Capillary motion

The condition for the line of contact is a boundary condition of the corresponding hydrodynamic problem and as such, it should take into account the force of viscous resistance in addition to the forces of surface tension. 

The subject of the present section is the capillary motion in a vertical narrow tube [2]. The moistening flow and the flow due to a surface gradient of surface tension will be considered, respectively, in Sections 17.3 and 17.5. 

Consider the rise of a liquid in a vertical capillary cylindrical tube with radius a, one end of which is immersed into a tank with liquid, and the other end is opened into the atmosphere (Fig. 17.5). 

In a narrow tube with a circular cross section, the shape of the liquid meniscus approximates a spherical segment with constant radius of curvature R = a/cos 0, where 0 is a static contact angle. The deviation of the meniscus shape from a sphere can be caused by the influence of gravity. The ratio of hydrostatic gravitational force to the surface tension force is characterized by a dimensionless pa- 

At Bo 1, the surface tension force can be neglected in comparison with gravity. At Bo 1, on the other hand, gravity is immaterial. 

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The cause of the capillary motion is indicated in the extra" supply terms of momentum pg in (6), which are postulated for the liquid and gas with... 

Herein, cl and cG are parameters responding to the capillary forces which has an effect between the solid and gas phase and between the liquid and gas phase, respectively. They depend on the form and nature of the pores and of the surface tensions between the phases. This new approach to the interaction forces allows the description of capillary motion in porous solids, see de Boer Didwania [6]. 

The dilational rheology behavior of polymer monolayers is a very interesting aspect. If a polymer film is viewed as a macroscopy continuum medium, several types of motion are possible [96], As it has been explained by Monroy et al. [59], it is possible to distinguish two main types capillary (or out of plane) and dilational (or in plane) [59,60,97], The first one is a shear deformation, while for the second one there are both a compression - dilatation motion and a shear motion. Since dissipative effects do exist within the film, each of the motions consists of elastic and viscous components. The elastic constant for the capillary motion is the surface tension y, while for the second it is the dilatation elasticity e. The latter modulus depends upon the stress applied to the monolayer. For a uniaxial stress (as it is the case for capillary waves or for compression in a single barrier Langmuir trough) the dilatational modulus is the sum of the compression and shear moduli [98]... 

Horizontal Capillarity—When the capillary motion is horizontal, it is due entirely to the capillary phenomenon itself, so that from Eq (15-10)... 

The Rooting-Zone Soil Root-zone soil includes the A horizon below the surface layer. The roots of most plants are confined within the first meter of soil depth. In agricultural lands, the depth of plowing is 15-25 cm. In addition, the diffusion depth, which is the depth below which a contaminant is unlikely to escape by diffusion, is on the order of a meter or less for all but the most volatile contaminants. Soil-water content in the root zone is somewhat higher than that in surface soils. The presence of clay in this layer serves to retain water. Contaminants in root-zone soil are transported upward by diffusion, volatilization, root uptake, and capillary motion of water transported downward by diffusion and leaching and transformed chemically primarily by biodegradation or hydrolysis. 

The Deeper Unsaturated Soil The deeper unsaturated soil includes the soil layers below the root zone and above the saturated zone, where all pore spaces are filled with water. This compartment can encompass both the B and the C soil horizons. The soil in this layer typically has a lower organic carbon content and lower porosity than the root-zone soil. Contaminants in this layer move downward to the groundwater zone primarily by capillary motion of water and leaching. Chemical transformation in this layer is primarily by biodegradation. 

Capillarity may be defined as the phenomena resulting from the fact that a free liquid surface has a finite or zero contact angle with a solid wall and will attain this angle when placed in contact with the wall. It is commonly thought of as the rise (or fall) of liquids in small tubes or finely porous media. More generally, capillary motion can be said to be any flow that is governed in some measure by the forces associated with surface tension. Ordinary capillarity is observed in a fine tube open at both ends that is placed vertically in a pool of liquid exposed to the atmosphere, with the liquid seen to attain a level in the tube above the level of the pool. The actual rise velocity of the free surface of the liquid in the tube from the level of the pool is one simple example of capillary motion. ... 

The subject of capillarity and capillary motion can perhaps best be introduced by using the classical example of the rise of a liquid in a circular capillary tube of radius a, that sits vertically in a pool of the liquid open to the atmosphere, as shown in Fig. 10.2.1. It is assumed that the surface tension at the liquid-air interface is uniform with any possible gradients neglected, leaving the discussion of the effects arising from such gradients to Section 10.4. 

Levich (8 ) has discussed capillary motion in two-dimensional creeping flows in which the surface was flat. Yih (17) pointed out inconsistencies in Levich s analysis which were associated with the assumptions of a linear distribution of surface tension with distance along the interface, and with the deflection of the surface which inevitably occurs when capillary flow exists. He noted that under certain circumstances steady flows may not exist. Ostrach (18, 19) has discussed scaling problems in capillary flows. 

Fig. 17.9 Thermo-capillary motion of liquid in a shallow rectangular tray (o) and the change of surface tension coefficient along the tray (/ ).

Pores within the fibrous mass may not lead to the exposed surface, but may have dead ends or simply be occluded. Methods of estimating capillary motion in such porous structures are considered by Neiss and Winter [69]. 

The real physical picture of surface-tension-driven capillary motion appears to be much more... 

Electric field Liquid Porous plug capillary Motion of the liquid Electroosmosis... 

The drug release pattern from such porous matrices is strongly influenced by the penetration process of the external liquids inside the microstructure of the matrix. If the liquid can wet the matrix (contact angle below 90 ) the penetration takes place basically via a capillary motion through the pores. In this case the basic physical factors influencing the penetration are the contact angle the pore size and gojy e the surface tension of liquid and its viscosity. If the liquid does not wet the... 

Kozeny, J. (1927) "Capillary Motion of Water in Soils", Sitzungsberichte der Akactemie der Wissenschaften in Wien, Mathematisch-Naturwissenschaftliche Klasse, V136, N 5-6, p 271-306. Sitzb. Akad. Wiss., 136, 271-306. 

The marching velocity of a capillary meniscus can also be obtained from the surface energy considerations, by relating the instantaneous position or velocity of the capillary front with the gradients of the net interfacial energy. The final forms of the governing equations, as expected, turn out to be of identical nature as the equations of capillary motion described earlier. For the mathematical details, one may refer to the recent work of Yang et al. [9]. 

The behavior at later times may be explained by the shear-thinning rheology of the two liquids as predicted by (1.69), the velocity of the capillary flow decreases with the penetration distance, consequently the shear-rate decreases and the viscosity increases. Hence a coupling is estabHshed between viscosity and velocity, leading to the reduction of the velocity of the capillary motion. 

Capillary motion occurs at about 6 orders of magnitude faster than diffusion. Both processes can be decoupled, with consequent ramifications for diffusion and damage. 

Capillary motion occurs inside microcracks that develop within composite laminates under mechanical loads or thermal exposures. These microcracks tend to span the thickness of individual plies or ply groups and have a breadth of less than 1 pm, thus acting as capillaries that attract fluid. 

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