Fluctuations at the onset of discontinuous shear thickening in a suspension

Abstract

Discontinuous shear thickening (DST) in concentrated suspensions is accompanied by pronounced fluctuations in the measured viscosity under a fixed shear rate. In this work, the suspension flow is simulated by a discrete-particle method, in which a repulsive force of magnitude F R between neighboring particles maintains viscous liquid lubricating films for stress σ < σ 0 ∼ F R a − 2 with a being the particle radius; when the films rupture, frictional contacts form. The suspension rheology displays continuous or discontinuous shear thickening for ϕ below or above ϕ c, respectively. The apparent critical point ( ϕ c , γ ˙ c ) on the viscosity curve dividing these behaviors is identified as the point at which ∂ ⟨ σ ⟩ / ∂ γ ˙ → ∞. The probability distribution of σ at a fixed γ ˙ has a well-defined peak at conditions away from this point but broadens to an essentially flat distribution for γ ˙ → γ ˙ c at ϕ c. The stress fluctuations, determined from force moments on the particles, provide a microscopically based susceptibility, χ ^ σ ∼ ∫ r = 2 a L / 2 ⟨ σ ′ ( x , t ) σ ′ ( 0 , t ) ⟩ d 3 x, with x being the pair center separation, r = | x |, L the simulation domain size, and σ ′ the stress fluctuation from ⟨ σ ⟩; χ ^ σ displays strong growth on an approach to ( ϕ c , σ c). An exchange of hydrodynamic for contact stresses is shown to be the basis for the shear thickening, and the relationship of the development of the contact network to the onset of DST is considered.