Liquid-solid interface, capillary

The LOFO approach, based on capillary interactions induced by liquid-solid interfaces, is used for transferring prefabricated thin solid metal films onto molecu-larly modified solid substrates. In spite of the fact that the glass/metal pad during the lift-off process leaves a relatively rough (1 nm) surface, several types of device have been fabricated by LOFO [154-156]. 

Capillary Rise. In the absence of external forces, a body of liquid tends to assume a shape of minimum area. It is normally prevented from assuming spherical shape by the force of gravity, as well as by contact with other objects. When a liquid is in contact with a solid surface, there exists a specific surface free energy for the interface, or interfacial tension yi2- A solid surface itself has a surface tension 72. vvhich is often large in comparison with the surface tensions of liquids. Let a liquid with surface tension 7i be in contact with a solid with surface tension yj, with which it has an interfacial tension 7i2- Under what circumstances will a liquid film spread freely over the solid surface and wet it This will happen if, in creating a liquid-solid interface and an equal area of liquid surface at the expense of an equal area of solid surface, the free energy of the entire system decreases ... 

Thermoporometry. Thermoporometry is the calorimetric study of the liquid-solid transformation of a capillary condensate that saturates a porous material such as a membrane. The basic principle involved is the freezing (or melting) point depression as a result of the strong curvature of the liquid-solid interface present in small pores. The thermodynamic basis of this phenomenon has been described by Brun et al. [1973] who introduced thermoporometry as a new pore structure analysis technique. It is capable of characterizing the pore size and shape. Unlike many other methods, this technique gives the actual size of the cavities instead of the size of the openings [Eyraud. 1984]. 

The surface charges of the liquid-solid interface play crucial roles in the EOF phenomenon. When a buffer solution is introduced into the capillary, the negatively charged wall attracts the positively charged ions from solution,... 

The capillary pressure of water is determined by a balance of the interfacial energies among the three phases solid, liquid, and vapor, the wetting angle of liquid-solid, and the radii of the pores, which are dependent on the pore structure in the medium and the amount of water existing in the pores. The osmotic pressure is dependent on the pore structure and the liquid-solid interface. Therefore, one must predict the pressure p statistically from the pore structure distribution model. 

When a gas-liquid or liquid-liquid interface is made to move inside a capillary tube, the surface properties affect the liquid-solid interface. However, taking into account that the solid cannot change its shape and size, it will be only the liquid that changes in such a way that, the pressure A/ necessary to intrude or expel the fluid from the capillary is given by the Young-Laplace equation as follows ... 

A liquid-solid contact angle away from 90° induces the formation of a meniscus on the free surface of the liquid in a vertical tube (the solid phase). In the nonwetting case, the meniscus concaves upwards to the air. The upwards meniscus is the result of a downward surface tension at the liquid-tube interface, causing a capillary depression. In the wetting case, the meniscus has a concave-downward configuration. The downwards meniscus is the result of an upward surface tension at the liquid-tube interface, causing a capillary rise. 

One of the most common ways to characterize the hydrophobicity (or hydrophilicity) of a material is through measurement of the contact angle, which is the angle between the liquid-gas interface and the solid surface measured at the triple point at which all three phases interconnect. The two most popular techniques to measure contact angles for diffusion layers are the sessile drop method and the capillary rise method (or Wihelmy method) [9,192]. 

Surface and Interfacial Tension. Some properties of liquid surfaces are suggestive of a skin that exercises a contracting force or tension parallel to the surface. Mathematical models based on this effect have been used in explanation of surface phenomena, such as capillary rise. The terms surface tension (gas—liquid or gas—solid interface) and interfacial tension (liquid—liquid or liquid—solid) relate to these models which do not reflect the actual behavior of molecules and ions at interfaces. Surface tension is the force per unit length required to create a new unit area of gas—liquid surface (mN/m (= dyn/cm)). It is numerically equal to the free-surface energy. Similady, interfacial tension is the force per unit length required to create a new unit area of liquid—liquid interface and is numerically equal to the interfacial free energy. 

The type II isotherm is associated with solids with no apparent porosity or macropores (pore size > 50 nm). The adsorption phenomenon involved is interpreted in terms of single-layer adsorption up to an inversion point B, followed by a multi-layer type adsorption. The type IV isotherm is characteristic of solids with mesopores (2 nm < pore size < 50 nm). It has a hysteresis loop reflecting a capillary condensation type phenomenon. A phase transition occurs during which, under the eflcct of interactions with the surface of the solid, the gas phase abruptly condenses in the pore, accompanied by the formation of a meniscus at the liquid-gas interface. Modelling of this phenomenon, in the form of semi-empirical equations (BJH, Kelvin), can be used to ascertain the pore size distribution (cf. Paragr. 1.1.3.2). 

In membrane filtration, water-filled pores are frequently encountered and consequently the liquid-solid transition of water is often used for membrane pore size analysis. Other condensates can however also be used such as benzene, hexane, decane or potassium nitrate [68]. Due to the marked curvature of the solid-liquid interface within pores, a freezing (or melting) point depression of the water (or ice) occurs. Figure 4.9a illustrates schematically the freezing of a liquid (water) in a porous medium as a fimction of the pore size. Solidification within a capillary pore can occur either by a mechanism of nucleation or by a progressive penetration of the liquid-solid meniscus formed at the entrance of the pore (Figure 4.9b). 

The curvature of the interface depends on the relative magnitudes of the adhesive forces between the liquid and the capillary wall and the internal cohesive forces in the liquid. When the adhesive forces exceed the cohesive forces, 9 lies in the range 0° < 9 < 90° when the cohesive forces exceed the adhesive forces, 90° < 9 < 180°. When 9 > 90°, the cos 9 term is negative, resulting in a convex meniscus towards the vapor phase and the liquid level in the capillary falling below the liquid level in the container (capillary depression). This occurs with liquid mercury in glass where 9 = 140° and also with water in capillary tubes coated internally with paraffin wax. Thus, liquid mercury is used in the evaluation of the porosity of solid adsorbents in the mercury injection porosimetry technique (see Section 8.5). 

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