In our experiments with shear-thinning supensions, should we consider the viscosity change with change in shear rate? E.g., capillary number (Ca) and Reynold's number (Re) both contain viscosity as well as characteristic velocity for viscous forces. We are varying the flow rate and so the shear rate changes. Should I change the viscosity accordingly? Or is using a single value is fine?
I'm guessing this is an issue with experiments and not with computational work where the formulation is usually non-dimensionalized and one can simply vary the Ca or Re directly.
Could you use a rheological model? Maybe some simple one, such as the power law! I suspect that would be a better idea than a single value.
Unfortunately you do not state explicitly the type of suspension you are working with. I assume it is a bubble suspension because of your concern regrading the capillary number. If I am incorrect ignore the rest of my comments below.
A plot of the apparent viscosity of a bubble suspension with a given volume fraction, say \phi_b, as a function of the capillary number Ca shows shear thinning behavior. Such a plot starts out with constant viscosity at low Ca numbers then shows "shear thinning behavior" as the Ca number is increased. At sufficiently high Ca numbers the apparent viscosity reaches a low viscosity plateau. Check out the model due to Rust & Manga, JNNF, 104,53-63 (2002).
Such a plot assumes that the viscosity of the fluid phase is constant. Now if the fluid viscosity is shear thinning, it would make sense to incorporate shear thinning behavior in the Ca number of the Rust/Manga model. I would suggest a power-law model for starters. I suspect the low Ca and high Ca limits would remain the same, but the transition region between the two viscosity plateaus will be altered. Good luck-sounds like a nice project.
It would not be proper to use a single value of viscosity for shear-thinning suspensions. When the flow-rate is changing, the shear rate is changing and therefore for shear-thinning suspensions the viscosity is changing. This must be reflected in the non-dimensional numbers involving viscosity. For shear-thinning suspensions within the range of shear-rates for practical use, a power-law model would suffice wherein the shear stress = K (shear rate)n.
The Reynolds number in that case needs to be formulated as
Re = (Dn V 2-nρ)/{8n-1K[(3n+1)/4n]n}
where, D is pipe inside diameter V is fluid velocity and ρ is fluid density.
For further reading about non-Newtonian fluid behavior and rheology of suspensions, you may see the following books.
Thanks everyone for your responses! I already have the viscosity variation because it's a standard fluid. I'll calculate dimensionless quantities accordingly.
Hi,
Like Monika Dash mentioned, you could use various models available from the software. I would suggest you choose best-fit model if you are not sure about the shear-thinning pattern. This would throw the best possible model to follow.
Good luck!
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