Eötvös number
Encyclopedia
In fluid dynamics
the Eötvös number (Eo) is a dimensionless number named after Hungarian physicist Loránd Eötvös
(1848-1919). It is also known as the Bond number. The term Eötvös number is more frequently used in Europe, while Bond number is commonly used in other parts of the world.
Together with Morton number
it can be used to characterize the shape of bubbles or drops moving in a surrounding fluid.
Eötvös number may be regarded as proportional to buoyancy
force divided by surface tension
force.
A different statement of the equation is as follows:
where
The Bond number is a measure of the importance of surface tension forces compared to body forces. A high Bond number indicates that the system is relatively unaffected by surface tension effects; a low number (typically less than one is the requirement) indicates that surface tension dominates. Intermediate numbers indicate a non-trivial balance between the two effects.
One over the Bond Number, ie.
is sometimes referred to as the Jesus number, 
, since bodies can walk on water if they have a large Jesus number, that is if 
.
The Bond number is the most common comparison of gravity and surface tension effects and it may be derived in a number of ways, such as scaling
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 dimensionless numbers are related to the Bond number:
Where
and 
are respectively the Eötvös
, Goucher, and Deryagin numbers. The "difference" between the Goucher and Deryagin numbers is that the Goucher number (arises in wire coating problems) uses the letter
to represent length scales while the Deryagin number (arises in plate film thickness problems) uses 
.
Fluid dynamics
In physics, fluid dynamics is a sub-discipline of fluid mechanics that deals with fluid flow—the natural science of fluids in motion. It has several subdisciplines itself, including aerodynamics and hydrodynamics...
the Eötvös number (Eo) is a dimensionless number named after Hungarian physicist Loránd Eötvös
Loránd Eötvös
Baron Loránd Eötvös de Vásárosnamény , more commonly called Baron Roland von Eötvös in English literature, was a Hungarian physicist. He is remembered today largely for his work on gravitation and surface tension.-Life:...
(1848-1919). It is also known as the Bond number. The term Eötvös number is more frequently used in Europe, while Bond number is commonly used in other parts of the world.
Together with Morton number
Morton number
In fluid dynamics, the Morton number is a dimensionless number used together with the Eötvös number to characterize the shape of bubbles or drops moving in a surrounding fluid or continuous phase, c.The Morton number is defined as...
it can be used to characterize the shape of bubbles or drops moving in a surrounding fluid.
Eötvös number may be regarded as proportional to buoyancy
Buoyancy
In physics, buoyancy is a force exerted by a fluid that opposes an object's weight. In a column of fluid, pressure increases with depth as a result of the weight of the overlying fluid. Thus a column of fluid, or an object submerged in the fluid, experiences greater pressure at the bottom of the...
force divided by surface tension
Surface tension
Surface tension is a property of the surface of a liquid that allows it to resist an external force. It is revealed, for example, in floating of some objects on the surface of water, even though they are denser than water, and in the ability of some insects to run on the water surface...
force.
-
is the Bond Number or Eötvös number -
: difference in density of the two phases, (SISiSi, si, or SI may refer to :- Measurement, mathematics and science :* International System of Units , the modern international standard version of the metric system...
units : kg/m3) -
: gravitational accelerationGravitational accelerationIn physics, gravitational acceleration is the acceleration on an object caused by gravity. Neglecting friction such as air resistance, all small bodies accelerate in a gravitational field at the same rate relative to the center of mass....
, (SISiSi, si, or SI may refer to :- Measurement, mathematics and science :* International System of Units , the modern international standard version of the metric system...
units : m/s2) -
: characteristic length, (SISiSi, si, or SI may refer to :- Measurement, mathematics and science :* International System of Units , the modern international standard version of the metric system...
units : m) -
: surface tensionSurface tensionSurface tension is a property of the surface of a liquid that allows it to resist an external force. It is revealed, for example, in floating of some objects on the surface of water, even though they are denser than water, and in the ability of some insects to run on the water surface...
, (SISiSi, si, or SI may refer to :- Measurement, mathematics and science :* International System of Units , the modern international standard version of the metric system...
units : N/m)
A different statement of the equation is as follows:
where
-
is the Bond Number or Eötvös number -
is the densityDensityThe mass density or density of a material is defined as its mass per unit volume. The symbol most often used for density is ρ . In some cases , density is also defined as its weight per unit volume; although, this quantity is more properly called specific weight...
, or the density difference between fluids. -
the acceleration associated with the body forceBody forceA body force is a force that acts throughout the volume of a body, in contrast to contact forces.Gravity and electromagnetic forces are examples of body forces. Centrifugal and Coriolis forces can also be viewed as body forces.This can be put into contrast to the classical definition of surface...
, almost always gravity. -
the 'characteristic length scale', e.g. radius of a drop or the radius of a capillary tube. -
is the surface tension of the interface.
The Bond number is a measure of the importance of surface tension forces compared to body forces. A high Bond number indicates that the system is relatively unaffected by surface tension effects; a low number (typically less than one is the requirement) indicates that surface tension dominates. Intermediate numbers indicate a non-trivial balance between the two effects.
One over the Bond Number, ie.
is sometimes referred to as the Jesus number, , since bodies can walk on water if they have a large Jesus number, that is if .The Bond number is the most common comparison of gravity and surface tension effects and it may be derived in a number of ways, such as scaling
Scale analysis
Scale analysis may refer to:* Scale analysis * Scale analysis...
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
Scale analysis
Scale analysis may refer to:* Scale analysis * Scale analysis...
. Other dimensionless numbers are related to the Bond number:
Where
and are respectively the EötvösEötvös number
In fluid dynamics the Eötvös number is a dimensionless number named after Hungarian physicist Loránd Eötvös . It is also known as the Bond number...
, Goucher, and Deryagin numbers. The "difference" between the Goucher and Deryagin numbers is that the Goucher number (arises in wire coating problems) uses the letter
to represent length scales while the Deryagin number (arises in plate film thickness problems) uses .