Correction of Wall Adhesion Effects in Batch Settling of Strong Colloidal Gels

TL;DR

This work tackles the problem of wall adhesion bias in batch settling measurements of strongly flocculated colloidal gels. It introduces a highly simplified 1D analytic approximation to the equilibrium stress state, based on a visco-plastic constitutive framework, to yield closed-form expressions for the average network pressure $\bar p_N(z)$ and solids concentration $\bar{\phi}_\infty(z)$. By fitting these expressions to equilibrium solids-volume-fraction profiles or to equilibrium bed-height data, the authors demonstrate robust recovery of the compressive yield strength $P_y(\phi)$ and the wall-adhesion strength $\tau_y(\phi)$ via nonlinear regression, even in the presence of modest measurement errors. The method is validated against the full 2D visco-plastic and hyper-elastic solutions and multiple experimental datasets, showing that wall adhesion effects can be routinely corrected and that accurate rheological functions can be inferred from equilibrium data. This has practical implications for characterizing strong colloidal gels and improving predictions of sedimentation and thickening processes.

Abstract

The batch settling test is widely used to estimate the compressive rheology of strongly flocculated colloidal suspensions, in particular the compressive yield strength and hydraulic permeability. Recently it has been discovered that wall adhesion effects in these tests may be significantly greater than previously appreciated, which can introduce unbounded errors in the estimation of these rheological functions. Whilst a methodology to solve the underlying static problem and correct for wall adhesion effects has been developed, this method is quite complex and unwieldy, involving solution of a 2D hyper-elastic constitutive model for strong colloidal gels. In this paper we develop a highly simplified 1D visco-plastic approximation to the hyper-elastic model which admits analytic expressions for the equilibrium solids concentration profile and bed height. These expressions facilitate robust estimation of the compressive yield and wall adhesion strength via nonlinear regression of experimental data in the presence of small measurement errors.

Figures (8)

• Figure 1: Comparison of (a) network shear stress $\tau_N$, (b) network pressure $p_N$ and solids volume fraction $\phi_\infty$ distributions for visco-plastic constitutive model.
• Figure 2: Comparison of (a) network shear stress $\tau_N$, (b) network pressure $p_N$ and solids volume fraction $\phi_\infty$ distributions for hyper-elastic constitutive model.
• Figure 3: Approximation of the function $F_1(p)$ (solid) for various values of $S_\infty$ with $S_\infty\left(\frac{p}{k}+1\right)$ (solid).
• Figure 4: Comparison of typical predictions of (a) average network pressure $\bar{p}_N$ and (b) average equilibrium solids volume fraction $\bar{\phi}_\infty(z)$ for $R_s$=0.011 [m] (gray) and $R_l$=0.055 [m] (black) column widths and (c) error summary for network pressure (dashed) and solids volume fraction (solid) between 2D visco-plastic and 1D approximate solutions of equilibrium stress state.
• Figure 5: Measured data (points) and model fits (1D model - solid lines, 2D model - dashed lines) of the equilibrium solids volume fraction profile $\bar{\phi}_\infty(z)$ for $R_s$=0.011 [m] (gray) and $R_l$=0.055 [m] (black) column widths for calcium carbonate suspensions under flocculant types and dosages (a)-(c) summarized in Table \ref{['tab:suspensions']}.