Numerical study of rotational diffusion in sheared semidilute fibre suspension

Abstract

Fibre-level computer simulation is carried out to study the rotational diffusion and structural evolution of semidilute suspensions of non-Brownian, rigid-rod-like fibres under shear flow in a Newtonian fluid. The analyses use a hybrid approach where the lattice-Boltzmann method is coupled with the external boundary force method. The probability distribution of the orbit constant, $p({C}_{b} )$, in the semidilute regime is predicted with this method. The paper emphasizes assessment of the characteristics of a rotary diffusion model – anisotropic in nature (Koch, Phys. Fluids, vol. 7, 1995, pp. 2086–2088) – when used in suspensions with fibres of different aspect ratios (ranging from ${r}_{p} = 16$ to $72$) and with different volume concentrations (ranging from ${c}_{v} = 7. 58\ensuremath{\times} 1{0}^{\ensuremath{-} 3} $ to $6. 14\ensuremath{\times} 1{0}^{\ensuremath{-} 2} $). A measure of the scalar Folgar–Tucker constant, ${C}_{I} $, is extracted from the anisotropic diffusivity tensor, $ \mathbisf{C} $. The scalar ${C}_{I} $ is mostly $O(1{0}^{\ensuremath{-} 4} )$ in the semidilute regime and compares very well with the experimental observations of Stover (PhD thesis, School of Chemical Engineering, Cornell University, 1991) and Stover, Koch & Cohen (J. Fluid Mech., vol. 238, 1992, pp. 277–296). The ${C}_{I} $ values provide substantial numerical evidence that the range of ${C}_{I} $ (0.0038–0.0165) obtained by Folgar & Tucker (J. Rein. Plast. Compos., vol. 3, 1984, pp. 98–119) in the semidilute regime is actually overly diffusive. The paper also branches out to incorporate anisotropic diffusion (through the use of the Koch model) in the second-order evolution equation for $ \mathbisf{A} $ (a second-order orientation tensor). The solution of the evolution equation with the Koch model demonstrates unphysical behaviour at low concentrations. The most plausible explanation for this behaviour is error in the closure approximation; and the use of the Koch model in a spherical harmonics-based method (Montgomery-Smith, Jack & Smith, Compos. A: Appl. Sci. Manuf., vol. 41, 2010, pp. 827–835) to solve for the orientation moments corroborates this claim.

Dynamics of non-Brownian fiber suspensions under periodic shear

“…To ensure a reproducible initial state, the sample is sheared at a steady moderate strain rate (Re z 0.1) before the start of each measurement. 28,29 The total strain applied during this "preshear" is on the order of 10 2 . The pre-shear is turned off, and then aer a few minutes rest (this time is not important), the sample is subjected to periodic strain with a strain by oscillating the inner cylinder.…”

Rheology of bi-disperse dense fiber suspensions

“…Modeling the poly-disperse fiber suspension will be the immediate next step to gaining a more accurate understanding of the industrial applications of fiber suspensions. In addition, it will be an interesting study to determine how the model to predict anisotropic diffusivity changes from previous studies 66 when the effect of friction is considered for numerical simulations of dense bi-disperse fiber suspensions. Moreover, the next step would be to explore the effect of surface physical chemistry and surface roughness on bi-disperse suspension rheology.…”

Multi-flexible fiber flows: A direct-forcing immersed boundary lattice-Boltzmann lattice-spring approach

“…Their semi-dilute regime results for rheological properties showed deviations from hydrodynamic interaction theories. Salahuddin et al (2012Salahuddin et al ( , 2013) used a lattice-Boltzmann equation to simulate fluid and fibers were modeled as a chain of rods where 4 nodes were distributed on the circumference of each cross section of the fiber. The interaction between fluid and fiber was treated by an external boundary force.…”