Three-dimensional simulations of Bingham plastic flows with the multiple-relaxation-time lattice Boltzmann model

This paper presents a three-dimensional (3D) parallel multiple-relaxation-time lattice Boltzmann model (MRT-LBM) for Bingham plastics which overcomes numerical instabilities in the simulation of non-Newtonian fluids for the Bhatnagar–Gross–Krook (BGK) model. The MRT-LBM and several related mathematical models are briefly described. Papanastasiou’s modified model is incorporated for better numerical stability. The impact of the relaxation parameters of the model is studied in detail. The MRT-LBM is then validated through a benchmark problem: a 3D steady Poiseuille flow. The results from the numerical simulations are consistent with those derived analytically which indicates that the MRT-LBM effectively simulates Bingham fluids but with better stability. A parallel MRT-LBM framework is introduced, and the parallel efficiency is tested through a simple case. The MRT-LBM is shown to be appropriate for parallel implementation and to have high efficiency. Finally, a Bingham fluid flowing past a square-based prism with a fixed sphere is simulated. It is found the drag coefficient is a function of both Reynolds number (Re) and Bingham number (Bn). These results reveal the flow behavior of Bingham plastics

Dynamic Sealing Using Magneto-Rheological Fluids

Micropumps are microfluidic components which are widely used in applications such as chemical analysis, biological sensing and micro-robots. However, one obstacle in developing micropumps is the extremely low efficiency relative to their macro-scale counterparts. This paper presents a dynamic sealing method for external gear pumps to reduce the volumetric losses through the clearance between the tips of gears and the housing by using magneto-rheological (MR) fluids. By mitigating these losses, we are able to achieve high efficiency and high volumetric accuracy with current mechanical architectures and manufacturing tolerances. Static and dynamic sealing using MR fluids are investigated theoretically and experimentally. Two Mason numbers $Mn\left(p\right)$ and $Mn\left(\Omega\right)$ which are defined in terms of pressure gradient of the flow and velocity of the moving boundary respectively are used to characterize and evaluate the sealing performance. A range of magnetic field intensities is explored to determine optimal sealing effectiveness, where effectiveness is evaluated using the ratio of volumetric loss and friction factor. Finally, we quantify the effectiveness of this dynamic sealing method under different working conditions for gear pumps.Comment: 9 pages; 10 figures

Simulations of extensional flow in microrheometric devices

We present a detailed numerical study of the flow of a Newtonian fluid through microrheometric devices featuring a sudden contraction–expansion. This flow configuration is typically used to generate extensional deformations and high strain rates. The excess pressure drop resulting from the converging and diverging flow is an important dynamic measure to quantify if the device is intended to be used as a microfluidic extensional rheometer. To explore this idea, we examine the effect of the contraction length, aspect ratio and Reynolds number on the flow kinematics and resulting pressure field. Analysis of the computed velocity and pressure fields show that, for typical experimental conditions used in microfluidic devices, the steady flow is highly three-dimensional with open spiraling vortical structures in the stagnant corner regions. The numerical simulations of the local kinematics and global pressure drop are in good agreement with experimental results. The device aspect ratio is shown to have a strong impact on the flow and consequently on the excess pressure drop, which is quantified in terms of the dimensionless Couette and Bagley correction factors. We suggest an approach for calculating the Bagley correction which may be especially appropriate for planar microchannels