To improve the performance of particle image velocimetry in measuring instantaneous velocity fields, direct cross-correlation of image fields can be used in place of auto-correlation methods of interrogation of double- or multiple-exposure recordings. With improved speed of photographic recording and increased resolution of video array detectors, cross-correlation methods of interrogation of successive single-exposure frames can be used to measure the separation of pairs of particle images between successive frames. By knowing the extent of image shifting used in a multiple-exposure and by a priori knowledge of the mean flow-field, the cross-correlation of different sized interrogation spots with known separation can be optimized in terms of spatial resolution, detection rate, accuracy and reliability.

Theory of cross-correlation analysis of PIV images : Image analysis as measuring technique in flows

1. Introduction to colloid science and rheology 2. Hydrodynamic effects 3. Brownian hard spheres 4. Stable colloidal suspensions 5. Non-spherical particles 6. Weakly flocculated suspensions 7. Thixotropy 8. Shear thickening 9. Rheometry of suspensions 10. Suspensions in viscoelastic media 11. Advanced topics.

Colloidal Suspension Rheology

Controlled manipulation of particles from very large volumes of fluid at high throughput is critical for many biomedical, environmental and industrial applications. One promising approach is to use microfluidic technologies that rely on fluid inertia or elasticity to drive lateral migration of particles to stable equilibrium positions in a microchannel. Here, we report on a hydrodynamic approach that enables deterministic focusing of beads, mammalian cells and anisotropic hydrogel particles in a microchannel at extremely high flow rates. We show that on addition of micromolar concentrations of hyaluronic acid, the resulting fluid viscoelasticity can be used to control the focal position of particles at Reynolds numbers up to Re≈10,000 with corresponding flow rates and particle velocities up to 50 ml min−1 and 130 m s−1. This study explores a previously unattained regime of inertio-elastic fluid flow and demonstrates bioparticle focusing at flow rates that are the highest yet achieved. Controlled manipulation of particles from very large volumes of fluid at high throughput is critical for many real-world applications. Here, the authors show bioparticle focusing in a microchannel for a previously unattained regime of inertio-elastic flow at Reynolds numbers up to 10,000.

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Inertio-elastic focusing of bioparticles in microchannels at high throughput

We numerically study the effect of solid boundaries on the swimming behavior of a motile microorganism in viscoelastic media. Understanding the swimmer-wall hydrodynamic interactions is crucial to elucidate the adhesion of bacterial cells to nearby substrates which is precursor to the formation of the microbial biofilms. The microorganism is simulated using a squirmer model that captures the major swimming mechanisms of potential, extensile, and contractile types of swimmers, while neglecting the biological complexities. A Giesekus constitutive equation is utilized to describe both viscoelasticity and shear-thinning behavior of the background fluid. We found that the viscoelasticity strongly affects the near-wall motion of a squirmer by generating an opposing polymeric torque which impedes the rotation of the swimmer away from the wall. In particular, the time a neutral squirmer spends at the close proximity of the wall is shown to increase with polymer relaxation time and reaches a maximum at Weissenberg number of unity. The shear-thinning effect is found to weaken the solvent stress and therefore, increases the swimmer-wall contact time. For a puller swimmer, the polymer stretching mainly occurs around its lateral sides, leading to reduced elastic resistance against its locomotion. The neutral and puller swimmers eventually escape the wall attraction effect due to a releasing force generated by the Newtonian viscous stress. In contrast, the pusher is found to be perpetually trapped near the wall as a result of the formation of a highly stretched region behind its body. It is shown that the shear-thinning property of the fluid weakens the wall-trapping effect for the pusher squirmer.

Effect of solid boundaries on swimming dynamics of microorganisms in a viscoelastic fluid

Insect wing shapes are diverse and a renowned source of inspiration for the new generation of autonomous flapping vehicles, yet the aerodynamic consequences of varying geometry is not well understood. One of the most defining and aerodynamically significant measures of wing shape is the aspect ratio, defined as the ratio of wing length (R) to mean wing chord (c). We investigated the impact of aspect ratio, AR, on the induced flow field around a flapping wing using a robotic device. Rigid rectangular wings ranging from AR = 1.5 to 7.5 were flapped with insect-like kinematics in air with a constant Reynolds number (Re) of 1400, and a dimensionless stroke amplitude of 6.5c (number of chords traversed by the wingtip). Pseudo-volumetric, ensemble-averaged, flow fields around the wings were captured using particle image velocimetry at 11 instances throughout simulated downstrokes. Results confirmed the presence of a high-lift, separated flow field with a leading-edge vortex (LEV), and revealed that the conical, primary LEV grows in size and strength with increasing AR. In each case, the LEV had an arch-shaped axis with its outboard end originating from a focus-sink singularity on the wing surface near the tip. LEV detachment was observed for AR > 1.5 around mid-stroke at ~70% span, and initiated sooner over higher aspect ratio wings. At AR > 3 the larger, stronger vortex persisted under the wing surface well into the next half-stroke leading to a reduction in lift. Circulatory lift attributable to the LEV increased with AR up to AR = 6. Higher aspect ratios generated proportionally less lift distally because of LEV breakdown, and also less lift closer to the wing root due to the previous LEV's continuing presence under the wing. In nature, insect wings go no higher than AR ~ 5, likely in part due to architectural and physiological constraints but also because of the reducing aerodynamic benefits of high AR wings.

https://iopscience.iop.org/article/10.1088/1748-3190/10/5/056020/pdf

The effect of aspect ratio on the leading-edge vortex over an insect-like flapping wing.

Through the use of stereoscopic 3-D particle image velocimetry (3-D PIV), the flow field surrounding a sphere sedimenting at a distance of one, two and three ball diameters from the wall is measured. A Newtonian (constant shear viscosity, inelastic) fluid, a Boger (constant shear viscosity, elastic) fluid and a shear-thinning (variable shear viscosity, elastic) fluid are used to study the effects of shear-thinning and elasticity. There are significant differences in the flow fields that can be observed for the different types of fluids and the different distances from the wall from which the sphere is dropped. We find that the structure of the flow field and the motion perpendicular to the wall are dependent on the distance from the wall at which the sphere sediments.

3-D particle image velocimetry of the flow field around a sphere sedimenting near a wall: Part 2. Effects of distance from the wall

The flow fields surrounding a sphere sedimenting through a liquid near a vertical wall are characterized using 3D stereoscopic particle-image velocimetry (PIV) experiments. Three different fluids, a Newtonian reference fluid, a constant (shear) viscosity Boger fluid, and a shear-thinning elastic fluid, are used to determine the effects of both elasticity and shear-thinning on the flow field. All three fluids have similar zero shear viscosities. The Weissenberg number is manipulated by varying the diameter and the composition of the ball. Significant differences are found for the different types of fluid, demonstrating both the influence of elasticity and shear-thinning on the velocity fields. In addition, the impact of the wall on the flow field is qualitatively different for each fluid. We find that the flow behind the sphere is strongly dependent on the fluid properties as well as the elasticity. Also, the presence of a negative wake is found for the shear-thinning fluid at high Weissenberg number (Wi > 1).

3D particle image velocimetry of the flow field around a sphere sedimenting near a wall: Part 1. Effects of Weissenberg number

The flow fields for a sphere sedimenting through a Newtonian and two non-Newtonian liquids near a wall in a square tank are investigated using 3-D stereoscopic particle image velocimetry (PIV) and line integral convolution (LIC) methods. The PIV data were taken using an angular stereoscopic configuration with tilt and shift arrangements for the Scheimpflug condition and a pair of liquid correction prisms. Data were recorded from planes perpendicular and parallel to the wall for each fluid case over a range of distances from the wall. The PIV and LIC results highlight significant differences in the wake structure for all three cases. Out of plane flow was also found to persist up to two sphere diameters downstream in the wake for all cases.

Combined Stereoscopic Particle Image Velocimetry and Line Integral Convolution Methods: Application to a Sphere Sedimenting Near a Wall in a Non-Newtonian Fluid

Jared A. Tatum

Papers

3-D particle image velocimetry of the flow field around a sphere sedimenting near a wall: Part 2. Effects of distance from the wall

3D particle image velocimetry of the flow field around a sphere sedimenting near a wall: Part 1. Effects of Weissenberg number

Combined Stereoscopic Particle Image Velocimetry and Line Integral Convolution Methods: Application to a Sphere Sedimenting Near a Wall in a Non-Newtonian Fluid

An Experimental Investigation of the Response of Polymeric Systems Containing Particles in Extension-Dominated Flow Fields