Abstract
We study the effect of fiber additives on rheology and sedimentation of particle suspensions in a base viscoelastic suspending fluid in the case when the suspension is subjected to shear flow. We found experimentally that fiber additives (3–6 mm in length and 8–12 μm in diameter at a mass fraction of 0–0.4%) increase the suspension viscosity and retard the particle sedimentation significantly. At the same mass concentration, long and thin fibers reduce the sedimentation velocity and increase the viscosity to a much greater extent than short and thick fibers. We revealed that both rheology and sedimentation are controlled by a single conformational parameter (overlap parameter) defined as the number of fibers per unit volume multiplied by fiber length cubed.
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Notes
The standard way of defining the best fit is to choose the parameters so that the sum of the squares of the deviations of the theoretical curve(s) from the experimental points for a range of independent variables: \( {x}^2\left({p}_1,{p}_2,\dots \right)=\frac{1}{n^{eff}-p}\sum_i\sum_j{w}_{ji}{\left[{y}_{ji}-{f}_j\left({x}_{1i},{x}_{2i}\dots; {p}_1,{p}_2,\dots \right)\right]}^2 \)
is at its minimum. Here, y ji are the measured values of the dependent (output) variable y j for the values of the independent (input) variables x 1 = x 1i , x 2 = x 2i , … ; n eff is the total number of experimental points used in the fitting, and p is the total number of adjustable parameters used in the fitting (the difference d = n eff − p is usually referred to as the number of degrees of freedom).
The quantities w ji represent the weights of each experimental point. Instrumental weights: \( {w}_{ji}=1/{\sigma}_{ji}^2 \) , where σ ji are the errors of the measurement. (From the Help of Origin graphics software package)
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Acknowledgments
The study was conducted under Research Contract No. Slb-FAC-24/01/2014-IPM_RAN/TCS between Schlumberger Technology Corporation and the Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences. The authors thank Professor R.V. Goldstein for his help throughout the work. The final preparation of the paper was supported by the Russian Foundation for Basic Research (Grant No. 15-08-01365).
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Bazilevsky, A.V., Kalinichenko, V.A., Plyashkevich, V.A. et al. Sedimentation of particles in shear flows of viscoelastic fluids with fibers. Rheol Acta 56, 787–799 (2017). https://doi.org/10.1007/s00397-017-1036-x
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DOI: https://doi.org/10.1007/s00397-017-1036-x