment and simulation over flow conditions ranging from fully laminar to turbulent, demonstrating the accuracy of the simulation model over the entire turbulent transition range.

Out-of-Plane Motion Effects in Microscopic Particle Image Velocimetry

In microscopic particle image velocimetry (microPIV) experiments, the entire volume of a flowfield is illuminated, resulting in all of the particles in the field of view contributing to the image. Unlike in light-sheet PIV, where the depth of the measurement volume is simply the thickness of the laser sheet, in microPIV, the measurement volume depth is a function of the image forming optics of the microscope. In a flowfield with out-of-plane motion, the measurement volume (called the depth of correlation) is also a function of the magnitude of the out-of-plane motion within the measurement volume. Equations are presented describing the depth of correlation and its dependence on out-of-plane motion. The consequences of this dependence and suggestions for limiting its significance are also presented

Aspect Ratio Effects on Turbulent and Transitional Flow in Rectangular Microchannels as Measured With MicroPIV

Microscopic particle image velocimetry (microPIV) was used to measure velocities in rectangular microchannels with aspect ratios ranging from 0.97 to 5.69 for 200 Re 3267. Mean velocity profiles, velocity fluctuations, and Reynolds stresses were determined from the microPIV data. Transition to turbulence was observed at Re = 1765– 2315 for the five aspect ratios studied, agreeing very well with both recent microscale experiments and macroscale duct flow and indicating no evidence of early transition for any of the aspect ratios studied. The onset of fully turbulent flow was observed at Re= 2600– 3200. For the fully turbulent flow, the u /umax and v /umax fluctuations at the channel centerline were 6% and 3%‐3.5% and generally agreed well with macroscale results. As aspect ratio increased, the u /umax and u /umax profiles became flatter, with nearly uniform values extending for some distance from the centerline of the channel. This region of uniform u /umax and u /umax became larger with increasing aspect ratio. The Reynolds shear stress for fully turbulent flow also displayed a strong dependence on aspect ratio. For the W /H = 0.97 microchannel, uv /u max steadily increased in value moving from the centerline to the wall, but for the higher aspect ratio microchannels, uv /u max remained close to zero in the center region of the microchannel before increasing in value at locations close to the wall, and this region of near zero uv /u max became larger with increasing aspect ratio. This behavior in the Reynolds shear stress is due to the region of uniform velocity and, hence, small mean shear, near the channel centerline of the high aspect ratio microchannels. DOI: 10.1115/1.2170122

Planar velocity measurements in a weakly compressible mixing layer

High-vector-density planar velocity fields were obtained for a weakly compressible mixing layer using particle image velocimetry (PIV). The velocity ratio of the mixing layer was 0.53, the density ratio was 0.67, and the convective Mach number was 0.38. At the location where the PIV images were obtained, Rex =3 .7 × 10 6 and Reδω =1 .8 × 10 5 .T he instantaneous planar velocity fields fall into three regimes characterized by the size and number of large-scale structures present. The largescale rollers are either circular or elliptical, with the elliptical rollers having, in general, horizontal major axes. The transverse velocity fluctuations and Reynolds shear stress are suppressed for the weakly compressible mixing-layer as compared to the incompressible case. The spatial correlations of velocity fluctuations also occupy as maller fraction of the mixing-layer thickness than for an incompressible mixing layer. The linear stochastic estimate of a roller structure is elliptical with the major axis oriented in the streamwise direction and with an eccentricity greater than for the incompressible case. The linear stochastic estimate of a braid suggests that the braids are vertically oriented, as opposed to the oblique orientation seen in incompressible mixing layers. In addition, the braids in the weakly compressible case have a vertically oriented stagnation line, as opposed to the braids in the incompressible mixing layer where stagnation occurs at a point.

The Depth of Correlation in Micro-PIV for High Numerical Aperture and Immersion Objectives

The analytical model for the depth of correlation (measurement depth) of a microscopic particle image velocimetry (micro-PIV) experiment derived by Olsen and Adrian has been modified to be applicable to experiments using high numerical aperture optics. A series of measurements are presented that experimentally quantify the depth of correlation of micro-PIV velocity measurements which employ high numerical aperture and magnification optics. These measurements demonstrate that the modified analytical model is quite accurate in estimating the depth of correlation in micro-PIV measurements using this class of optics

Directional dependence of depth of correlation due to in-plane fluid shear in microscopic particle image velocimetry

An analytical model for the microscopic particle image velocimetry (microPIV) correlation signal peak in a purely shearing flow was derived for the case of in-plane shearing (out-of-plane shearing was not considered). This model was then used to derive equations for the measured velocity weighting functions for the two velocity components, and the weighting functions were in turn used to define the depths of correlation associated with the two measured velocity components. The depth of correlation for the velocity component perpendicular to the shear was found to be unaffected by the shear rate. However, the depth of correlation for the velocity component in the direction of the shear was found to be highly dependent on the shear rate, with the depth of correlation increasing as the shear rate increased. Thus, in a flow with shear, there is not a single value for the depth of correlation within an interrogation region. Instead, the depth of correlation exhibits directional dependence, with a different depth of correlation for each of the two measured velocity components. The increase in the depth of correlation due to the shear rate is greater for large numerical aperture objectives than for small numerical aperture objectives. This increase in the depth of correlation in a shearing flow can be quite large, with increases in the depth of correlation exceeding 100% being very possible for high numerical aperture objectives. The effects of out-of-plane shear are beyond the capabilities of this analysis, although the possible consequences of out-of-plane shear are discussed.

Particle imaging technique for measuring the deformation rate of hydrogel microstructures

A technique for measuring the instantaneous deformation rate of hydrogel microstructures is introduced. In developing this technique, we have adapted microscopic particle image velocimetry, a method for measuring velocity fields in microfluidic devices. Small fluorescent seed particles are incorporated into the hydrogel microstructure, and as the structure swells or contracts, the displacement of the seed particles over some small time Δt is measured using a cross-correlation technique. By providing local deformation rate data in hydrogel microstructures, this technique will allow for optimization of device designs as well as providing a means for determining the validity of hydrogel expansion models.