Local effective permeability distributions for non-Newtonian fluids by the lattice Boltzmann equation

A size-dependent constitutive model of bulk metallic glasses in the supercooled liquid region

“…According to the normalization method, S σf can be defined as:where σ f 0 is the steady stress corresponding to the benchmark condition. The steady flow behavior of BMGs can be analyzed in the framework of Weibull statistics3334. The Weibull equation describes the transition probability P f as a function of steady stress σ f at a critical strain rate in form of:where σ 0 is a scaling parameter, n is the Weibull modulus and V is the volume of BMGs sample, the parameter σ z denotes the stress at which there is a zero transition probability, which is usually taken to be zero.…”

Size-dependent flowing characteristics of a Zr-based bulk metallic glass in the supercooled liquid region

“…The transition from Newtonian to non-Newtonian flow can be analyzed in the framework of Weibull statistics [21,22]. The Weibull equation describes the transition probability P f as a function of a given compressive flow stress ( trans ) at critical strain rate (in which the transition happens) in form of where 0 is a scaling parameter, n is the Weibull modulus and V is the volume of the tested sample, the parameter u denotes the stress at which there is a zero transition probability, which is usually taken to be zero.…”

Lattice Boltzmann simulations of viscoplastic fluid flows through complex flow channels

“…3 shows velocity profiles obtained by the LBM simulations using Eqs. (14) and (15). The left panel corresponds to the Bingham fluid and the right panel is the result for the Casson fluid.…”

“…They demonstrated the applicability of the LBM to power-law model [6] fluids. Results of LB simulations for the power-law model fluids have been given by a number of researchers [7][8][9][10][11][12][13][14][15] since the work of Aharonov and Rothman [5]. Although the power law model has the disadvantage which the viscosity of the power law model can be potentially infinite at low shear-rate regions, these studies would be very valuable for understanding the most essential effect of shear-thinning fluids.…”