Computation of rheological properties of suspensions of rigid rods: stress growth after inception of steady shear flow

Numerical solution of the Fokker–Planck equation for fiber suspensions: Application to the Folgar–Tucker–Lipscomb model

“…Therefore, the distribution function needed to be re-normalized in a post-processing step after each time iteration [18], which could incorporate inaccuracies in the calculations. Strand et al [19] applied the Galerkin method to resolve the Fokker-Planck equation, using basis functions that were spherical harmonics. A set of ordinary differential equations in time was then obtained and solved by the spectral method.…”

Oriented suspension mechanics with application to improving flow linear dichroism spectroscopy

“…We describe the model and its numerical discretisation below. Following Strand, Kim and Karrila [49] (see also Bird et al [5]), assuming α 0 = 1 and investigating steady state behaviour, the Fokker-Planck equation reduces to…”

“…Mathematical modelling of these suspensions is computationally challenging due to the additional independent variables associated with the particle degrees of freedom and the coupling between particle dynamics, velocity gradients and rheology. Rational simplification of the flow problem via lubrication theory, the application of a spectral method [49] and multicore parallelisation of the array of spatially-local orientation problems, will be shown to enable practical solution with workstation hardware.…”

Numerical Research on the Three-Dimensional Fiber Orientation Distribution in Planar Suspension Flows

“…However, the solving procedure and the Péclet number range was not mentioned in Advani and Tucker 1987). The maximum Péclet number reported in Kamal and Mutel (1989) is 2×10 4 and the maximum numbers are 60 and 100 in Strand et al (1987) and Han and Im (1999), respectively.…”

“…Consequently, the reduced two-dimensional model has been applied for a large variety of flows (Olson et al, 2004;Krochak et al, 2009;Chinesta et al, 2003). For a threedimensional solution, there are only a few researches that have concerned the numerical methods, where the finite difference (Advani and Tucker, 1987;Kamal and Mutel, 1989) and the finite element (Strand et al, 1987;Han and Im, 1999) have mainly been employed. However, the solving procedure and the Péclet number range was not mentioned in Advani and Tucker 1987).…”