Abstract
A function correlating the relative viscosity of a suspension of solid particles in liquids to their concentration is derived here theoretically using only general thermodynamic ideas, with out any consideration of microscopic hydrodynamic models. This function (η r = exp (1/2B * C 2)) has a great advantage over the many different functions proposed in literature, for it depends on a single parameter,B *, and is therefore concise. To test the validity of this function, a least-squares regression analysis was undertaken of available data on the viscosity and concentration of suspensions of coal particles in fuel oil, which promise to be a useful alternative to fuel oil in the near future. The proposed function was found to accurately describe the concentration-dependent behaviour of the relative viscosity of these suspensions. Furthermore, an attempt was made to obtain information about the factors affecting the value ofB *, however the results were only qualitative because of, among other things, the inaccuracy of the viscosity measurements in such highly viscous fluids.
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Abbreviations
- η :
-
shear viscosity of the suspension
- η 0 :
-
shear viscosity of the Newtonian suspending medium
- η r = η/η0 :
-
relative viscosity
- φ :
-
solid volume concentration
- c :
-
solid weight concentration
- φ m :
-
maximum attainable volume concentration of solids
- φ ∞ :
-
solid volume concentration at which the relative viscosity of the suspension becomes infinite
- c m :
-
maximum attainable solid weight concentration
- ϱ s :
-
density of the solid phase
- ϱ l :
-
density of the liquid phase
- ϱ m :
-
density of the suspension
- k n :
-
coefficients of theø-power series expansion ofη r
- {α j }:
-
sets of parameters specifying the thermodynamic state of the solid phase of a suspension
- T :
-
absolute temperature (K)
- f (c, T, α j) :
-
formal expression for the relative variation of the viscosity with concentration = [1 /η (∂η/∂c)] T,αj
- d :
-
median size of the granulometric distribution
- η B :
-
plastic or Bingham viscosity
- K :
-
consistency factor
- n :
-
flow index
- g ([c m −c],T, α j ):
-
function including an asymptotic divergence asc tends toc m , formally describing the concentration dependent behaviour of the shear viscosity of a suspension
- A (T, α j) :
-
regression analysis parameters
- B (T, α j) :
-
regression analysis parameters
- B * (T, α j ):
-
regression analysis parameters
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Borghesani, A.F. Concentration-dependent behaviour of the shear viscosity of coal-fuel oil suspensions. Rheol Acta 24, 189–197 (1985). https://doi.org/10.1007/BF01333246
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DOI: https://doi.org/10.1007/BF01333246