An object moving through a gas or liquid experiences a force in direction opposite to its motion. Terminal velocity is achieved when the drag force is equal in magnitude but opposite in direction to the force propelling the object. Shown is a sphere in Stokes flow, at very low Reynolds number.
Stokes flow (named after George Gabriel Stokes), also named creeping flow or creeping motion,[1] is a type of fluid flow where advective inertial forces are small compared with viscous forces.[2] The Reynolds number is low, i.e. . This is a typical situation in flows where the fluid velocities are very slow, the viscosities are very large, or the length-scales of the flow are very small. Creeping flow was first studied to understand lubrication. In nature, this type of flow occurs in the swimming of microorganisms and sperm.[3] In technology, it occurs in paint, MEMS devices, and in the flow of viscous polymers generally.
The equations of motion for Stokes flow, called the Stokes equations, are a linearization of the Navier–Stokes equations, and thus can be solved by a number of well-known methods for linear differential equations.[4] The primary Green's function of Stokes flow is the Stokeslet, which is associated with a singular point force embedded in a Stokes flow. From its derivatives, other fundamental solutions can be obtained.[5] The Stokeslet was first derived by Oseen in 1927, although it was not named as such until 1953 by Hancock.[6] The closed-form fundamental solutions for the generalized unsteady Stokes and Oseen flows associated with arbitrary time-dependent translational and rotational motions have been derived for the Newtonian[7] and micropolar[8] fluids.
^Kim, S. & Karrila, S. J. (2005) Microhydrodynamics: Principles and Selected Applications, Dover. ISBN 0-486-44219-5.
^Kirby, B.J. (2010). Micro- and Nanoscale Fluid Mechanics: Transport in Microfluidic Devices. Cambridge University Press. ISBN 978-0-521-11903-0. Archived from the original on 2019-04-28. Retrieved 2010-01-15.
^Dusenbery, David B. (2009). Living at Micro Scale. Harvard University Press, Cambridge, Massachusetts ISBN 978-0-674-03116-6
^Leal, L. G. (2007). Advanced Transport Phenomena: Fluid Mechanics and Convective Transport Processes.
^Chwang, A. and Wu, T. (1974). "Hydromechanics of low-Reynolds-number flow. Part 2. Singularity method for Stokes flows" Archived 2012-03-07 at the Wayback Machine. J. Fluid Mech. 62(6), part 4, 787–815.
^Brennen, Christopher E. "Singularities in Stokes' Flow" (PDF). caltech.edu. p. 1. Archived from the original (PDF) on 10 September 2021. Retrieved 18 July 2021.
^Shu, Jian-Jun; Chwang, Allen T. (2001). "Generalized fundamental solutions for unsteady viscous flows". Physical Review E. 63 (5): 051201. arXiv:1403.3247. Bibcode:2001PhRvE..63e1201S. doi:10.1103/PhysRevE.63.051201. PMID 11414893. S2CID 22258027.
generally. The equations of motion for Stokesflow, called the Stokes equations, are a linearization of the Navier–Stokes equations, and thus can be solved...
Stokes number (Stk), named after George Gabriel Stokes, is a dimensionless number characterising the behavior of particles suspended in a fluid flow....
Navier–Stokes equations. Direct numerical simulation (DNS), based on the Navier–Stokes equations, makes it possible to simulate turbulent flows at moderate...
for 'bulk' description of turbulent flow, for example using the Reynolds-averaged Navier–Stokes equations. For flow in a pipe or tube, the Reynolds number...
inviscid flow, the Navier–Stokes equation can be simplified to a form known as the Euler equation. This simplified equation is applicable to inviscid flow as...
imperfections in the flow system. If the Reynolds number is very small, much less than 1, then the fluid will exhibit Stokes, or creeping, flow, where the viscous...
In fluid dynamics, Stokes problem also known as Stokes second problem or sometimes referred to as Stokes boundary layer or Oscillating boundary layer...
measurement Flowmeter Mass flow rate Orifice plate Poiseuille's law Stokesflow "Glossary". Ocean Surface Currents. University of Miami Rosenstiel School...
Navier–Stokes equations and compressible Favre-averaged Navier-Stokes equations (C-RANS and C-FANS): Start with the C-NS. Assume that any flow variable...
dynamics, the Stokes stream function is used to describe the streamlines and flow velocity in a three-dimensional incompressible flow with axisymmetry...
the flow velocity used in Stokes' calculations, to solve the problem known as Stokes' paradox. His approximation leads to an improvement to Stokes' calculations...
(disambiguation) StokesflowStokes' law Stokes' law of sound attenuation Stokes line Stokes number Stokes parameters Stokes radius Stokes relations Stokes shift...
fluid dynamics, the Stokes drift velocity is the average velocity when following a specific fluid parcel as it travels with the fluid flow. For instance, a...
v} instead of v 2 {\displaystyle v^{2}} ; for a sphere this is known as Stokes' law. The Reynolds number will be low for small objects, low velocities...
justification was provided by Claude-Louis Navier and George Gabriel Stokes in the Navier–Stokes equations, and boundary layers were investigated (Ludwig Prandtl...
{v}}_{slip}} can also be derived directly from the expression for fluid flow in the Stokes limit for an incompressible fluid, which is η ∇ 2 u = ∇ p {\displaystyle...
The squirmer is a model for a spherical microswimmer swimming in Stokesflow. The squirmer model was introduced by James Lighthill in 1952 and refined...
equations of Newton's law for fluid momentum at low Reynolds number (Stokesflow), Fourier's law for heat, and Fick's law for mass are very similar, since...
Stokes – using a perturbation series approach, now known as the Stokes expansion – obtained approximate solutions for nonlinear wave motion. Stokes's...
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