creeping flow

Creeping flow

Fluid at very low Reynolds number. In the flow of fluids, a Reynolds number (density · length · velocity/viscosity) describes the relative importance of inertia effects to viscous effects. In creeping flow the Reynolds number is very small (less than 1) such that the inertia effects can be ignored in comparison to the viscous resistance. Creeping flow at zero Reynolds number is called Stokes flow.

Mathematically, viscous fluid flow is governed by the Navier-Stokes equation. In creeping flow the nonlinear momentum terms are unimportant, and the Navier-Stokes equation can be linearized. See Fluid flow, Fluid mechanics, Navier-Stokes equation, Reynolds number, Viscosity

Examples of creeping flow include very small objects moving in a fluid, such as the settling of dust particles and the swimming of microorganisms. Other examples include the flow of fluid (ground water or oil) through small channels or cracks, such as in hydrodynamic lubrication or the seepage in sand or rock formations. The flow of high-viscosity fluids may also be described by creeping flow, such as the extrusion of melts or the transport of paints, heavy oils, or food-processing materials.

creeping flow

[′krē·piŋ ‚flō]
(fluid mechanics)
Fluid flow in which the velocity of flow is very small.
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References in periodicals archive ?
Lie Group Analysis of Creeping Flow of a Second-Grade Fluid .
Due to the small scale of the calculation model, the pore size is less than 0.1 mm, and the Reynolds number is far less than 1; thus the creeping flow (Stokes Flow) interface was utilized to solve the flow problem instead of the Laminar Flow (N-S equation) interface in this paper.
, based on this concept was developed, inducing perfectly axisymetric creeping flow, showing high distributive and dispersive capabilities without generating excessive pressure drops as shown by Bouquey et al.
Creeping flow pattern was observed at low Re (Re=1) for all step height as per Fig.
Among the topics are a boundary element solution of thermal creeping flow in a nanometer single mixer, evaluating interface cracks, rotational symmetry applied to boundary element computation for nuclear fusion plasma, fundamental solutions for inverse obstacle acoustic scattering, the volume integral equation method for analyzing scattered waves in an elastic half space, and analyzing layered soil problems with an alternative multi-region boundary element method technique and a new infinite boundary element formulation.
For very low Reynolds numbers (Re<0.1), the so-called "creeping flow" conditions apply and the drag coefficient for a sphere takes a simple form, first derived by Stokes:
For Re > 35, upward deviation of f values from the linear relation is observed indicating transition from the creeping flow. The additional pressure losses are due to contributions from the creeping flow as well as the boundary layer flow with in the transition region.
The equations of conservation of mass, momentum and energy for steady, creeping flow (very low Reynolds Number, inertialess) must be solved.
This approach has been used to study the creeping flow of power law fluids (Bruschke and Advani, 1993; Chen and Wung, 1989; Spelt et al., 2005a) and finite Reynolds number flow has been considered by Spelt et al.
However, no attempt so far has been made to extend this method for quasi-hyperbolic constitutive equations in the limit of creeping flow.
To further reduce the difficulty of the problem, creeping flow conditions (i.e.
It is now well known that the so-called Stokes paradox does not exist for the creeping flow of shear-thinning (n < 1) fluids past an unconfined circular cylinder (Tanner, 1993; Marusic-Paloka, 2001) and reliable results are now available for the creeping flow of power law fluids (Tanner, 1993; Whitney and Rodin, 2001; Ferreira and Chhabra, 2004).

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