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Velocity gradient

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


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TL;DR: In this paper, the authors analyzed the linear stability of the flow of an Oldroyd-B fluid through a linear array of cylinders confined in a channel by computing both the steady-state flows and the linear stabilisation of these states by finite element analysis.
Abstract: The linear stability of the flow of an Oldroyd-B fluid through a linear array of cylinders confined in a channel is analyzed by computing both the steady-state flows and the linear stability of these states by finite element analysis. The linear stability of two-dimensional base flows to three-dimensional perturbations is computed both by time integration of the linearized evolution equations for infinitesimal perturbations and by an iterative eigenvalue analysis based on the Arnoldi method. These flows are unstable to three-dimensional perturbations at a critical value of the Weissenberg number that is in very good agreement with the experimental observations by Liu [Viscoelastic Flow of Polymer Solutions around Arrays of Cylinders: Comparison of Experiment and Theory, Ph.D. dissertation, Massachusetts Institute of Technology, Cambridge, MA, 1997] for flow of a polyisobutylene Boger fluid through a linear periodic array of cylinders. The wave number of the disturbance in the neutral or spanwise direction also is in good agreement with experimental measurements. For closely spaced cylinders, the mechanism for the calculated instability is similar to the mechanism proposed by Joo and Shaqfeh [J. Fluid Mech. 262 (1994) 27] for the non-axisymmetric instability observed in viscoelastic Couette flow, where perturbations to the shearing component of the velocity gradient interact with the polymer stresses in the base flow. However, when the cylinder spacing is increased, we discover a new mechanism for instability that involves the coupling between the elongational component of the velocity gradient and the streamwise normal stress in the base state. In addition, the most unstable disturbance in the Couette geometry is over-stable (leading to time-periodic states) whereas the instability calculated for closely spaced cylinders grows monotonically with time. This apparent inconsistency is resolved by the observation that in a complex flow, the evolution of the perturbations to the base flow can be transient in a Lagrangian frame of reference, while steady in an Eulerian frame.

32 citations

Journal ArticleDOI
TL;DR: A detailed seismic investigation of the continental crust has produced evidence of definite regularities in the general layering of the consolidated crust despite its high degree of inhomogeneity as discussed by the authors, which can be interpreted as the result of partial melting (weakening) of rocks and their possible horizontal mobility inside this layer.

32 citations

Journal ArticleDOI
TL;DR: In this article, the orientation distribution function for rigid colloidal particles immersed in Couette flow with an electric field parallel to the velocity gradient is derived, and simple streaming birefringence experiments with variable or constant electric fields can be devised to test this theory.
Abstract: The orientation distribution function for rigid colloidal particles immersed in Couette flow with an electric field parallel to the velocity gradient is derived in this study. Simple streaming birefringence experiments with variable or constant electric fields can be devised to test this theory which promises to yield a new method for measuring some geometrical and physical properties of colloidal particles.

32 citations

Journal ArticleDOI
TL;DR: In this paper, a multi-particle collision dynamics (MPC) model for a fluid of harmonic dumbbells is developed, where all particles are confined between two solid walls moving oppositely, so that both steady and oscillatory shear flows can be investigated.
Abstract: In order to investigate the rheological properties of viscoelastic fluids by mesoscopic hydrodynamics methods, we develop a multi-particle collision dynamics (MPC) model for a fluid of harmonic dumbbells. The algorithm consists of alternating streaming and collision steps. The advantage of the harmonic interactions is that the integration of the equations of motion in the streaming step can be performed analytically. Therefore, the algorithm is computationally as efficient as the original MPC algorithm for Newtonian fluids. The collision step is the same as in the original MPC method. All particles are confined between two solid walls moving oppositely, so that both steady and oscillatory shear flows can be investigated. Attractive wall potentials are applied to obtain a nearly uniform density everywhere in the simulation box. We find that both in steady and oscillatory shear flow, a boundary layer develops near the wall, with a higher velocity gradient than in the bulk. The thickness of this layer is proportional to the average dumbbell size. We determine the zero-shear viscosities as a function of the spring constant of the dumbbells and the mean free path. For very high shear rates, a very weak ``shear thickening'' behavior is observed. Moreover, storage and loss moduli are calculated in oscillatory shear, which show that the viscoelastic properties at low and moderate frequencies are consistent with a Maxwell fluid behavior. We compare our results with a kinetic theory of dumbbells in solution, and generally find good agreement.

32 citations

Journal ArticleDOI
TL;DR: In this paper, a lattice Boltzmann method combined with a higher-order immersed boundary method using a smooth velocity field near boundaries is proposed to avoid the discontinuity of the velocity gradient on the boundary.

32 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202318
202233
2021127
2020116
2019134
201892