Liquids and Liquid Surfaces

A liquid is defined as a medium which takes the shape of its container without necessarily filling it. Water is the most abundant liquid on earth and is essential for living systems, and non-aqueous liquids are widely used as solvents in synthetic, analytical, electrochemistry, polymer chemistry, spectroscopy, chromatography and crystallography. Molten metals are also considered to be liquid solvents. We may also consider another property that distinguishes liquids the response of a liquid to an applied force is mainly inelastic that is a liquid does not return to its original shape following the application, then removal, of a force. 

The densities of liquids under normal pressures are not too dissimilar to those of their solids between the melting and boiling points. Generally a liquid is less dense than its solid at the melting point, but there are a few exceptions of which water is one ice floats on water. These less dense solids have rather open crystal structures. Silicon, germanium and tin are other examples. Another similarity between normal liquids and solids is that they have a low compressibility due to there not being a great deal of space between the molecules in a liquid. 

If we were able to observe the molecules in a liquid, we could see an extremely violent agitation in the liquid surface. The extent of this agitation may be calculated by considering the number of molecules that must evaporate each second from the surface, in order to maintain the measurable equilibrium vapor pressure of the liquid. When a liquid is in 

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It is common observation that a liquid takes the shape of a container that surrounds or contains it. However, it is also found that, in many cases, there are other subtle properties that arise at the interface of liquids. The most common behavior is bubble and foam formation. Another phenomena is that, when a glass capillary tube is dipped in water, the fluid rises to a given height. It is observed that the narrower the tube, the higher the water rises. The role of liquids and liquid surfaces is important in many everyday natural processes (e.g., oceans, lakes, rivers, raindrops, etc.). Therefore, in these systems, one will expect the surface forces to be important, considering that the oceans cover some 75% of the surface of the earth. Accordingly, there is a need to study surface tension and its effect on surface phenomena in these different systems. This means that the structures of molecules in the bulk phase need to be considered in comparison to those at the surface. 

The role of liquids and liquid surfaces is important in many everyday natural processes (e.g., oceans, lakes, rivers, and rain drops). In everyday life, the most important liquid one is concerned with is water. 

A typical material balance is shown in Table 1. The purpose of material balance is to show the following infoimation of a process stream ( ) its total and component flow rates, (2) its operattug conditions (temperature and pressure), (3) its physical properties (density and viscoaty of vapor or/and liquid, and liquid surface tension (for two-phase flow only)), and (4) its name or description. 

For heterogeneous nucleation of a solid particle, relationship among solid-surface, solid-liquid, and liquid-surface interfacial energies and the wetting angle... 

In gas analysis the burettes are generally vertical graduated tubes provided with a tap at the upper end. The lower end is connected by means of tubing to a reservoir containing mercury or water, by means of which the pressure on the gas enclosed between the tap and the liquid surface may be adjusted and ascertained. 

The capillary effect is apparent whenever two non-miscible fluids are in contact, and is a result of the interaction of attractive forces between molecules in the two liquids (surface tension effects), and between the fluids and the solid surface (wettability effects). 

The topic of capillarity concerns interfaces that are sufficiently mobile to assume an equilibrium shape. The most common examples are meniscuses, thin films, and drops formed by liquids in air or in another liquid. Since it deals with equilibrium configurations, capillarity occupies a place in the general framework of thermodynamics in the context of the macroscopic and statistical behavior of interfaces rather than the details of their molectdar structure. In this chapter we describe the measurement of surface tension and present some fundamental results. In Chapter III we discuss the thermodynamics of liquid surfaces. 

An approximate treatment of the phenomenon of capillary rise is easily made in terms of the Young-Laplace equation. If the liquid completely wets the wall of the capillary, the liquids surface is thereby constrained to lie parallel to the wall at the region of contact and the surface must be concave in shape. The... 

The exact treatment of capillary rise must take into account the deviation of the meniscus from sphericity, that is, the curvature must correspond to the AP = Ap gy at each point on the meniscus, where y is the elevation of that point above the flat liquid surface. The formal statement of the condition is obtained by writing the Young-Laplace equation for a general point (x, y) on the meniscus, with R and R2 replaced by the expressions from analytical geometry given in... 

Equations II-12 and 11-13 illustrate that the shape of a liquid surface obeying the Young-Laplace equation with a body force is governed by differential equations requiring boundary conditions. It is through these boundary conditions describing the interaction between the liquid and solid wall that the contact angle enters. 

As is evident firom the theory of the method, h must be the height of rise above a surface for which AP is zero, that is, a flat liquid surface. In practice, then, h is measured relative to the surface of the liquid in a wide outer tube or dish, as illustrated in Fig. n-6, and it is important to realize that there may not be an appreciable capillary rise in relatively wide tubes. Thus, for water, the rise is 0.04 mm in a tube 1.6 cm in radius, although it is only 0.0009 mm in one of 2.7-cm radius. 

Several convenient ways to measure surface tension involve the detachment of a solid from the liquid surface. These include the measurement of the weight in a drop falling from a capillary and the force to detach a ring, wire, or thin plate from the surface of a liquid. In this section we briefly describe these methods and their use. 

A zero or near-zero contact angle is necessary otherwise results will be low. This was found to be the case with surfactant solutions where adsorption on the ring changed its wetting characteristics, and where liquid-liquid interfacial tensions were measured. In such cases a Teflon or polyethylene ring may be used [47]. When used to study monolayers, it may be necessary to know the increase in area at detachment, and some calculations of this are available [48]. Finally, an alternative method obtains y from the slope of the plot of W versus z, the elevation of the ring above the liquid surface [49]. 

Derive, from simple considerations, the capillary rise between two parallel plates of infinite length inclined at an angle of d to each other, and meeting at the liquid surface, as illustrated in Fig. 11-23. Assume zero contact angle and a circular cross section for the meniscus. Remember that the area of the liquid surface changes with its position. 

One may consider a molecule in the surface region as being in a state intermediate between that in the vapor phase and that in the liquid. Skapski [11] has made the following simplified analysis. Considering only nearest-neighbor interactions, if n, and denote the number of nearest neighbors in the interior of the liquid and the surface region, respectively, then, per molecule... 

Unfortunately, however, one cannot subject a liquid surface to an increased pressure without introducing a second component into the system, such as some inteit gas. One thus increases the density of matter in the gas phase and, moreover, there will be some gas adsorbed on the liquid surface with a corresponding volume change. 

A schematic picture of how concentrations might vary across a liquid-vapor interface is given in Fig. III-ll. The convention indicated by superscript 1, that is, the F = 0 is illustrated. The dividing line is drawn so that the two areas shaded in full strokes are equal, and the surface excess of the solvent is thus zero. The area shaded with dashed strokes, which lies to the right of the dividing... 

Before proceeding to the main subject of this chapter—namely, the behavior and properties of spread films on liquid substrates—it is of interest to consider the somewhat wider topic of the spreading of a substance on a liquid surface. Certain general statements can be made as to whether spreading will occur, and the phenomenon itself is of some interest. 

Finally, Newmann and co-workers [30] (see also Ref. 31) have argued that while free energy contributions may not be strictly additive as in Eq. IV-11, there should, in principle, be an equation of state relating the work of adhesion to the separate liquid surface tensions such as... 

The equilibrium shape of a liquid lens floating on a liquid surface was considered by Langmuir [59], Miller [60], and Donahue and Bartell [61]. More general cases were treated by Princen and Mason [62] and the thermodynamics of a liquid lens has been treated by Rowlinson [63]. The profile of an oil lens floating on water is shown in Fig. IV-4. The three interfacial tensions may be represented by arrows forming a Newman triangle ... 

Referring to Fig. IV-4, the angles a and /3 for a lens of isobutyl alcohol on water are 42.5° and 3°, respectively. The surface tension of water saturated with the alcohol is 24.5 dyn/cm the interfacial tension between the two liquids is 2.0 dyn/cm, and the surface tension of n-heptyl alcohol is 23.0 dyn/cm. Calculate the value of the angle 7 in the figure. Which equation, IV-6 or IV-9, represents these data better Calculate the thickness of an infinite lens of isobutyl alcohol on water. 

IHP) (the Helmholtz condenser formula is used in connection with it), located at the surface of the layer of Stem adsorbed ions, and an outer Helmholtz plane (OHP), located on the plane of centers of the next layer of ions marking the beginning of the diffuse layer. These planes, marked IHP and OHP in Fig. V-3 are merely planes of average electrical property the actual local potentials, if they could be measured, must vary wildly between locations where there is an adsorbed ion and places where only water resides on the surface. For liquid surfaces, discussed in Section V-7C, the interface will not be smooth due to thermal waves (Section IV-3). Sweeney and co-workers applied gradient theory (see Chapter III) to model the electric double layer and interfacial tension of a hydrocarbon-aqueous electrolyte interface [27]. 

C. Liquid-Surface Interactions Surface Changes and Autophobicity... 

Surfactant-coated surfaces may also rearrange on contact with a liquid as shown by Israelachvili and co-workers [77]. This mechanism helps to explain hysteresis occurring on otherwise smooth and homogeneous surfaces. 

As an extension of Problem 11, integrate a second time to obtain the equation for the meniscus profile in the Neumann method. Plot this profile as y/a versus x/a, where y is the vertical elevation of a point on the meniscus (above the flat liquid surface), x is the distance of the point from the slide, and a is the capillary constant. (All meniscus profiles, regardless of contact angle, can be located on this plot.)... 

The preceding upper limit to particle size can be exceeded if more than one bubble is attached to the particle, t A matter relating to this and to the barrier that exists for a bubble to attach itself to a particle is discussed by Leja and Poling [63] see also Refs. 64 and 65. The attachment of a bubble to a surface may be divided into steps, as illustrated in Figs. XIII-8a-c, in which the bubble is first distorted, then allowed to adhere to the surface. Step 1, the distortion step, is not actually unrealistic, as a bubble impacting a surface does distort, and only after the liquid film between it and the surface has sufficiently thinned does... 

Filins at Liquid-Liquid Interfaces and on Nonaqueous Liquid Surfaces... 

The case of a vapor adsorbing on its own liquid surface should certainly correspond to mobile adsorption. Here, 6 is unity and P = the vapor pressure. The energy of adsorption is now that of condensation Qu, and it will be convenient to define the Langmuir constant for this case as thus, from Eq. xvn-39. 

Gragson D E and Richmond G I 1998 Investigations of the structure and hydrogen bonding of water molecules at liquid surfaces by vibrational sum frequency spectroscopy J. Phys. Chem. 102 3847... 

In this section we discuss the frequency spectrum of excitations on a liquid surface. Wliile we used linearized equations of hydrodynamics in tire last section to obtain the density fluctuation spectrum in the bulk of a homogeneous fluid, here we use linear fluctuating hydrodynamics to derive an equation of motion for the instantaneous position of the interface. We tlien use this equation to analyse the fluctuations in such an inliomogeneous system, around equilibrium and around a NESS characterized by a small temperature gradient. More details can be found in [9, 10]. 

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