A B C
ACHE CAD, PLASTICATING SCREWS CAF, COMPRESSED ASBESTOS FIBRE JOINTING CALANDRIA CALCIUM CALCULATING TIME CHARACTERISTICS OF IGNITION OF HYBRID GAS SUSPENSIONS CALDER HALL CALORIE CALORIFIC VALUE OF FUEL CALORIMETRY CANDU NUCLEAR POWER REACTORS CANONICAL PARTITION FUNCTION CAP BUBBLES CAPACATIVE HEAT EXCHANGERS CAPILLARITY Capillary action CAPILLARY CONVECTION CARBOLIC ACID CARBON CARBON ARC CARBON DIOXIDE CARBON DIOXIDE POLLUTION CARBON DIOXIDE, AS A POLLUTANT CARBON DISULFIDE COMBUSTION CARBON MONOXIDE CARBON STEELS CARBON SUBNITRIDE COMBUSTION CARBON THERMOMETERS CARBONACEOUS FUELS CARBONTETRACHLORIDE CARNOT CYCLE CARNOT, NLS CARRYUNDER CARTESIAN COORDINATES CASTING OF METALS CATALYSIS CATALYSTS CATALYTIC ACTIVITY CATALYTIC CONVERSION CATALYTIC CONVERTERS CATALYTIC CRACKING OF PALM OIL CATALYTIC RICH GAS PROCESS, CRG CATHODE CAUCHY SURFACE CAUCHY'S CONVEYENCE PRINCIPLE CAUCHY'S THEOREM CAUSTIC SODA CAVITATING FLOWS CAVITATION CAVITIES, FOR NUCLEATION CAVITY, SQUARE CEA CEC CELL GROWTH CELL POTENTIAL CELLULOSIC FIRES CELSIUS TEMPERATURE SCALE CENTIGRADE TEMPERATURE SCALE CENTRIFUGAL FILTERS CENTRIFUGAL FLOWMETERS CENTRIFUGAL FLUIDIZED BED CENTRIFUGAL SCRUBBER CENTRIFUGAL SEPARATORS CENTRIFUGES CENTRIPETAL BUOYANCY CENTRIPETAL FORCE CERAMIC CRUCIBLE PLASMA FURNACE CERAMICS CERENKOV RADIATION CERMETS CFCS, CHLOROFLUOROCARBON CFD CFD MODELS CHAIN REACTION CHANG-LIN TIEN CHANNEL CONTROL Channel Flow CHANNEL INSTABILITY CHANNEL IRREGULARLY HEATED CHANNELING EFFECT CHAOS CHAR CHARACTERISTIC DRYING CURVE CHARACTERISTIC EQUATIONS, FOR SUPERSONIC FLOW CHARACTERISTICS, METHOD OF CHARACTERISTICS, OF DIFFERENTIAL EQUATIONS CHARCOAL CHARGE CARRIERS CHARGE COUPLED DEVICES, CCD CHARLES LAW CHEBYSHEV EQUATION CHEBYSHEV POLYNOMIAL EXPANSION CHEBYSHEV POLYNOMIALS CHELATION CHEMICAL COMPLEXITY CHEMICAL EQUILIBRIUM CHEMICAL KINETICS CHEMICAL LASERS CHEMICAL POTENTIAL CHEMICAL REACTION CHEMICAL REACTION FOULING CHEMICAL THEORIES, FOR CATALYSIS CHEMICAL THERMODYNAMICS CHEMISORPTION CHEN CORRELATION CHEVRON SEPARATORS Chezy Formula CHF CORRELATIONS CHF, CRITICAL HEAT FLUX CHILTON-COLBURN ANALOGY CHIMNEY PLUMES CHIMNEYS CHLOR-ALKALI ELECTROLYSIS CHLORINE CHLOROFLUOROCARBON, CFC CHLOROFORM CHOKED FLOW CHROMATIC DISPERSION CHROMATOGRAPHY CHUGGING INSTABILITIES Churn Flow CIRCUIT BREAKER CIRCULATION RATIO CISE CORRELATIONS CLADDING CLAPEYRON EQUATION CLAPEYRON-CLAUSIUS EQUATION CLARIFICATION CLARIFIERS Classification of foam structures CLASSIFICATION OF HEAT EXCHANGERS CLASSIFIERS CLAUSIUS CLAUSIUS NUMBER CLAUSIUS-CLAPEYRON EQUATION CLAUSIUS-MOSOTTI EQUATION CLEANING TECHNIQUES, HEAT EXCHANGERS Climate study CLIMATIZATION CLIMBING FILM EVAPORATOR Closed cell foam CLOSED CYCLE GAS TURBINE CLOSED CYCLE MHD GENERATORS CLOSED SYSTEM CLOSURE LAWS CLOUD POINT SPECIFICATION CNEN CO-GENERATION SYSTEMS CO-ORDINATE TRANSFORMATION METHODS COAGULATION COAGULATION, OF AEROSOLS COAGULATION, OF DROPS COAL COAL BURNERS COAL CARBONIZATION COAL COMBUSTION COAL GAS COAL GASIFICATION COAL RESEARCH ESTABLISHMENT, CRE COAL SLURRY COALESCENCE Coanda Effect COARSE VARIABLES FOR DYNAMICS COARSE-GRAINED APPROXIMATION COATINGS COAXIAL TWISTING FLOW COEFFICIENT OF PERFORMANCE, COP COHERENCE FUNCTION COHERENCE STRICTURES, IN TURBULENT FLOW COHERENCE, OF RADIATION COHERENT SYSTEM OF UNITS COIL IN TANK COILED TUBE BOILERS Coiled Tube, Flow and Pressure Drop in Coiled Tubes, Heat Transfer in COILED WIRE INSERTS COKE COKE OVENS COKE-OVEN GAS COLBURN CORRELATION COLBURN FACTOR COLBURN HEAT TRANSFER FACTOR COLBURN J-FACTOR COLBURN, ALLAN PHILIP (1904-1955) COLBURN-CHILTON ANALOGY COLD ROD EFFECTS COLEBROOK-WHITE EQUATION, FOR FRICTION FACTOR COLEBROOK-WHITE FORMULA COLLECTION EFFICIENCY COLLIGATIVE PROPERTIES COLLIGEND COLLOCATION COLLOIDAL DISPERSIONS COLOR SEGREGATION IN METAL-HALIDE LAMPS COLUMN CHROMATOGRAPHY COLUMNS COMBINATORIAL MODELING COMBINED BRINKMAN-ELECTRIC BOUNDARY LAYER COMBINED CYCLES COMBINED HEAT AND MASS TRANSFER Combined heat transfer by radiation, conduction, and convection COMBINED RADIATION AND COMBUSTION COMBUSTION COMBUSTION CHAMBER COMBUSTION PRODUCTS COMFORT CONDITIONS COMITATO NAZIONALE PER LA RICERCA E PER LO SVILUPPO DELL'ENERGIA NUCLEARE E DELLE ENERGIE ALTERNATIVE, ENEA COMMERCIAL PLASMATRON COMMISSARIAT A L'ENERGIE ATOMIQUE, CEA COMMISSION OF THE EUROPEAN COMMUNITY, CEC COMMON MODE FAILURE COMMONWEALTH SCIENTIFIC AND INDUSTRIAL RESEARCH ORGANISATION, CSIRO COMPACT HEAT EXCHANGERS COMPILER COMPLEX COMPOUND CATALYSIS COMPLEXIFICATION COMPLEXING IONS COMPLEXITY COMPOSITE FLOW COMPOSITE MATERIALS COMPOSITE MATERIALS, ABLATION OF COMPOSITE MATERIALS, COMPUTATION OF COMPOSITE POROUS LAYER COMPOSITES, THERMAL CONDUCTIVITY OF COMPOUND AUGMENTATION COMPRESSED ASBESTOS FIBER JOINTING, CAF COMPRESSIBILITY EFFECTS COMPRESSIBILITY FACTOR Compressible Flow COMPRESSION PLASMA FLOWS COMPRESSION POINT COMPRESSION ZONE COMPRESSION-IGNITION ENGINES COMPRESSORS COMPTON SCATTERING COMPUTATIONAL FLUID DYNAMIC MODELS Computational fluid dynamics Computational methods Computational methods for radiative transfer in disperse systems COMPUTER AIDED DESIGN, CAD COMPUTER PROGRAMMES COMPUTERS CONCAVE SURFACE, FLOW OVER CONCENTRATING COLLECTOR CONCENTRATION-DEPENDENT CHLORIDE DIFFUSIVITY Concept of regularization CONCRETE CONCURRENT MULTISCALE PROBLEMS CONDENSATE INUNDATION CONDENSATION COEFFICIENT CONDENSATION CURVE CONDENSATION IN ENCLOSURES CONDENSATION IN TUBE BANKS CONDENSATION IN TUBES CONDENSATION OF A PURE VAPOR CONDENSATION OF MOVING VAPOR INSIDE VERTICAL TUBES CONDENSATION OF MULTICOMPONENT VAPORS CONDENSATION ON OUTSIDE OF TUBES IN CROSSFLOW CONDENSATION RELAXATION OF SUPERSATURATED VAPOR CONDENSATION SHOCKS CONDENSATION, OF DROPS CONDENSATION, OVERVIEW CONDENSERS CONDUCTANCE PROBES, FOR LOCAL VOID FRACTION CONDUCTANCE, ELECTRICAL CONDUCTION CONDUCTION AND CONVECTION COMBINED CONDUCTION COMBINED WITH RADIATION CONDUCTION DRYING CONDUCTION EQUATION CONDUCTION IN HEAT EXCHANGER WALLS CONDUCTIVE HEAT FLUX CONDUCTIVITY CONDUCTIVITY RATIO CONDUCTIVITY, ELECTRICAL CONDUCTIVITY, OF PLASMA CONE CLASSIFIER Configuration factors for radiation transfer between diffuse surfaces CONFINED SPRAY FLAME CONFORMAL MAPPING CONFORMAL POTENTIALS CONICAL SHOCK WAVE CONJUGATE HEAT TRANSFER CONSERVATION EQUATIONS CONSERVATION EQUATIONS, SINGLE-PHASE Conservation equations, Two-phase Conservation Laws CONSERVATIVE SYSTEMS CONSTANT RATE PERIOD, DRYING CURVE CONSTITUTIVE EQUATIONS CONSTITUTIVE RELATION, THERMODYNAMICS Contact angle CONTACT CONDUCTANCE CONTACT DISCONTINUITIES CONTACT RESISTANCE CONTAINMENT CONTINUITY EQUATION CONTINUITY SHOCKS CONTINUITY WAVES CONTINUOUS CASTING CONTINUOUS CRYSTALLIZERS CONTINUOUS FILTERS CONTINUOUS WAVE LASERS Continuum Continuum Hypothesis CONTINUUM MECHANICS CONTINUUM MODELS Contraction, Flow and Pressure Loss in CONTRACTORS CONTROL THEORY CONVECTION CONDENSATION CONVECTION DRYING CONVECTION RADIATION CONVECTIVE BOILING CONVECTIVE HEAT FLUX CONVECTIVE HEAT TRANSFER CONVECTIVE HEAT 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COUPLED CONDUCTION AND CONVECTION COUPLED HEAT AND MASS FLUXES Coupled radiation and convection Coupled radiation, convection and conduction COVALENT BONDING COWPER STOVES CRACKING CRAMER'S RULE CRE CREAGER-OFITSEROV PROFILE CREEPING FLOW CRITICAL CHOKING CRITICAL CONCENTRATION CRITICAL DEPOSITION VELOCITY Critical Flow CRITICAL FLOW RATE, IN ORIFICES CRITICAL HEAT FLUX IN BOILING LIQUID METALS CRITICAL HEAT FLUX IN COILS CRITICAL HEAT FLUX, CHF CRITICAL POINT, DRYING CURVE CRITICAL POINT, THERMODYNAMICS CRITICAL PRESSURE CRITICAL PRESSURE RATIO Critical Reynolds number CRITICAL SEDIMENTATION POINT CRITICAL STATE CRITICAL SURFACE TENSION CRITICAL TEMPERATURE CRITICAL TEMPERATURE, FOR SUPERCONDUCTIVITY CRITICAL TRANSITION VELOCITY CRITICAL ZONE CRITICALITY CROCCO TRANSFORMATION CROCCO'S THEOREM CROSS CORRELATION CROSS FLOW HEAT TRANSFER CROSS FLUXES CROSS SECTIONS CROSS SPECTRUM Crossflow CRUDE OIL CRYOGENIC FLUIDS CRYOGENIC PLANT CRYOGENIC PUMP CRYOGENIC USE OF STEEL CRYOSCOPIC 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Capillary action

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Capillary action is the physical phenomenon arising due to surface tension on the interface of immiscible media. Commonly, capillary phenomena occur in liquid media and are brought about by the curvature of their surface that is adjacent to another liquid, gas, or its own vapor.

Surface curvature in a fluid gives rise to an additional so-called capillary pressure ρσ whose value is related to an average surface curvature H

(R1 and R2 are the radii of curvature of principal normal sections) via the Laplace equation.

(1)

where σ12 is the surface or interfacial tension (see Surface and Interfacial Tension) on the boundary between phases 1 and 2, p1 and p2 are the pressures in the phases. The pressure is higher in the phase to which the concavity of the interface is presented. For a plane interface, H=0 and pσ=0.

Capillary phenomena include various cases of equilibrium and flow of fluid surface under the action of surface tension forces and of external forces, primarily gravity. In the simplest case when the external forces are absent, e.g., under weightlessness conditions, a limited fluid volume takes the shape of a sphere due to surface tension forces. This state corresponds to a stable equilibrium of the fluid since a sphere has the minimum surface and, consequently, the minimum surface energy.

As shown in Figure 1, when the liquid (1) comes in contact with the gas vapor (2) and the solid (3), the shape of the free liquid surface depends on wetting. Interaction of surface tension forces at the liquid-gas σ12, liquid-solid σ13, and gas-solid σ23 interfaces is responsible for a curved area of the liquid surface (meniscus) near the solid. An angle θ made by the tangent to the liquid surface and the solid surface, known as a wetting angle, is determined by the balance of forces within the surface tension. According to the Young equation,

If σ23 > σ13, i.e., if the surface tension between gas and a solid is greater than between a solid and a liquid, then θ < π/2 and the solid surface is said to be wetted by the liquid. If σ23 < σ13, then θ > π/2, and this indicates that the solid is not wetted by the liquid. The cases θ = 0 and θ = π correspond to absolute wetting and nonwetting of the surface by the liquid.

Solid surface in contact with gas and liquid gases.

Figure 1. Solid surface in contact with gas and liquid gases.

The wetting angle depends on the liquid and the surface it is in contact with. For instance, liquid alkaline metals and cryogenic liquids wet metal surfaces nearly absolutely and the angle θ approaches zero. Teflon and paraffin are virtually nonwettable by water and some other liquids. It should be borne in mind that the wetting angle strongly depends on the surface state, i.e., surface contamination—the presence of surface active agents—and surface roughness, which enhances wettability.

As a result of displacement of the interface of the three phases, the wetting angle displays hysteresis; that is, on the surface wetted earlier, the wetting angle appears to be smaller than in the case of displacement of the interphase boundary on an initially dry surface.

A most commonly encountered and visual example of capillary phenomena are the suction of liquid in narrow tubes with wettable walls (Figure 2a) and the expulsion of the liquid out of them if the walls are nonwettable (Figure 2b). At each point of the curved free liquid surface, capillary pressure is built up that leads to a liquid rise in the tube. The height of rise h is determined by the relation between external (in this case, gravitational) and surface tension forces. This relation is expressed by the Bond Number

where p1 and pg are the densities of the liquid and gaseous (vapor) phases, respectively, and L, the characteristic linear dimension of interface. The condition Bo=1 governs the linear dimension of a at which the indicted forces are equal

a2, known as the capillary constant, is a constant of the liquid-vapor or liquid 1-liquid 2 interface which is independent of the tube diameter and material its wall is made of. Under terrestrial conditions, at pressures substantially lower than critical a=1−3 mm for most liquids.

Level rise and depression due to capillary action.
Level rise and depression due to capillary action.

Figure 2. Level rise and depression due to capillary action.

Tubes with diameter dc<a are said to be capillary. If the capillary radius rc<0.05 a, then the meniscus has the shape close to a sphere with the curvature radius

(2)

and the height h of the liquid is determined by Jurin's formula

(3)

As rc increases, the meniscus shape steadily departs from the spherical and the capillary rise also steadily deviates from the value calculated via Eq. (3). Rayleigh suggested a formula in the form of a power series which allows for this effect, and is valid for rc<0.46 a:

The terms on the right-hand side, beginning with the second, are the correction for deviation of the meniscus shape from the sphere.

In very narrow (dc << a) capillary tubes, the vapors of an absolutely wetting liquid absorbing on the walls form a multimolecular liquid film. The presence of the film decreases the curvature radius of the meniscus as compared to that calculated through Eq. (2) at θ=0. In this case, the capillary pressure on the meniscus exceeds the value calculated by the Laplace equation (1) at R1=R2=rc.

In a plane capillary tube, i.e., the gap between two plates at distance dp apart, the meniscus surface is of cylindrical shape with the radius

therefore, the height of the capillary rise is half that in a cylindrical capillary at dc=dp.

If the capillary walls are not wetted, the liquid meniscus is convex and the level of liquid in it deviates below the level of a free liquid by a value also determined by Eq. ( 3).

In vessels with the characteristic dimension L>>a, the liquid surface is plane except the small area near the vessel walls, where the liquid rises or lowers by about the quantity a.

The difference in capillary pressures due to different curvature of liquid menisci may give rise to a liquid flow in the capillary (Figure 3), where the flow of wetting liquid is directed toward the meniscus with the smaller curvature radius. This is used, for instance, when entraining the working liquid from the condensation to the evaporation zone in heat pipes. (See Heat Pipes.) The capillary pressure can be calculated theoretically only for capillaries of the simplest form: a plane slot which has been considered above; a circular cylindrical capillary; and capillaries of triangular, square, and some other shapes of cross-section. For capillaries with cross-sections of intricate irregular shape (such as the case, in particular, with capillary paths of heat pipe wicks), an accurate value of capillary pressure can be found only experimentally.

Difference in radius of curvature inducing flow in a capillary.

Figure 3. Difference in radius of curvature inducing flow in a capillary.

Capillary absorption plays an essential role in liquid movement in the soil, ground and porous coatings of heat-releasing surface with boiling liquids on them. Capillary impregnation of materials is widely applied in chemical technology.

Many properties of disperse systems, such as permeability and strength, depend to a large extent on capillary phenomena because in the fine pores of these bodies, a high capillary pressure is realized.

At a given temperature T, the intermolecular cohesive forces in a concave surface layer are stronger than on the plane surface. Therefore, the number of molecules leaving the surface and, as a result, the saturation pressure over the concave surface, is lower than those over the plane surface. For a convex surface, this pressure is higher. The relation between pressures p and p0 over curved and plane surfaces, respectively, is described by the Kelvin equation

where is the individual gas constant and pl, the liquid density.

In narrow pores, the vapors of wetting liquid are condensed at the temperature of vapor saturation over the plane surface (capillary condensation). This underlies vapor collecting by fine-pored sorbents.

Curvature of a free liquid surface exposed to external forces gives rise to so-called capillary waves, that is, the rippled surface of liquid.

The joint action of surface tension, viscosity, inertia, and gravitational forces and their correlation account for the diverse flow regimes, i.e., phase distribution throughout the volume in Two-Phase Flows in channels. (See Multiphase Flows.)

The measurement of some physical values characterizing capillary phenomena forms the basis for experimental methods determining surface tension coefficients of liquids. For instance, in measuring the height h of liquid rise in the capillary Eq. (3) is used to find the surface tension coefficient σ12.

Leonardo da Vinci (16th century), B. Pascal (17th century) and Jurin (18th century) pioneered investigations into capillary phenomena in experiments with capillary tubes. The theory of capillary phenomena was further developed by P. Laplace (1806), T. Young (1879) and I. S. Gromeka (1876).

REFERENCES

Adamson, A. W. (1976) Physical Chemistry of Surfaces, Wiley and Sons, New York.

References

  1. Adamson, A. W. (1976) Physical Chemistry of Surfaces, Wiley and Sons, New York.

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