Shape of liquids

In optical tweezer experiments, the optical scattering force is used to trap particles, but the force can also be used to control the shape of liquid droplets26. An infrared laser with 43-mW power focused onto a microdroplet on a superhydrophobic surface enabled up to 40% reversible tuning of the equatorial diameter of the droplet26. Such effects must naturally also be taken into account when exciting laser modes in droplets in experiments with levitated drops. 

Liquid Evaporation time (s) Shape of liquid drop... 

The shape of liquid droplets emerging at the GDL/ channel interface is governed by the wetting char-... 

The shapes of liquid drops falling through air can be conveniently represented by two oblate semispheroids with a common semimajor axis a and minor semiaxes bi and 2 (B8, FI). Several workers have reported measurements of the aspect ratio, (hj + b2)/2a, and these are shown as a function of Eo in Fig. 7.10. The data can be represented by the relationships... 

The influence of this surface energy can also be clearly seen on the macroscopic shape of liquid droplets, which in the absence of all other forces will always form a shape of minimum surface area - that is, a sphere in a gravity-free system. This is the reason why small mercury droplets are always spherical. 

In the next section we examine the shapes of liquid surfaces possessing an axis of symmetry. 

B. Hegemann, K. Baker, and J, Jonas. Temperature and density effects on the collision induced depolarized Rayleigh line shapes of liquid carbon disulfide. J. Chem. Phys., 0 570-571 (1984). 

J. F. Padday, Surface Tension, Part II. The Measurement of Surface Tension in Surface and Colloid Science, Vol. 1, E. Matijevic, Ed. Wiley-Interscience (1969), p. 101 (review of methods, contains some required tables) J.F. Padday, Surface Tension, Part III. Tables Relating the Size and Shape of Liquid Drops to the Surface Tension, ibid, p. 151. (Collation of Bashforth and Adams tables and extensions or modifications to make them more suitable for actual situations contains an introduction to explain the conversion of parameters in different geometries.)... 

Wellek, R. M., Arawal, A. K. Skelland, A. H. P. 1966 Shapes of liquid drops moving in liquid media. AIChE Journal 12, 854-862. 

Analyze and compare the structure and shape of liquids and gases in terms of particle spacing and particle motion. 

Generation of solid colloidal particles in aerosols has certain advantages over precipitation from homogeneous solutions described in Chapter IV. During precipitation from solutions it is usually impossible to predict a priori the shape of the resulting particles, while particles prepared by the aerosol methods are usually spherical because of the natural shape of liquid droplets dispersed in gas. Also, it was pointed out earlier (see Chapter IV) that in the case of particles of internally mixed composition, the molar ratio of constituents in the solid phase differs from that in solution [13], while in the case of aerosol technique the content of resulting solid particles is determined by the molar ratio of components in solution that is dispersed in the gas phase to form aerosol droplets. ... 

An inlEractive tiool to study the equilibrium surface shapes of liquids subject to surface tension and other energies under various constraints by evolving the surface toward a minimal-energy state by the gradient descent method. 

Let us consider a liquid drop suspended in a gas phase. The shape of liquid drop is determined by two factors — surface tension at the liquid-gas (vapor) interface ( Lv) and gravity. The surface tension force acting on the liquid drop tends to impose a minimal surface area, making the drop spherical. This force scales as yiy x d (where d is the diameter of liquid drop). Meanwhile, the gravitational body force imposed on the liquid tries to flatten the liquid. This force scales as pgd (where p is the liquid density and g is the gravitational acceleration constant). The body force can be neglected if the liquid drop size is smaller than the so-called capillary length, Kc. 

The capillary length for clean water at ambient conditions is 2.7 mm. In other words, when the liquid drop is smaller than this capillary length, the gravitational effect is negligible and can be ignored in prediction of the equilibrium shape of liquid. 

The surface tension determines capillary effects, wetting phenomena and a shape of liquid drops, in particular, the spherical shape of small radius drops when the gravity is not essential. The corresponding excess pressure in a drop of radius p is Ap = 2a/p (Laplace-Young formula). Small drops of the nematic phase are, strictly speaking, not spherical due to anisotropy of the surface tension but practically they may be considered spherical. The surface tension of both a liquid crystal and a solid substrate determines orientation of the liquid crystal director on the substrate. 

FIGURE 1.30 Shapes of liquid crystals (local molecular orientation [LMO]) with digitized contours model of series II kerogens (sporopollenin) (a) 002 dark-field image. Inset is a sketch of a LMO. (b) The same in 11 dark field. (From M. VUley. Simulation ther-mique de revolution des kerog nes. These d Etat Orleans 1979. With permission.)... 

The shape of liquid menisci is controlled by the competition of the capillary effects, caused by the surface (or interfacial) tension, y, and the forces acting on the liquid volume. The action of capillary forces results in the capillary pressure, AP, across a curved liquid interface... 

The inward pull creates some internal pressure and forces liquid surfaces to contract to minimal area. Surface tension is responsible for the shapes of liquid droplets. Although easily deformed, droplets of water tend to be pulled into spherical shapes by the cohesive forces of the surface layer. 

C. B. Gorman, H. A. Biebuyck, and G. M. Whitesides, "Control of the Shape of Liquid Lenses on a Modified Gold Surface Using an Applied Electrical Potential across a Self-Assembled Monolayer," Langmuir, vol. 11, pp. 2242-2246, Jun 1995. 

FIGURE 22.5 Even though the effects of gravity can alter the ideal shape of liquid droplets, the tendency of small liquid droplets toward a spherical shape is obvious. This tendency is caused by surface tension. 

J. Buehrle, S. Herminghaus, and F. Mugele, Impact of line tension on the equilibrium shape of liquid droplets on patterned substrates, Langmuir, 18,9771-9777 [2002]. 

Chapter 5 investigates the shape of liquid drops, bubbles, and the liquid surface in the vicinity of a solid surface, using the Laplace-Young equation. The last chapter. Chapter 6, contains a number of interesting properties and applications, such as the vibrational oscillations of soap film membranes and the application of soap films to the analogue solutions of the differential equations of Poisson and Laplace. 

In this chapter, the solubility of surfactant compounds in liquid water (and in selected nonaqueous solvents) will be considered. Surfactants are defined here as amphiphilic molecules (molecules containing both polar and nonpolar structural fragments) whose aqueous phase behavior displays explicitly stated features [3]. The most characteristic feature of surfactants is their ability to interact with water to form lyotropic liquid-crystal phases, but surf tant behavior is also jeflected by the influence of water on the temperature of the crystal solubility boundary relative to the melting point, and by the distinctive shape of liquid-liquid miscibility gaps (when they exist). Solubility is but one aspect of the broader subject of phase behavior—albeit a very important aspect. The aqueous phase behavior of surfactants has recently been treated in considerable detail [3]. 

Gorman, G.B., Biebuyck, H.A., and Whitesides, G.M. (1995) Gontrol of the shape of liquid lenses on a modified gold surface using an applied electrical potential across a self-assembled monolayer. Langmuir, 11, 2242-2246. Abbott, N.L. and Whitesides, G.M. (1994) Potential-dependent wetting of aqueous-solutions on self-assembled... 

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