In
fluid dynamics, the capillary number (Ca) is a
dimensionless quantity representing the relative effect of
viscous
The viscosity of a fluid is a measure of its resistance to deformation at a given rate. For liquids, it corresponds to the informal concept of "thickness": for example, syrup has a higher viscosity than water.
Viscosity quantifies the inte ...
drag forces versus
surface tension forces acting across an interface between a
liquid and a
gas
Gas is one of the four fundamental states of matter (the others being solid, liquid, and plasma).
A pure gas may be made up of individual atoms (e.g. a noble gas like neon), elemental molecules made from one type of atom (e.g. oxygen), or ...
, or between two
immiscible liquids. Alongside the
Bond number
Bond or bonds may refer to:
Common meanings
* Bond (finance), a type of debt security
* Bail bond, a commercial third-party guarantor of surety bonds in the United States
* Chemical bond, the attraction of atoms, ions or molecules to form chemical ...
, commonly denoted
, this term is useful to describe the forces acting on a fluid front 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 capillary number is defined as:
:
where
is the
dynamic viscosity of the liquid,
is a characteristic velocity and
is the surface tension or
interfacial tension between the two fluid phases.
Being a dimensionless quantity, the capillary number's value does not depend on the system of units. In the petroleum industry, capillary number is denoted
instead of
.
For low capillary numbers (a rule of thumb says less than 10
−5), flow in
porous media
A porous medium or a porous material is a material containing pores (voids). The skeletal portion of the material is often called the "matrix" or "frame". The pores are typically filled with a fluid (liquid or gas). The skeletal material is usu ...
is dominated by
capillary force
Capillary action (sometimes called capillarity, capillary motion, capillary rise, capillary effect, or wicking) is the process of a liquid flowing in a narrow space without the assistance of, or even in opposition to, any external forces l ...
s,
[Ding, M., Kantzas, A.: Capillary number correlations for gas-liquid systems, SEP 2004-062 (2004)] whereas for high capillary numbers the capillary forces are negligible compared to the viscous forces. Flow through the pores in an oil reservoir has capillary number values in the order of 10
−6, whereas flow of oil through an oil well drill pipe has a capillary number in the order of unity.
The capillary number plays a role in the dynamics of
capillary flow
Capillary action (sometimes called capillarity, capillary motion, capillary rise, capillary effect, or wicking) is the process of a liquid flowing in a narrow space without the assistance of, or even in opposition to, any external forces li ...
; in particular, it governs the dynamic
contact angle
The contact angle is the angle, conventionally measured through the liquid, where a liquid–vapor interface meets a solid surface. It quantifies the wettability of a solid surface by a liquid via the Young equation. A given system of solid, liq ...
of a flowing droplet at an interface.
Multiphase formulation
Multiphase flows forms when two or more partially or immiscible fluids are brought in contact.
The Capillary number in multiphase flow has the same definition as the single flow formulation, the ratio of viscous to surface forces but has the added(?) effect of the ratio of fluid viscosities:
where
and
are the viscosity of the continuous and the dispersed phases respectively.
Multiphase microflows are characterized by the ratio of viscous to surface forces, the capillary number (Ca), and by the ratio of fluid viscosities:
See also
*
Bond number
Bond or bonds may refer to:
Common meanings
* Bond (finance), a type of debt security
* Bail bond, a commercial third-party guarantor of surety bonds in the United States
* Chemical bond, the attraction of atoms, ions or molecules to form chemical ...
*
Reynolds number
*
Capillary pressure
*
Froude number
References
Dimensionless numbers of fluid mechanics
{{Fluiddynamics-stub