[Jonas Holdeman]

Can anyone provide references to work involving a small cylinder free to move and rotate, placed in a shearing flow field, with axis perpendicular to the flow and perpendicular to the velocity gradient? In a frame that follows the rotating cylinder (the rotation driven by the vorticity), I would expect the cylinder to drag flow lines around to the side with faster flow resulting in a force on the cylinder in the direction of the negative velocity gradient.

Actually, my interest is in a heuristic for tracking a spherical (tracer) particle moving in a velocity gradient. If it were a massless point particle moving in a stationary field it would follow a stream line. Of course it would be impossible to compute the trajectories of a great many real particles simultaneously, but perhaps a simple heuristic could be developed for the motion of a tracer particle of finite size.

[FMDenaro]

Originally Posted by Jonas Holdeman

Can anyone provide references to work involving a small cylinder free to move and rotate, placed in a shearing flow field, with axis perpendicular to the flow and perpendicular to the velocity gradient? In a frame that follows the rotating cylinder (the rotation driven by the vorticity), I would expect the cylinder to drag flow lines around to the side with faster flow resulting in a force on the cylinder in the direction of the negative velocity gradient.

Actually, my interest is in a heuristic for tracking a spherical (tracer) particle moving in a velocity gradient. If it were a massless point particle moving in a stationary field it would follow a stream line. Of course it would be impossible to compute the trajectories of a great many real particles simultaneously, but perhaps a simple heuristic could be developed for the motion of a tracer particle of finite size.

Hello,
are you interested in particle-laden flows? Because I suppose that is different from 2D cylinder moving in the flow...

In the former case, several papers exist, computing thousand of trajectories...let me know better...

[Jonas Holdeman]

I was doing some reading about thermo-capillary flow in a liquid bridge. These are thermally-driven flows in a fluid between the ends of two cylinders at different temperatures, held in place by surface tension. The flow is driven by the temperature dependence of the surface tension (somewhat like a lid-driven cavity). The principle flow is toroidal, but under certain conditions an azimuthal hydro-thermal flow can develop. Since the fluid is supported by surface tension, the dimensions of the system are a couple of millimeters at most of millimeters at most.

When particles are added to visualize the flow, these were first observed by D. Schwabe to collect in a distorted helical string (called a particle accumulation structure - PAS) that flows around the main (distorted toroidal) flow. Particles initially spread throughout the volume are quickly swept across streamlines into the PAS. There are several theories about how/why this occurs.

Compared with usual visualization setups, the particles are quite large, ~20-30 micrometers (.02-.03 mm) in a volume ~2 mm across, and the velocity gradient at the fluid free surface are quite large. So the size of the particles relative to the flow must be a factor, as inertia-less point particles would be expected to follow streamlines and not migrate across the lines to accumulate in the PAS.

I am just trying to understand the mechanism of PAS formation. My interest in the cylinders is because this 2D case /model is something I might be able to compute.

[FMDenaro]

Ok, so you suppose the mass of particle are quite relevant and a simple Lagrangian tracking is not a good choice.

The equations for trasport of particle with inertia are derived from the historical Maxey-Riley equations. Many papers were developed and recently the interest is for some particular flows (e.g. turbophoresis) simulated with DNS/LES. You can look in some journals as JFM or PoF.

However, as you want to simulate 2D flows, you have necessarily a laminar hypothesis and you can try solving the MR equations with acceptable computational cost.

[Jonas Holdeman]

As I said earlier, I have just been doing some reading on this subject using papers I can access. This is from a survey paper "Understanding particle Accumulation Structures (PAS) in Thermocapillary Liquid Bridges" by H. Kuhlmann & F. Muldoon, J. Jpn. Soc. Microgravity Appl., Vol 29, No. 2, 2012, pp64-76. According to these authors, the Maxey-Riley equations and several variants have been studied as inertial mechanism to produce the PAS. Their conclusion is that regarding the PAS as a limit cycle, inertial effects can be stable or unstable, and that the rate of PAS formation is too slow, approaching zero when the density of the tracer particles is equal to that of the fluid.

Hoffman & Kuhlmann have proposed a collision model which seems more successful. When finite-sized particles approach the capillary surface following a stream line, they are forbidden to stick out beyond the surface. Instead this is treated as a collision, with the particle transferring to a new trajectory closer to the limit cycle (PAS). This clears the particles from most of the volume, concentrating them in the attractor/PAS. PAS formation times are more reasonable.

To me this seems rather ad hoc/model dependent. As the velocity gradient is very large at the free surface, I would rather see a mechanism that moves particles in these high gradient situations across the streamlines rather than treating it as a collision with the surface, hence my original inquiry at the start of this thread.

[FMDenaro]

Sorry, I am not aware about details of the flow problem you are citing...

At the best of my knowledge the failing in PAS can be due to several factors... The MR equations were proposed in several forms, other terms can be considered, for example I remember Michaelides, POF, 1992 that developed a procedure for the Basset (history) term.