Forces capillary

In the solid state, the capillary force can be expressed as an increase or decrease in chemical potential of a species in the vicinity of a curved interface relative to a 

FIGURE 7.1 Capillary forces arising due to differences in surface curvature lead to net transport of matter from the convex to concave regions, resulting in smoothing of the surface over time. 

Consider the increase in solubility that arises at a spherical interface relative to a planar interface. For 1 mol of material transfered from a flat to a spherical interface, the change in surface area, dA, is given by 8 rr dr = 7ir Vj /Anr ) Thus  

The more general expression for solubility in the vicinity of a curved (but nonspher-ical) interface is 

Equations 7.2 and 7.3 indicate that highly convex surfaces (r = small, positive) lead to enhanced solubility relative to a planar interface, which drives the dissolution or removal of atoms from such areas. In contrast, highly concave surfaces (r = small, negative) lead to suppressed solubility relative to a planar interface. 

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In a reservoir at initial conditions, an equilibrium exists between buoyancy forces and capillary forces. These forces determine the initial distribution of fluids, and hence the volumes of fluid in place. An understanding of the relationship between these forces is useful in calculating volumetries, and in explaining the difference between free water level (FWL) and oil-water contact (OWC) introduced in the last section. 

Blood flow attributable to capillary force residence time regulated at will... 

Sulfonates for Enhanced Oil Recovery. The use of hydrocarbon sulfonates for reducing the capillary forces in porous media containing cmde oil and water phases was known as far back as 1927—1931 (164,165). Interfacial tensions between 10 and 10 N/m or less were estabUshed as necessary for the mobilization and recovery of cmde oil (166—169). 

Surfactants aid dewatering of filter cakes after the cakes have formed and have very Httle observed effect on the rate of cake formation. Equations describing the effect of a surfactant show that dewatering is enhanced by lowering the capillary pressure of water in the cake rather than by a kinetic effect. The amount of residual water in a filter cake is related to the capillary forces hoi ding the Hquids in the cake. Laplace s equation relates the capillary pressure (P ) to surface tension (cj), contact angle of air and Hquid on the soHd (9) which is a measure of wettabiHty, and capillary radius (r ), or a similar measure appHcable to filter cakes. 

Extremely wide variation in solvent strength with temperature and pressure. Gollapse of structure due to capillary forces is prevented during solvent removal. 

Fig. 10. Analysis of the atomic lattice images of the lead compound entering CNTs by capillary forces (a)detailed view of the high resolution image of the filling material, (b)tetragonal PbO atomic arrangement, note the layered structure and (c)tetragonal PbO observed in the [111] direction, note that the distribution of lead atoms follows the contrast pattern observable in (a), (d)bidimensional projection of the deduced PbO filling orientation inside CNTs as viewed in the tube axis direction, note that PbO layers are parallel to the cylindrical CNT cavity.

KapiUarititt, /. capillarity. Kapillaritittsanziehung./. capillary attraction. Kapillar-kraft,/, capillary force, -kreislauf, n. capillary circulation, -rohr, -rohrchen, n, -rohre, /. capillary tube, -spaonung, /. capillary tension, -stromung, /. capillary flow, -versuch, m. capillary test or experiment. -wirkung./. capillary action. 

The small pore size and the uniform distribution result in capillary forces which should allow wicking heights and thus battery heights of up to 30 cm. Due to the cavities required for gas transfer and under the effect of gravity, the electrolyte forms a filling profile, i.e., fewer cavities remain at the bottom than at the top. Therefore with absorptive glass mats a rather flat battery... 

The prime requirements for the separators in alkaline storage batteries are on the one hand to maintain durably the distance between the electrodes, and on the other to permit the ionic current flow in as unhindered a manner as possible. Since the electrolyte participates only indirectly in the electrochemical reactions, and serves mainly as ion-transport medium, no excess of electrolyte is required, i.e., the electrodes can be spaced closely together in order not to suffer unnecessary power loss through additional electrolyte resistance. The separator is generally flat, without ribs. It has to be sufficiently absorbent and it also has to retain the electrolyte by capillary forces. The porosity should be at a maximum to keep the electrical resistance low (see Sec. 9.1.2.3) the pore size is governed by the risk of electronic shorts. For systems where the electrode substance... 

It can be shown, (Gibbs, Scientific Papers, I. J. J. Thomson, Applications of Dynamics to Physics and Chemistry), that a chemical equilibrium can be modified by the action of capillary forces. Thus, a state of equilibrium in solution may conceivably be modified if the latter is in the form of thin films, such as soap bubbles. Since, according to Freundlich (Kapillarchemie, 116), there is at present no direct evidence of the existence of such modification (which would no doubt be exceedingly, though possibly measurably, small) we shall not enter any further into the matter here. 

In the above we have assumed that no other forces than the electrical are acting at the surface of separation. In general, there will be the capillary forces as well, and we have to take account of the influence of the electrical double layer in considering the adsorption of an electrolyte. If w is the area of the surface, o the interfacial tension, e the charge per unit area, and E the difference of potential, we shall have ... 

A capillary system is said to be in a steady-state equilibrium position when the capillary forces are equal to the hydrostatic pressure force (Levich 1962). The heating of the capillary walls leads to a disturbance of the equilibrium and to a displacement of the meniscus, causing the liquid-vapor interface location to change as compared to an unheated wall. This process causes pressure differences due to capillarity and the hydrostatic pressures exiting the flow, which in turn causes the meniscus to return to the initial position. In order to realize the above-mentioned process in a continuous manner it is necessary to carry out continual heat transfer from the capillary walls to the liquid. In this case the position of the interface surface is invariable and the fluid flow is stationary. From the thermodynamical point of view the process in a heated capillary is similar to a process in a heat engine, which transforms heat into mechanical energy. 

From the frame of the quasi-one-dimensional model it is possible to determine the hydrodynamic and thermal characteristics of the flow in a heated capillary, accounting for the influence of the capillary force. 

The solution of Eq. (10.50) determines the steady states of the liquid velocity, as well as the position of the meniscus in a heated micro-channel. Equation (10.50) can have one, two or three steady solutions. This depends on the value of the parameter (in the generic case parameter B), which takes into account the effect of the capillary forces. 

The change of velocify due to liquid evaporation l and influence of the capillary forces L versus Xf for > 1 is illustrated in Fig. 10.6. In the case 2> 1 the curves L(Xf) and L(xf) have only one point of intersection, which determines the stationary values of ml = L.st and Xf = Xf,st. It is not difficult to show that this point is stable. Indeed a displacement of the meniscus from its initial position Xf,st to the position x[ ) leads to the situation, when the velocity due to the liquid evaporation Hl exceeds the velocity due to the capillary force u[. This leads to the return of the meniscus to its initial position. If the meniscus displaces to the left, > u, this also leads to the return of the system to its initial state. 

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