Correction of wall adhesion effects in batch settling of strong colloidal gels

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 (D.R. Lester et al, J. Rheol., 58(5):12471276, 2014) 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.

Correction of wall adhesion effects in the centrifugal compression of strong colloidal gels

“…This form captures the experimentally‐observed rapid increase in compressive strength just above gel‐point, along with the progression toward power‐law behavior seen typically at higher concentrations. A power‐law index of seems to be typical of electrolyte‐flocculated and coagulated systems, whereas the strongly polymer‐flocculated CaCO 3 used by Lester et al showed a somewhat higher value of ca. 5.…”

“…In each case the default analysis assumes that the unbuoyed self‐weight at any height point z in a sediment of total equilibrium height h eq , viz is balanced by the compressive strength at that level, P y ( ϕ { z }): in the above Δ ρ is the suspension inter‐phase density difference, g , the magnitude of the gravitational or centrifugal acceleration and ϕ(z) the local volume‐fraction. The above only holds exactly in the absence of wall adhesion, of course, whereas in its presence a vertical force balance gives which shows that otherwise wall effects can only be ignored or neglected when the second term on the RHS is negligible compared to the first, that is, when …”

“…This particular method is however very sensitive to any adhesion to the tube walls, to the point where it is possible to exploit that sensitivity and invert raw data acquired using two or more columns of differing diameter to determine both the compressive and the wall shear strength functions with good accuracy. The exact method of inversion is way too involved to be of routine use, but it has subsequently proved possible to develop a very simple but accurate approximate scheme that is very straightforward to implement . The same approach renders the modeling of sedimentation dynamics with wall adhesion tractable too (Lester et al—to be published), whereas this would be a very formidable challenge otherwise.…”

Dynamic and rate-dependent yielding in model cohesive suspensions

“…Since cohesive suspensions, strongly flocculated ones at least, are "ratchet poroelastic" [18] and strain-hardening in effect, the ratio of shear to compressive strength decays from unity at the gel-point to a lower asymptotic value at high volume-fraction. The latter is expected to proportional to the apparent yield strain in shear, defined as, γ Y app = (σ Y ) / G [19,20], and where the yield stress σ Y could either be the true yield stress or the adhesive, depending upon the context (e.g. whether any bounding surfaces are rough or smooth).…”

“…whether any bounding surfaces are rough or smooth). It is of interest to ask how this apparent yield strain, which turns out to be convenient and compact way of the parameterizing the importance or otherwise of wall or shear effects in solid-liquid separation [19,20], compares with the true yield strain. It should be fairly obvious that γ Y app ≥ γ bond in the present terms, where the latter is the critical strain above which softening occurs: equal in the absence of the kind of strain hardening shown in fig.…”