Non-Newtonian fluid ratholing 1

[Mechanical Farmer]

Hello,

Long time listener, first time caller.

I have been diving into the behavior of non-Newtonian (shear thinning, specifically) and believe that I am experiencing rat-holing in a Pseudoplastic flow.

My question is this: Provided this is a correct assumption, is there a way to determine the thickness of the "stagnant" layer on the pipe walls. Is there a way to determine a radial pressure gradient from the centerline of the pipe to the pipe walls?

 

[Mechanical Farmer]

Why don't you tell us what your product is?
Pierre

Because this is a public forum and I am discussing a highly protected process. Any information regarding material feed, output, temperature, pressure, etc. could be considered violation of my Non Disclosure and subject me to both termination of employment and legal consequences. If you would like to discuss in more detail I would be more than happy to have an NDA set up with you to discuss directly.

 

[pierreick]

Because this is a public forum and I am discussing a highly protected process. Any information regarding material feed, output, temperature, pressure, etc. could be considered violation of my Non Disclosure and subject me to both termination of employment and legal consequences. If you would like to discuss in more detail I would be more than happy to have an NDA set up with you to discuss directly.

Got it,

Pierre

 

[Mechanical Farmer]

Got it,

Pierre

yea, this might be a whole lot more of a productive conversation without that barrier. But a lot of good info has come out of it.

 

[Mechanical Farmer]

Not quite, but close. All materials assume a zero-slip at the wall. However, most materials will have a steady increase of fluid velocity towards the center. A true Bingham fluid will have a shell of immobile material, with velocity 0 m/s, and with a layer thickness determined by the required shear to begin flow. After that is achieved, you would have Your "worst case" fluid looks to be of this type, though likely with a small immobile layer because 14 Pa is not a lot of stress to overcome. Your "best case" fluid does not appear to be a Bingham fluid, so the profile should match quite closely in shape with what you have calculated. So your two fluids should look similar to below, with the "worst-case" fluid being the orange profile. The area of zero velocity is likely much smaller due than pictured, but I just made this for a visual explanation of a difference between a thick, shear-thinning liquid and a similarly thick, shear-thinning Bingham liquid.

I'm still not understanding the philosophy of having to overcome yield stress at the pipe wall. I don't see what's physically happening to cause the material to yield a r<R and not at r=R
I would assume that if a had a pipe of infinite diameter, I would have measurable and small layer of material deforming between the pipe wall and an infinitely large plug. It sounds to me like what you are saying is that in this scenario, I would instead have a small and measurable layer of material deforming between two infinitely large segments of nondeforming material.

What is the phenomenon that prevents maximum shear at the pipe walls?

 

[TiCl4]

Think about it this way. Shear stress is proportional to the differential velocity as a function of r (the du/dy term). Microscopically, the shell is immobile, and the surface molecules of the shell are being "pulled" (or pushed, if you want to think about the layer-to-layer friction that way) by the first "layer" of mobile molecules, which are in turn being pulled by the next "layer", which is going faster than the first layer since it is closer to the center of the pipe. If the pull of the first layer exceeds the yield stress of the Bingham fluid, the first "layer" of immobile material will begin to flow. Since you are maintaining a constant pumping rate, overall velocity drops, meaning du/dy drops, meaning the shear experienced by the newly uncovered immobile layer is less. This process reaches equilibrium when the shear stress exerted by the initial layer is equal to the yield stress of the material. If the next layer of immobile material were to flow, total velocity would drop again, and the shear stress exerted on the newly formed mobile layer would fall under the yield stress, solidifying it again.

Ultimately, a Bingam fluid with a very large yield stress would have a thick shell, while a Bingham fluid with a small yield stress will have a very thin core, all other conditions held the same. Changing conditions for the same fluid (like pumping more mass/minute) will change the velocities, thus changing stresses, and thus changing shell thicknesses of the immobile layer.

Your picture of the pipe in the first page - the one with the rust-colored scale buildup - displays what the immobile shell would look like for an extremely high yield stress Bingham fluid.