I was going through some literature about the Bingham Papanastasiou model for modeling of viscoplastic flows. The model uses a term "m" which has unit of time. I am not able to visualize what the physical interpretation of this time is. Can someone kindly explain in a simple way?
Probably it may be relaxation time of the material, or somewhat related to it.
Hello Sameer,
Actually it is not a relaxation time, since Bingham fluids do not have a relaxation time, being inelastic - they react instantly to changes in the shear rate. In fact a Papanastasiou-Bingham fluid is a generalised Newtonian fluid, whereas relaxation times pertain to viscoelastic fluids.
You can view it just as a model parameter which reproduces better the pure viscoplastic behaviour when its value is large. If you want to assign s physical significance to it in my opinion it is better not to view "m" as a time, although it has the same units, but as the reciprocal of a shear rate: shear rate has units of 1/s, so its reciprocal has units of 1/(1/s) = s. In the Papanastasiou formula you see that m is multiplied by the magnitude of the shear rate, say g, so that m*g can be written as g/g0 where g0 = 1/m. The value of g0 is then indicative of the location of where the "bend" occurs in the stress-rate of strain graph of the Papanastasiou model. For a pure Bingham material this bend must occur immediately, so that g0 should be as close to zero as possible (i.e. m must be as large as possible).
I hope this helps.
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