TFML

Research Multiphase and index-matched flows

Tomo-PTV of buoyancy driven spheres

A small acrylic ball rises through a tank of salt water. It zigzags, speeds up, slows down, and trails vortices behind it. To measure the forces doing that, we first had to make the sphere invisible, then find it again.

Two papers from the lab. Links at the end.

Four high-speed cameras arranged around a tall transparent octagonal tank on an optical table
The octagonal tank, 70 cm tall, with four Phantom v2640 high-speed cameras looking in.

The experiment in four numbers

4high-speed cameras around the tank
4,800 Hzimaging speed
6.35–12.7mm acrylic spheres, free to rise
1500–3500sphere Reynolds number

Results

Size changes the wake and the path

Same liquid, same material, three diameters. Watch what the wake does.

7.93 mm ReT 1760 The wake hugs the body and sheds one ring at a time. The sphere rises almost straight.
9.53 mm ReT 2170 Still one ring at a time, shed in a steady rhythm, and the rise is still nearly vertical.
11.11 mm ReT 2880 Long threads trail behind, tear off as pairs of rings, and throw the sphere into a zigzag.
For the specialist

ReT ≈ 2880, 2170 and 1760 for d = 11.11, 9.53 and 7.93 mm. The two smaller spheres show the canonical two-ring (2R) regime: symmetric, periodic, phase-locked shedding with lift alternating about zero. |V₁₁| > |V₉| > |V₇| and Fd,11 > Fd,9 > Fd,7. Each recording covers roughly half a shedding cycle, a limit set by camera resolution rather than by the method.

Increasing diameter changes both wake structure and trajectory response. The largest sphere shows the strongest asymmetric wake.

Results

Flow and pressure around a rising sphere

One rise of the 11.11 mm sphere, with its wake, speed and forces on the same clock.

A composite figure: five wake snapshots labelled A to E on top, a time history of speed, drag and lift in the middle, and five more snapshots F to J below
A to J span about 220 ms of a single rise. Top and bottom, the wake as surfaces of equal swirl, sphere in black. Centre, speed |V| (blue, left axis) with drag Fd and lift Fl in millinewtons (right). Every dip in speed lines up with a peak in drag.
  • Drag peaks while the vortex threads stay attached, and collapses when they let go.
  • Lift swings come from a lopsided wake pulling on one flank.
  • These are measured forces, not modelled ones.
For the specialist

Forces are obtained by integrating the reconstructed surface pressure, F = −∮ p n dS, so they represent the dynamic component only (buoyancy is not included). For the 11.11 mm sphere (ReT ≈ 2880, m* = 0.65) the wake shows a primary and a secondary vortex ring per half-cycle, the asymmetric four-ring (4R) mode of Horowitz & Williamson (2010), with the sphere sitting near the 2R/4R boundary. The measured drag history is phase-locked to the attachment and pinch-off of the streamwise vortex threads; the transition from thread to rings at H–I is observed here for the first time as it happens.

Tomo-PTV connects the sphere trajectory, wake topology, pressure field and instantaneous forces.

Key idea

Refractive index matching: a blessing and a curse

A 62% sodium iodide solution has the same refractive index as acrylic, so light goes straight through the sphere.

An acrylic sphere sitting half in air and half in salt solution: the upper half is clearly visible, the submerged half has vanished
One sphere, half in air and half in the solution. The submerged half has vanished.
Camera image with ordinary tracers: the sphere glows as a bright disc Camera image with fluorescent tracers and a filter: only a faint dotted outline marks where the sphere is
What one camera sees. Left, ordinary tracers: the sphere glares. Right, fluorescent tracers behind a filter: only particles. The dotted circle was added afterwards.

A blessing

No refraction, so we can resolve the flow right up to the surface.

A curse

No edge, no silhouette, nothing left to tell us where the sphere is.

For the specialist

Working fluid 62 wt% NaI, density 1820 kg/m³, kinematic viscosity 1.1 × 10⁻⁶ m²/s, refractive index 1.489. Tracers: Rhodamine-B-coated PMMA, 1–20 µm, imaged through 550 nm long-pass filters. Acrylic spheres of 6.35–12.7 mm and density ratio m* = 0.65, released from a 400 mm pipe so they reach terminal velocity before entering the 110 × 75 × 25 mm measurement volume. ReT = 1500–3500, Ga = 848–2397. Tracks from Shake-The-Box, Eulerian fields by VIC#, pressure by GPU Omni3D integration.

RIM gives optical access, but hides the body.

Sphere detection

The clues to the sphere

An invisible sphere still leaves three fingerprints. Scored together, they give its centre.

Minimising this cost function for x yields the sphere centre.

A dense cloud of reconstructed tracer positions with a sphere-sized empty region ringed in red
Void no tracers inside Particles cannot enter the solid, so the sphere shows up as a hole in the particle cloud.
Three-dimensional rendering of the flow around the rising sphere, with upward-moving fluid shown in grey and the downwash beside it in red
Velocity up inside, down outside Grey is fluid pushed up ahead of the sphere, red the downwash returning beside it.
Q-criterion isosurfaces showing a vortex ring and wake structures with almost no swirl at the sphere location
Q-criterion no swirl inside Vorticity vanishes inside the rigid sphere but runs strong through the wake.
For the specialist

The cost function J(x) = D(x) + w₁[−Vinner + Vouter] + w₂[Qinner − Qouter] combines normalised tracer density in a sphere of radius R, mean vertical velocity in the upper hemisphere within 1.1R against a shell between 1.5R and 2R, and mean Q-criterion inside against a shell out to 2.5R. It is minimised by Polak–Ribière conjugate gradients with a backtracking line search. Weights w₁ = 3.08 and w₂ = 4.42 were calibrated for stable, jitter-free convergence. Positional uncertainty from the Hessian of J at the minimum: mean 0.7–1.2% d, worst case below 0.08 d; robust to ±10% weight changes, 25% search-radius changes and 10% added noise.

The output is a time-resolved sphere centre used for trajectory, pressure and force.

Read the papers

International Journal of Multiphase Flow 197, 105597 (2026), open access

On the application of refractive index matching to study the buoyancy-driven motion of spheres

Jibu Tom Jose, Aviel Ben-Harosh and Omri Ram

Companion method paper: Dynamic masking for boundary-aware velocity reconstruction in volumetric particle tracking with moving solids — Measurement Science and Technology (2026), accepted. Jibu Tom Jose, Arieh Jacobson, Dhanush Vittal Shenoy, Steven H. Frankel and Omri Ram. Code on GitHub, data on Zenodo.

How that reconstruction works, in plain language and without the mathematics, is the subject of its own page: Seeing the flow right next to a moving body.

This work was partially funded by the American Chemical Society Petroleum Research Fund (grant 65901-ND9). Jibu Tom Jose was supported by a Technion postdoctoral fellowship.

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