In
fluid dynamics
In physics, physical chemistry and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids – liquids and gases. It has several subdisciplines, including (the study of air and other gases in motion ...
the Eötvös number (Eo), also called the Bond number (Bo), is a
dimensionless number
Dimensionless quantities, or quantities of dimension one, are quantities implicitly defined in a manner that prevents their aggregation into unit of measurement, units of measurement. ISBN 978-92-822-2272-0. Typically expressed as ratios that a ...
measuring the importance of gravitational forces compared to surface tension forces for the movement of liquid front. Alongside the
capillary number, commonly denoted
, which represents the contribution of viscous drag,
is useful for studying the movement of fluid in
porous or
granular media, such as soil.
[Dynamics of viscous entrapped saturated zones in partially wetted porous media]
Transport in Porous Media (2018), 125(2), 193-210 The Bond number (or Eötvös number) is also used (together with
Morton number) to characterize the shape of
bubbles or
drops moving in a surrounding fluid. The two names used for this dimensionless term commemorate the Hungarian physicist
Loránd Eötvös
Baron Loránd Eötvös de Vásárosnamény (or simply Loránd Eötvös ; ; ; 27 July 1848 – 8 April 1919), also called Baron Roland von Eötvös in English literature, was a Hungarian physicist. He is remembered today largely for his work on ...
and the English physicist
Wilfrid Noel Bond,
respectively. The term Eötvös number is more frequently used in Europe, while Bond number is commonly used in other parts of the world.
The inverse of the Bond number is sometimes known as the Jesus number (Je), named after the Biblical passage of
Jesus walking on water.
Definition
Describing the ratio of gravitational to capillary forces, the Eötvös or Bond number is given by the equation:
*
: difference in
density
Density (volumetric mass density or specific mass) is the ratio of a substance's mass to its volume. The symbol most often used for density is ''ρ'' (the lower case Greek letter rho), although the Latin letter ''D'' (or ''d'') can also be u ...
of the two phases, (
SI units:
kg/
m3)
* ''g'':
gravitational acceleration
In physics, gravitational acceleration is the acceleration of an object in free fall within a vacuum (and thus without experiencing drag (physics), drag). This is the steady gain in speed caused exclusively by gravitational attraction. All bodi ...
, (
SI units : m/
s2)
* ''L'': characteristic length, (
SI units : m) (for example the radii of curvature for a drop)
*
:
surface tension
Surface tension is the tendency of liquid surfaces at rest to shrink into the minimum surface area possible. Surface tension (physics), tension is what allows objects with a higher density than water such as razor blades and insects (e.g. Ge ...
, (
SI units :
N/m)
The Bond number can also be written as
where
is the
capillary length
The capillary length or capillary constant is a length scaling factor that relates gravity and surface tension. It is a fundamental physical property that governs the behavior of menisci, and is found when body forces (gravity) and surface forces ...
.
A high value of the Eötvös or Bond number indicates that the system is relatively unaffected by surface tension effects; a low value (typically less than one) indicates that surface tension dominates.
Intermediate numbers indicate a non-trivial balance between the two effects. It may be derived in a number of ways, such as
scaling
Scaling may refer to:
Science and technology
Mathematics and physics
* Scaling (geometry), a linear transformation that enlarges or diminishes objects
* Scale invariance, a feature of objects or laws that do not change if scales of length, energ ...
the pressure of a drop of liquid on a solid surface. It is usually important, however, to find the right length scale specific to a problem by doing a ground-up
scale analysis.
Other similar dimensionless numbers are:
:
where Go and De are the Goucher and Derjaguin numbers, which are identical: the , named after Canadian scientist
Frederick Shand Goucher (1888–1973),
arises in wire coating problems and hence uses a radius as a typical length scale while the Derjaguin or Deryagin number, named after
Boris Derjaguin,
arises in plate film thickness problems and hence uses a Cartesian length.
In order to consider all three of the forces that act on a moving fluid front in the presence of a gas (or other fluid) phase, namely viscous, capillary and gravitational forces, the generalized Bond number, which is denoted commonly as Bo
*, can be used.
This is defined as:
:
Walking on water
The Bond number can be thought as the ratio of the weight of an object and the surface tension, as
where ''M'' is the mass of the object and ''L'' its contact perimeter length. An object or an insect can float on water due to surface tension if Bo < 1. Its inverse
is known as the Jesus number.
Conversely, an insect can float over water if Je >1. This principle allows for
animal locomotion on the surface of water.
References
{{DEFAULTSORT:Eotvos Number
Dimensionless numbers of fluid mechanics
Bubbles (physics)
Fluid dynamics