Velocity gradient

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

Large‐scale dynamical effects upon the solar wind flow parameters

Abstract: The Vela 3 proton data have been examined to determine the extent to which interplanetary compressions and rarefactions affect the large-scale nonshock statistics of the solar wind temperature T and density n. Considered as a joint function of velocity V and velocity gradient ΔV/Δt, the temperature is found to be much more strongly related to the velocity. The density shows significant V dependence, but ΔV/Δt appears to be more important. Simple analytic functions are derived from flow parameter values obtained during times of little velocity change (|ΔV/Δt| ≤ 1 km sec−1 hr−1) to describe the average T-V and n-V dependencies. Fluctuations about these norms in both n and T are demonstrated to be positively correlated with ΔV/Δt on a time scale of 9–12 hours. However, more rapid (≤6-hour) variations in T during periods of high V, low n, and negative ΔV/Δt (corresponding to the rarefaction phase of interacting stream events) lack this association. The large-scale compressional perturbation of n and T is not limited in importance to the relatively infrequent large interacting streams, but should be regarded as a fundamental and widely occurring solar wind process. The implication is that much, perhaps most, nonshock solar wind activity can be viewed as a steady succession of interacting streams of varying intensities. This circumstance limits the usefulness of the average relations in identifying the physical processes dominating the flow in the acceleration region of the corona.

Multiparticle collision dynamics modeling of viscoelastic fluids.

Abstract: In order to investigate the rheological properties of viscoelastic fluids by mesoscopic hydrodynamics methods, we develop a multiparticle collision (MPC) dynamics 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 flows, 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.

Effect of Diffusion on Dispersion

Abstract: This paper (SPE 115961) was accepted for presentation at the SPE Annual Technical Conference and Exhibition, Denver, 21–24 September 2008, and revised for publication. Original manuscript received for review 7 July 2008. Revised manuscript received for review 11 February 2010. Paper peer approved 3 May 2010. Summary It is known that dispersion in porous media results from an interaction between convective spreading and diffusion. However, the nature and implications of these interactions are not well understood. Dispersion coefficients obtained from averaged cup-mixing concentration histories have contributions of convective spreading and diffusion lumped together. We decouple the contributions of convective spreading and diffusion in core-scale dispersion and systematically investigate interaction between the two in detail. We explain phenomena giving rise to important experimental observations such as Fickian behavior of core-scale dispersion and powerlaw dependence of dispersion coefficient on Peclet number. We track movement of a swarm of solute particles through a physically representative network model. A physically representative network model preserves the geometry and topology of the pore space and spatial correlation in flow properties. We developed deterministic rules to trace paths of solute particles through the network. These rules yield flow streamlines through the network comparable to those obtained from a full solution of Stokes’ equation. Paths of all solute particles are deterministically known in the absence of diffusion. Thus, we can explicitly investigate purely convective spreading by tracking the movement of solute particles on these streamlines. Then, we superimpose diffusion and study dispersion in terms of interaction between convective spreading and diffusion for a wide range of Peclet numbers. This approach invokes no arbitrary parameters, enabling a rigorous validation of the physical origin of core-scale dispersion. In this way, we obtain an unequivocal, quantitative assessment of the roles of convective spreading and diffusion in hydrodynamic dispersion in flow through porous media. Convective spreading has two components: stream splitting and velocity gradient in pore throats in the direction transverse to flow. We show that, if plug flow occurs in the pore throats (accounting only for stream splitting), all solute particles can encounter a wide range of independent velocities because of velocity differences between pore throats and randomness of pore structure. Consequently, plug flow leads to a purely convective spreading that is asymptotically Fickian. Diffusion superimposed on plug flow acts independently of convective spreading (in this case, only stream splitting), and, consequently, dispersion is simply the sum of convective spreading and diffusion. In plug flow, hydrodynamic dispersion varies linearly with the pore-scale Peclet number when diffusion is small in magnitude compared to convective spreading. For a more realistic parabolic velocity profile in pore throats, particles near the solid surface of the medium do not have independent velocities. Now, purely convective spreading (caused by a combination of stream splitting and variation in flow velocity in the transverse direction) is non-Fickian. When diffusion is nonzero, solute particles in the low-velocity region near the solid surface can move into the main flow stream. They subsequently undergo a wide range of independent velocities because of stream splitting, and, consequently, dispersion becomes asymptotically Fickian. In this case, dispersion is a result of an interaction between convection and diffusion. This interaction results in a weak nonlinear dependence of dispersion on Peclet number. The dispersion coefficients predicted by particle tracking through the network are in excellent agreement with the literature experimental data for a broad range of Peclet numbers. Thus, the essential phenomena giving rise to hydrodynamic dispersion observed in porous media are (1) stream splitting of the solute front at every pore, causing independence of particle velocities purely by convection; (2) velocity gradient in pore throats in the direction transverse to flow; and (3) diffusion. Taylor’s dispersion in a capillary tube accounts only for the second and third of these phenomena, yielding a quadratic dependence of dispersion on Peclet number. Plug flow in the bonds of a physically representative network accounts only for the first and third phenomena, resulting in a linear dependence of dispersion on Peclet number. When all the three phenomena are accounted for, we can explain effectively the weak nonlinear dependence of dispersion on Peclet number.