Topic

# Capillary number

About: Capillary number is a research topic. Over the lifetime, 4181 publications have been published within this topic receiving 131709 citations. The topic is also known as: dynamic capillary number & first capillary number.

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TL;DR: In this paper, a force density proportional to the surface curvature of constant color is defined at each point in the transition region; this force-density is normalized in such a way that the conventional description of surface tension on an interface is recovered when the ratio of local transition-reion thickness to local curvature radius approaches zero.

7,863 citations

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TL;DR: In this article, the authors used Darcey's law to derive the equation K∇2ψ+∇K·∇ψ +g∂K/∂z=−ρsA∆ψ/∆t for the capillary conduction of liquids in porous mediums.

Abstract: The flow of liquids in unsaturated porous mediums follows the ordinary laws of hydrodynamics, the motion being produced by gravity and the pressure gradient force acting in the liquid. By making use of Darcey's law, that flow is proportional to the forces producing flow, the equation K∇2ψ+∇K·∇ψ+g∂K/∂z=−ρsA∂ψ/∂t may be derived for the capillary conduction of liquids in porous mediums. It is possible experimentally to determine the capillary potential ψ=∫dp/ρ, the capillary conductivity K, which is defined by the flow equation q=K(g−▿ψ), and the capillary capacity A, which is the rate of change of the liquid content of the medium with respect to ψ. These variables are analogous, respectively, to the temperature, thermal conductivity, and thermal capacity in the case of heat flow. Data are presented and application of the equations is made for the capillary conduction of water through soil and clay but the mathematical formulations and the experimental methods developed may be used to express capillary flow ...

5,340 citations

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TL;DR: In this paper, the authors present the results of network simulators (100 × 100 and 25 × 25 pores) based on the physical rules of the displacement at the pore scale, and they show the existence of the three basic domains (capillary fingering, viscous fingering and stable displacement) within which the patterns remain unchanged.

Abstract: Immiscible displacements in porous media with both capillary and viscous effects can be characterized by two dimensionless numbers, the capillary number C, which is the ratio of viscous forces to capillary forces, and the ratio M of the two viscosities. For certain values of these numbers, either viscous or capillary forces dominate and displacement takes one of the basic forms: (a) viscous fingering, (b) capillary fingering or (c) stable displacement. We present a study in the simple case of injection of a non-wetting fluid into a two-dimensional porous medium made of interconnected capillaries. The first part of this paper presents the results of network simulators (100 × 100 and 25 × 25 pores) based on the physical rules of the displacement at the pore scale. The second part describes a series of experiments performed in transparent etched networks. Both the computer simulations and the experiments cover a range of several decades in C and M. They clearly show the existence of the three basic domains (capillary fingering, viscous fingering and stable displacement) within which the patterns remain unchanged. The domains of validity of the three different basic mechanisms are mapped onto the plane with axes C and M, and this mapping represents the ‘phase-diagram’ for drainage. In the final section we present three statistical models (percolation, diffusion-limited aggregation (DLA) and anti-DLA) which can be used for describing the three ‘basic’ domains of the phase-diagram.

1,378 citations

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TL;DR: In this paper, the dynamics involved in the movement of the contact line when one liquid displaces an immiscible second liquid where both are in contact with a smooth solid surface are investigated.

Abstract: An investigation is made into the dynamics involved in the movement of the contact line when one liquid displaces an immiscible second liquid where both are in contact with a smooth solid surface. In order to remove the stress singularity at the contact line, it has been postulated that slip between the liquid and the solid or some other mechanism must occur very close to the contact line. The general procedure for solution is described for a general model for such slip and also for a general geometry of the system. Using matched asymptotic expansions, it is shown that for small capillary number and for small values of the length over which slip occurs, there are either 2 or 3 regions of expansion necessary depending on the limiting process being considered. For the very important situation where 3 regions occur, solutions are obtained from which it is observed that in general there is a maximum value of the capillary number for which the solutions exist. The results obtained are compared with existing theories and experiments.

1,218 citations

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TL;DR: In this article, the phase interface in a capillary and the spreading of viscous fluid drops on solid surfaces are solved, and the dependence of this angle on the velocity with allowance for capillary forces is determined.

Abstract: Fluid motion along a smooth, solid surface is examined when the free surface forms a final visible angle with the solid boundary. The dependence of this angle on the velocity with allowance for capillary forces is determined. The Reynolds number is small. The problem of the motion of the phase interface in a capillary and the spreading of viscous fluid drops on solid surfaces are solved. Experimental results are explained. Up to now, not only were analytical results lacking in this field, but also there was not even a precise formulation of the problem (see the review in [1]).

1,074 citations