**Are you an EPFL student looking for a semester project?**

Work with us on data science and visualisation projects, and deploy your project as an app on top of Graph Search.

Concept# Stokes' law

Summary

In fluid dynamics, Stokes' law is an empirical law for the frictional force – also called drag force – exerted on spherical objects with very small Reynolds numbers in a viscous fluid. It was derived by George Gabriel Stokes in 1851 by solving the Stokes flow limit for small Reynolds numbers of the Navier–Stokes equations.
The force of viscosity on a small sphere moving through a viscous fluid is given by:
where (in SI units):
Fd is the frictional force – known as Stokes' drag – acting on the interface between the fluid and the particle (newtons, kg m s−2);
μ (some authors use the symbol η) is the dynamic viscosity (Pascal-seconds, kg m−1 s−1);
R is the radius of the spherical object (meters);
v is the flow velocity relative to the object (meters per second).
Stokes' law makes the following assumptions for the behavior of a particle in a fluid:
Laminar flow
Spherical particles
Homogeneous (uniform in composition) material
Smooth surfaces
Particles do not interfere with each other.
For molecules Stokes' law is used to define their Stokes radius and diameter.
The CGS unit of kinematic viscosity was named "stokes" after his work.
Stokes' law is the basis of the falling-sphere viscometer, in which the fluid is stationary in a vertical glass tube. A sphere of known size and density is allowed to descend through the liquid. If correctly selected, it reaches terminal velocity, which can be measured by the time it takes to pass two marks on the tube. Electronic sensing can be used for opaque fluids. Knowing the terminal velocity, the size and density of the sphere, and the density of the liquid, Stokes' law can be used to calculate the viscosity of the fluid. A series of steel ball bearings of different diameters are normally used in the classic experiment to improve the accuracy of the calculation. The school experiment uses glycerine or golden syrup as the fluid, and the technique is used industrially to check the viscosity of fluids used in processes.

Official source

This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.

Ontological neighbourhood

Related publications (240)

Related people (45)

Related concepts (6)

Drag (physics)

In fluid dynamics, drag (sometimes called fluid resistance) is a force acting opposite to the relative motion of any object moving with respect to a surrounding fluid. This can exist between two fluid layers (or surfaces) or between a fluid and a solid surface. Unlike other resistive forces, such as dry friction, which are nearly independent of velocity, the drag force depends on velocity. Drag force is proportional to the velocity for low-speed flow and the squared velocity for high speed flow, where the distinction between low and high speed is measured by the Reynolds number.

Reynolds number

In fluid mechanics, the Reynolds number (Re) is a dimensionless quantity that helps predict fluid flow patterns in different situations by measuring the ratio between inertial and viscous forces. At low Reynolds numbers, flows tend to be dominated by laminar (sheet-like) flow, while at high Reynolds numbers, flows tend to be turbulent. The turbulence results from differences in the fluid's speed and direction, which may sometimes intersect or even move counter to the overall direction of the flow (eddy currents).

Stokes flow

Stokes flow (named after George Gabriel Stokes), also named creeping flow or creeping motion, is a type of fluid flow where advective inertial forces are small compared with viscous forces. 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.

Related courses (23)

MATH-647: Topics on the Euler and Navier-Stokes equations

This topics course focuses on recent and classical fundamental results on the Euler and Navier-Stokes equations, such as global existence of weak solutions, (non)uniqueness results, blow-ups, partial

ChE-330: Fluid mechanics and transport phenomena

The concept of Shell balances, the Navier-Stokes equations and generalized differential balances equations for heat and mass transport are given. These relations are applied to model systems. Integral

ME-444: Hydrodynamics

Nondimensionalized Navier-Stokes equations result in a great variety of models (Stokes, Lubrication, Euler, Potential) depending on the Reynolds number. The concept of boundary layer enables us then t

Related lectures (89)

Related units (8)

Hydrodynamics: Holomorphic Functions

Explores hydrodynamics principles and holomorphic functions' role in fluid dynamics.

Stokes Formula in Hydrodynamics

Explores Stokes formula in hydrodynamics, emphasizing flow along a sphere and boundary conditions.

Kalman-Hauad-Morning Relation

Delves into deriving the Kalman-Hauad-Morning relation in stationary turbulence, emphasizing homogeneity and isotropy assumptions, and culminates in the common Howard-Mohnen relation.

The thesis is dedicated to the study of two main partial differential equations (PDEs) in fluid dynamics: the Navier-Stokes equations, which describe the motion of incompressible fluids, and the transport equation with divergence-free velocity fields, whic ...

The goal of this work is to use anisotropic adaptive finite elements for the numerical simulation of aluminium electrolysis. The anisotropic adaptive criteria are based on a posteriori error estimates derived for simplified problems. First, we consider an ...

François Gallaire, Edouard Boujo, Yves-Marie François Ducimetière

We consider fluid flows, governed by the Navier-Stokes equations, subject to a steady symmetry-breaking bifurcation and forced by a weak noise acting on a slow timescale. By generalizing the multiple-scale weakly nonlinear expansion technique employed in t ...

2024