Velocity gradient

About: Velocity gradient is a research topic. Over the lifetime, 3013 publications have been published within this topic receiving 77120 citations.

Computer simulation of flow and molecular orientation in liquid crystal polymers

Abstract: The Ericksen-Leslie equations of motion for nematic liquid crystals are used to study the flow behaviour of nematic liquid crystal polymers. It is recogized that liquid crystal polymers are very viscous, and therefore the terms in governing equations which account for the director elasticity are neglected in comparison with the viscous terms. The resulting Ericksen anisotropic fluid equations are identical to those of Doi in the weak velocity gradient limit. The equations are solved using an ADI finite-difference technique, in geometries chosen to model the gross features of polymer processing equipment. The orthogonal mapping technique is used to map the irregularly shaped physical domains on a unit square computational domain. The results show that the molecular orientation is a strong function of the flow geometry. In particular, it is found that even a smal divergence in the channel profile causes the molecules to orient nearly perpendicular to the flow direction. Also, no stable orientation may exist in a channel of strongly varying shape, even a converging one.

Numerical analysis of extracellular fluid flow and chemical species transport around and within porous bioactive glass

Abstract: Modeling of the physical phenomena present at the biomaterial-tissue interface provides a valuable tool for examining the underlying mechanisms which influence the overall behavior of the implant-host system Based on histological data from a previous implantation study (E Schepers, M De Clercq, P Ducheyne, and R Kempeneers, "Bioactive glass particulate materials as a filler for bone lesions," J Oral Rehab; 18, 439-452, 1991, Ref 1) which documented the differentiation of mesenchymal cells to cells expressing the osteoblastic phenotype in porous bioactive glass, a finite element momentum and mass transport model was constructed In this analysis, the extracellular compositional variations and fluid flow conditions around and within porous bioactive glass granules were determined Numerical simulations demonstrated that the interstitial fluid flow around these granules (300-360 microns) is viscosity dominated (low Reynolds number flow) and that the fluid inside the granules remains stagnant This velocity field results in shear stresses proportional to the velocity gradient at the granule-fluid interface outside the particles and no shear stresses inside the particles A parametric study on the effect of interstitial fluid flow on chemical species (Na+, Ca+2, HPO(4)-2) transport outside the granules revealed three domains At low velocities (0-01 micron/s), the transport of species is diffusion controlled At intermediate velocities (10-10 microns/s), diffusion and convection contribute to the species transport The concentration of chemical species is nearly uniform at high velocities (100-800 microns/s) For all three cases, the transport of chemical species within the granules is diffusion controlled The differences in transport mechanisms and interstitial fluid flow conditions lead to variations in concentrations, reaction rates, and shear stresses between the inside and the outside of the glass granules These differences may influence cellular migration, attachment, differentiation, and the overall response to these bioactive materials

On the spatial distribution of small heavy particles in homogeneous shear turbulence

Abstract: We report on a novel experiment aimed at investigating the effects induced by a large-scale velocity gradient on the turbulent transport of small heavy particles. To this purpose, a homogeneous shear flow at Reλ = 540 and shear parameter S* = 4.5 is set-up and laden with glass spheres whose size d is comparable with the Kolmogorov lengthscale η of the flow (d/η ≈ 1). The particle Stokes number is approximately 0.3. The analysis of the instantaneous particle fields by means of Voronoi diagrams confirms the occurrence of intense turbulent clustering at small scales, as observed in homogeneous isotropic flows. It also indicates that the anisotropy of the velocity fluctuations induces a preferential orientation of the particle clusters. In order to characterize the fine-scale features of the dispersed phase, spatial correlations of the particle field are employed in conjunction with statistical tools recently developed for anisotropic turbulence. The scale-by-scale analysis of the particle field clarifies tha...

Transient behaviour and stability points of the Poiseuille flow of a KBKZ-fluid

Abstract: The Poiseuille flow of a KBKZ-fluid, being a nonlinear viscoelastic model for a polymeric fluid, is studied. The flow starts from rest and especially the transient phase of the flow is considered. It is shown that under certain conditions the steady flow equation has three different equilibrium points. The stability of these points is investigated. It is proved that two points are stable, whereas the remaining one is unstable, leading to several peculiar phenomena such as discontinuities in the velocity gradient near the wall of the pipe (‘spurt’) and hysteresis. Our theoretical results are confirmed by numerical calculationsof the velocity gradient.

A model-based validation framework for PIV and PTV

Abstract: The utility of particle image velocimetry (PIV) for measurement of velocity fields in many fluid flows is well established. This has created interest in overcoming difficulties with the technique when applied to increasingly larger fields of view where there exists a significant range of velocities and spatial velocity gradients are large. In this regard, a major deficiency with standard cross-correlation PIV is the inherent link between the density of vectors in the measurement field and the maximum measurable displacement. Several schemes exist to reduce this link. These iterative hierarchical/multiresolution schemes are strongly dependent on vector validation routines to remove spurious vectors. Here the design of a new framework for vector validation is described. This framework is general enough for use with both regular and irregularly spaced vector fields to make it applicable to particle image velocimetry (PIV), particle tracking velocimetry (PTV), and hybrid methods. It is based on the determination of a smoothed displacement field that robustly characterizes the measured field such that invalid vectors are attenuated more than valid vectors. In this particular study a thin-plate spline model is incorporated within an iterative regularized weighted least-squares routine to find a smoothed version of the displacement field that maintains pertinent velocity gradient information. The utility of the methodology is demonstrated for a complex flow profile containing four vortices where the valid displacement ranges from −1/4 to +1/4 of the area of interest (AOI) dimension. Results indicate that this validation strategy can discriminate between valid and invalid vectors remarkably well over a range of parameter settings. In the example presented a flow field with significant velocity gradients and having a high number of invalid vectors (25%) is accurately validated.