Does Fluid Near Solid Interfaces Move Faster Due to Viscosity Differences?

[diegolas]

Hi all,

This is my first post and my background is in Computer Science, so pardon me if my terminology is not correct or even I sound ignorant Physics-wise :)

Anyways, I implemented a semi-Lagrangian based Navier-Stokes (NS) solver and it's running smoothly on a CUDA-capable GPU and I wondered if you guys can help me with something I noticed (maybe it's a law or maybe I'm just wrong).

Question: I got the impression from watching how fluids behave in real life (and for instance in the beach), and I think the fluid near the solid interface (e.g. sand for that matter) moves faster than the one on top? Is it true? Why is it? Intuitively I thought it may have to do with the delta in the viscosity (say, solid/sand - water interface), so the fluid "slips" more easily? If so, if I was to generalize the fact, is it true that the water near the solid moves faster than the one in "the middle" and near the air (maybe if we assume ideal conditions, no gravity, etc)?

Is there any law describing this? I mean, probably can be guessed from NSE but I was wondering if this has any fancy name.

Could you please recommend me literature so I can dig in more about this? I don't have access to ScienceDirect right now, and I'm not probably buying any book in the near future, so if it's not too much asking, I'd like to suggest you guys point me to papers available online?

Cheers,
Diego

 

[boneh3ad]

What you are talking about is the boundary layer, which is opposite to what you describe. A fluid at te solid surface does not move at all, actually. This is one of the fundamental boundary conditions for the NS equations so it leads me to wonder how you were solving it without that BC.

At any rate, fluid near a surface has zero velocity (with respect to the surface) and increases as you move away from the surface. There are tons of papers on it from around the turn of the century, but they are so old you may have trouble finding them. I know you seem averse to books, but I would suggest looking at "Viscous Fluid Flow" by Frank White. It has everything you Should need. If you want to dig even deeper, "Boundary Layer Theory" by Schlichting is the "sacred text" on the subject.

 

[diegolas]

Thanks for the reply :)

Well, I didn't mention it but I was solving it with no-slip BC. But in any case, what I was trying to do is to inject external (arbitrary) forces so the fluid (water) behaves like real-life waves --maybe I have to look how water moves again.

Thanks for the bibliography, I'll try to get the books though I doubt the library has them xD

 

[boneh3ad]

If it is a university library then I guarantee they have them.

At any rate, th no-slip condition is simply a mathematical translation of what I said. The fluid is motionless with respect to the wall it contacts. No external forces are needed because the boundary condition takes care of that for you.

For example, if you solve just the plain NS equations over a flat plate you get the Blasius solution, which precisely shows the boundary layer. It is one of the few analytical solutions that are possible, yet one of the most important.

 

[PJC01]

Hi Diego,

Welcome to the field of fluid dynamics! Your observation is correct, and it is related to the concept of boundary layers in fluid flow. In general, fluids behave differently near solid boundaries compared to the bulk of the fluid. This is due to the presence of a thin layer of fluid called the boundary layer, where the velocity and other fluid properties change rapidly.

The reason for this is viscosity, which is a measure of a fluid's resistance to flow. In the case of a fluid near a solid boundary, the fluid molecules in the boundary layer experience a drag force from the solid surface, causing them to move slower compared to the molecules in the bulk of the fluid. This results in a velocity gradient, with the fluid near the solid moving slower and the fluid in the bulk moving faster.

This phenomenon is described by the Navier-Stokes equations, and there is also a law called the no-slip condition, which states that the fluid velocity at a solid boundary is equal to the velocity of the solid surface. This is why the fluid near the solid interface appears to move faster - it is trying to match the velocity of the solid surface.

As for literature, there are many resources available online that can help you dig deeper into this topic. Some recommended papers are "Boundary Layer Theory" by H. Schlichting and "Introduction to Fluid Mechanics" by Robert W. Fox, Alan T. McDonald, and Philip J. Pritchard. These are both classic texts in the field of fluid dynamics and can provide a good foundation for understanding boundary layers and related concepts.

I hope this helps and good luck with your research!

Best,