Two-tiered semi-empirical model for the viscosity of crystal-bearing magmas

Viscosity of Cohesive Sediment‐Laden Flows: Experimental and Empirical Methods

“…The results show the shear-thinning behavior of the mixture (Figure 4), which is a phenomenon commonly observed in sediment-laden flow where its viscosity decreases with increasing in shear rate (Fedotov, 2021;Rutter et al, 2006). During this phenomenon, the resistance to flow decreases, and thus, the mixture becomes more fluidlike as the shear rate increases.…”

“…Costa (2005) proposed an empirical formula to describe the η r ∼ ϕ relationship for suspensions from Newtonian to rheological regimes (Equation , Table 1): $$${\eta }_{r}={\left\{1-\alpha \,\mathrm{erf}\left(\frac{\sqrt{\pi }}{2}\phi \left[1+\frac{\beta }{{(1-\phi )}^{\gamma }}\right]\right)\right\}}^{-B/\alpha }$$$ where B = 2.5 (theoretically) and α , β , and γ are adjustable factors; α is in the range of (0, 1), with α = 1 representing the final suspension viscosity at ϕ m ≤ ϕ < 1 (Fedotov, 2021); β controls the slope of the initial increase in η r at low concentrations (Zhu et al., 2017); and γ determines the speed to reach the possible maximum η r value when ϕ → ϕ m . Costa's formula was developed by tuning the curve of the Gauss error function $$\mathrm{erf}(x)=\frac{2}{\sqrt{\pi }}\int \nolimits_{0}^{x}{e}^{{-t}^{2}}\text{dt}$$ ( t ≥ 0).…”

“…where B = 2.5 (theoretically) and α, β, and γ are adjustable factors; α is in the range of (0, 1), with α = 1 representing the final suspension viscosity at ϕ m ≤ ϕ < 1 (Fedotov, 2021); β controls the slope of the initial increase in η r at low concentrations (Zhu et al, 2017); and γ determines the speed to reach the possible maximum η r value when ϕ → ϕ m . Costa's formula was developed by tuning the curve of the Gauss error function…”