Spherical-shaped liquid droplets

The hydrophobic or hydrophilic nature of the solid and the liquid can dictate the shape and contact angle of the droplet. In practice, hydrophobic solids will have high interfacial surface tensions with aqueous droplets and smaller contact angles, resulting in droplets with a more spherical shape. Conversely, droplets formed on hydrophilic surfaces will be flatter, with a larger contact angle, due to the low interfacial tension between hydrophilic surfaces and the droplet. Gelot et al. [49] found that carbon black, which is hydrophobic, promoted formation of W/0 (water-in-toluene) emulsions. 

This value shows that in the vicinity of the three-phase contact line, the capillary pressure is much smaller than the disjoining pressure. Let us assume for a moment that the droplet shape remains spherical until the contact with the solid substrate. However, as we have already seen in the preceding section, the capillary pressure is much smaller than the disjoining pressure and cannot counterbalance the disjoining pressure. This means that the disjoining pressure action substantially distorts the spherical shape of droplets in the vicinity of the three-phase contact line. Droplets cannot retain their spherical shape up to the contact line. See further consideration of the profile of liquid droplets in Section 2.3. 

In a drop extractor, liquid droplets of approximate uniform size and spherical shape are formed at a series of nozzles and rise eountercurrently through the continuous phase which is flowing downwards at a velocity equal to one half of the terminal rising velocity of the droplets. The flowrates of both phases are then increased by 25 per cent. Because of the greater shear rate at the nozzles, the mean diameter of the droplets is however only 90 per cent of the original value. By what factor will the overall mass transfer rate change ... 

It is well known that when liquid droplets form on a flat substrate they adopt spherical cap shapes (neglecting gravity effects) with a contact angle 6. This angle depends solely on the interfacial energies as described by the Young s equation ... 

A small amount of a liquid tends to take a spherical shape For example, mercury drops are nearly spherical and water drips from a faucet in nearly spherical liquid droplets. Surface tension, which measures the resistance of a liquid to an increase in its surface area, is the physical property responsible for this behavior. 

Freely suspended liquid droplets are characterized by their shape determined by surface tension leading to ideally spherical shape and smooth surface at the subnanometer scale. These properties suggest liquid droplets as optical resonators with extremely high quality factors, limited by material absorption. Liquid microdroplets have found a wide range of applications for cavity-enhanced spectroscopy and in analytical chemistry, where small volumes and a container-free environment is required for example for protein crystallization investigations. This chapter reviews the basic physics and technical implementations of light-matter interactions in liquid-droplet optical cavities. 

A modified version of the TAB model, called dynamic drop breakup (DDB) model, has been used by Ibrahim et aU556l to study droplet distortion and breakup. The DDB model is based on the dynamics of the motion of the center of a half-drop mass. In the DDB model, a liquid droplet is assumed to be deformed by extensional flow from an initial spherical shape to an oblate spheroid of an ellipsoidal cross section. Mass conservation constraints are enforced as the droplet distorts. The model predictions agree well with the experimental results of Krzeczkowski. 311 ... 

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 this section we deal with mass fluxes across spherical boundaries like the surface of gas bubbles in liquids, droplets in air, suspended particles or algal cells in water. It is true that suspended solids are rarely shaped like ideal spheres. Nonetheless, the following discussion can serve as a conceptual starting point from which more complex structures can be analyzed. Obviously, such situations require the application of numerical models, yet some of the principles, like the existence of characteristic length and time scales, will remain the same. 

It is well known that short-range forces of attraction exist between molecules (see page 215), and are responsible for the existence of the liquid state. The phenomena of surface and interfacial tension are readily explained in terms of these forces. The molecules which are located within the bulk of a liquid are, on average, subjected to equal forces of attraction in all directions, whereas those located at, for example, a liquid-air interface experience unbalanced attractive forces resulting in a net inward pull (Figure 4.1). As many molecules as possible will leave the liquid surface for the interior of the liquid the surface will therefore tend to contract spontaneously. For this reason, droplets of liquid and bubbles of gas tend to attain a spherical shape. 

Consider the molecules in a liquid. As shown in Figure 3.1, for a liquid exposed to a gas the attractive van der Waals forces between molecules are felt equally by all molecules except those in the interfacial region. This imbalance pulls the latter molecules towards the interior of the liquid. The contracting force at the surface is known as the surface tension. Since the surface has a tendency to contract spontaneously in order to minimize the surface area, droplets of liquid and bubbles of gas tend to adopt a spherical shape this reduces the total surface free energy. For two immiscible liquids a similar situation applies, except that it may not be so immediately obvious how the interface will tend to curve. There will still be an imbalance of intermolecular forces resulting in an interfacial tension and the interface will adopt a configuration that minimizes the interfacial free energy. 

Wetting angle — A liquid droplet formed on a flat solid foreign substrate has the cap-shaped form of a spherical segment (Figure) with a volume,... 

Particle shape can vary with the formation method and the nature of the parent material. Particles formed by the condensation of vapor molecules are generally spherical, especially if they go through a liquid phase during condensation. Particles formed by breaking or grinding larger particles, termed attrition, are seldom spherical, except in the case where liquid droplets are broken up to form smaller liquid droplets. 

It is convenient to think of all aerosol particles as spheres for calculation, and this also helps visualize the processes taking place. But, with the exception of liquid droplets, which are always spherical, many shapes are possible. These shapes can he divided into three general classes. 

An extension of the use of RF plasma for particle heating is the spheroidization of solids. By careful control of plasma enthalpy, particle size, feed rate, and feed position, it is possible to melt each particle as it passes through the plasma. The liquid droplet forms a sphere due to surface tension and, on cooling, retains its spherical shape. Spheroidized particles are commercially useful because they will flow easily. 

It will be assumed here for simplicity that one parameter r (the radius in the case of a spherical liquid droplet) is sufficient to specify the size and shape of a particle. For solid particles (or liquid droplets), this assumption will be valid in spray combustion when either the particles are geometrically similar or their shape is of no consequence in the combustion process. Liquid droplets will obey this hypothesis in particular if they are spherical, which will not be true unless (1) they collide with each other so seldom that collision-induced oscillations are viscously damped to a negligible amplitude for most droplets, and (2) their velocity relative to the gas is sufficiently low. An alternative parameter to the radius is the mass of the droplet [10] the choice between this, the droplet volume, or the radius of a sphere of equal volume is a matter of individual preference. 

The drop model of nuclei (section 2.4) proved to be useful to explain fission (Bohr and Wheeler, 1939) due to the surface tension of a liquid, a droplet assumes a spherical shape. If energy is supplied, the droplet begins to oscillate between spherical and elongated shapes. With increasing distortion, elongation passes a threshold and the droplet splits into two parts. In nuclei, the repulsive Coulomb forces, which... 

---