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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 capillary number (Ca) is a
dimensionless quantity 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 ...
representing the relative effect of
viscous Viscosity is a measure of a fluid's rate-dependent resistance to a change in shape or to movement of its neighboring portions relative to one another. For liquids, it corresponds to the informal concept of ''thickness''; for example, syrup h ...
drag forces versus
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 ...
forces acting across an interface between a
liquid Liquid is a state of matter with a definite volume but no fixed shape. Liquids adapt to the shape of their container and are nearly incompressible, maintaining their volume even under pressure. The density of a liquid is usually close to th ...
and a
gas Gas is a state of matter that has neither a fixed volume nor a fixed shape and is a compressible fluid. A ''pure gas'' is made up of individual atoms (e.g. a noble gas like neon) or molecules of either a single type of atom ( elements such as ...
, or between two
immiscible Miscibility () is the property of two chemical substance, substances to mix in all mixing ratio, proportions (that is, to fully dissolution (chemistry), dissolve in each other at any concentration), forming a homogeneity and heterogeneity, homoge ...
liquids. Alongside the Bond number, commonly denoted \mathrm, 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: :\mathrm = \frac where \mu is the
dynamic viscosity Viscosity is a measure of a fluid's rate-dependent resistance to a change in shape or to movement of its neighboring portions relative to one another. For liquids, it corresponds to the informal concept of ''thickness''; for example, syrup h ...
of the liquid, V is a characteristic velocity and \sigma is the surface tension or
interfacial tension Surface tension is the tendency of liquid surfaces at rest to shrink into the minimum surface area possible. Surface tension is what allows objects with a higher density than water such as razor blades and insects (e.g. water striders) to ...
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 N_c instead of \mathrm. For low capillary numbers (a rule of thumb says less than 10−5), flow in
porous media In materials science, 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 sk ...
is dominated by capillary forces,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; in particular, it governs the dynamic
contact angle The contact angle (symbol ) is the angle between a liquid surface and a solid surface where they meet. More specifically, it is the angle between the surface tangent on the liquid–vapor interface and the tangent on the solid–liquid interfac ...
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:   \mathrm = \frac, \frac where \mu and \hat 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: \mathrm = \frac and \frac.


See also

* Bond number *
Reynolds number In fluid dynamics, the Reynolds number () is a dimensionless quantity that helps predict fluid flow patterns in different situations by measuring the ratio between Inertia, inertial and viscous forces. At low Reynolds numbers, flows tend to ...
*
Capillary pressure In fluid statics, capillary pressure () is the pressure between two immiscible fluids in a thin tube (see capillary action), resulting from the interactions of forces between the fluids and solid walls of the tube. Capillary pressure can serve as b ...
*
Froude number In continuum mechanics, the Froude number (, after William Froude, ) is a dimensionless number defined as the ratio of the flow inertia to the external force field (the latter in many applications simply due to gravity). The Froude number is ba ...


References

{{DEFAULTSORT:Capillary Number Dimensionless numbers of fluid mechanics