Several models are available in the literature describing the viscosity of suspensions, but only a few incorporate the complex nature of the matrix. When they do so, they use the power law model. We propose a viscosity model based on the Cross model for non-Newtonian suspensions, consisting of non-Brownian particles in aqueous xanthan gum (XG) solutions. Aqueous solutions of xanthan gum with and without calcium carbonate particles (CC) were tested. We prepared mixtures with tap water at XG wt% in the semidilute regime, and CC vol% between 5% and 30%. Two different mixing protocols were used, differing in whether or not solutions were prepared via dilution with the stock XG solution. The base xanthan gum viscosities were collapsed into a master curve based on the Cross model. The shear-thinning behaviour is described as a function of polymer concentration by scaling laws for the Cross parameters, the zero-shear viscosity <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="397_2025_1508_Article_IEq1.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="17" /> </InlineMediaObject> <EquationSource Format="TEX">$\eta _{0}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>η</mi> <mn>0</mn> </msub> </math></EquationSource> </InlineEquation>, infinite shear viscosity <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="397_2025_1508_Article_IEq2.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="24" /> </InlineMediaObject> <EquationSource Format="TEX">$\eta _{\infty }$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>η</mi> <mi>∞</mi> </msub> </math></EquationSource> </InlineEquation>, consistency index K and the m index. Protocol 1 mixtures could give rise to suspensions viscosities lower than the base XG fluid. This behaviour was attributed to the mixing procedure and named the “dilution effect”. Protocol 2 was developed to correct the mixing procedure. A predictive model was formulated by deriving an effective viscosity equation using the Cross model. The results show the relative effective viscosity to be roughly independent of the shear rate between <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="397_2025_1508_Article_IEq3.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="36" /> </InlineMediaObject> <EquationSource Format="TEX">$1 \ \mathrm{s^{-1}}$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>1</mn> <mspace width="4pt" /> <msup> <mi mathvariant="normal">s</mi> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> </mrow> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="397_2025_1508_Article_IEq4.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="60" /> </InlineMediaObject> <EquationSource Format="TEX">$1000 \ \mathrm{s^{-1}}$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>1000</mn> <mspace width="4pt" /> <msup> <mi mathvariant="normal">s</mi> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> </mrow> </math></EquationSource> </InlineEquation>. A collapse of the average relative effective viscosities was achieved using an existing model for Newtonian suspensions.

An effective viscosity model for suspensions of non-Brownian particles in aqueous xanthan gum matrices

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2025年7月5日

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Federico Peruzzini,
Jonathan M. Dodds,
Christopher J. Cunliffe,
Henry C.-H. Ng,
Robert J. Poole

摘要

Several models are available in the literature describing the viscosity of suspensions, but only a few incorporate the complex nature of the matrix. When they do so, they use the power law model. We propose a viscosity model based on the Cross model for non-Newtonian suspensions, consisting of non-Brownian particles in aqueous xanthan gum (XG) solutions. Aqueous solutions of xanthan gum with and without calcium carbonate particles (CC) were tested. We prepared mixtures with tap water at XG wt% in the semidilute regime, and CC vol% between 5% and 30%. Two different mixing protocols were used, differing in whether or not solutions were prepared via dilution with the stock XG solution. The base xanthan gum viscosities were collapsed into a master curve based on the Cross model. The shear-thinning behaviour is described as a function of polymer concentration by scaling laws for the Cross parameters, the zero-shear viscosity $\eta _{0}$ $η_{0}$ , infinite shear viscosity $\eta _{\infty }$ $η_{\infty}$ , consistency index K and the m index. Protocol 1 mixtures could give rise to suspensions viscosities lower than the base XG fluid. This behaviour was attributed to the mixing procedure and named the “dilution effect”. Protocol 2 was developed to correct the mixing procedure. A predictive model was formulated by deriving an effective viscosity equation using the Cross model. The results show the relative effective viscosity to be roughly independent of the shear rate between $1 \ \mathrm{s^{-1}}$ $1 s^{- 1}$ and $1000 \ \mathrm{s^{-1}}$ $1000 s^{- 1}$ . A collapse of the average relative effective viscosities was achieved using an existing model for Newtonian suspensions.