Liquid drop energy

For the case of fission, Strutinsky (1967) chose a simple but very successful way to describe the energy of a nucleus by combining liquid drop energy (Eldm) with local shell (5L7) and pairing (6P) corrections ... 

Use the above parameterization (assuming that parameters per differential element of volume, surface and integrated curvature are shape-independent) in Eq. (17) to calculate the liquid-drop energy associated with neutral clusters, and then add to it the charging energy according to Eq. (26) to determine the total LDM energy E (available experimental values for a and W can also be used). 

If, when a liquid drop is placed on a smooth surface, the forces of adhesion between the solid and the liquid are greater than the forces of cohesion of the liquid, then the liquid will spread and will perfectly wet the surface spontaneously. If the forces reach an intermediate balance determined by the interfacial energies ylv, ysj and ysv, then the liquid drop will form a definite contact angle (0) with the solid surface (Figure 4.12). 

Components of interfacial tension (energy) for the equilibrium of a liquid drop on a smooth surface in contact with air (or the vapor) phase. The liquid (in most instances) will not wet the surface but remains as a drop having a definite angle of contact between the liquid and solid phase. 

If pnliL is large, Q approaches unity. If ////// is small, Q approaches a value of 1.5. Thus the effect of circulation is small when a liquid drop falls in a gas although is large when a gas bubble rises in a liquid. If the fluid within the drop is very viscous, the amount of energy which has to be transferred in order to induce circulation is large and circulation effects are therefore small. 

IVa represents a physical bond resulting from highly localized intermolecular dispersion forces. It is equal to the sum of the surface free energies of the liquid, 7, and the solid, 72. loss the interfacial free energy, 7,2. It follows that Eq. (2.1) can be related to a model of a liquid drop on a solid shown in Fig. 2.2. Resolution of forces in the horizontal direction at the point A where the three phases are in contact yields Young s equation... 

Fig. 2.2. Contact angle, 0. and surface energies, Vlv> 7sl nd ysv, for a liquid drop on a solid surface.

As described earlier, when a solid particle or a liquid drop is broken down in size the free energy of the system increases (because the magnitude of surface area per... 

In considering the physical forces acting in fission, use may be made of the Bohr liquid drop model of the nucleus. Here it is assumed that in its uonual energy state, a nucleus is spherical and lias a homogeneously distributed electrical charge. Under the influence of the activation eneigy furnished by the incident nentron, however, oscillations are set up which tend to deform the nucleus. In the ellipsoid form, the distribution of the protons is such that they are concentrated in the areas of the two foci. The electrostatic forces of repulsion between the protons at the opposite ends of the ellipse may then further deform the nucleus into a dumbbell shape. Rrom this condition, there can be no recovery, and fission results. 

As we learned in Chapter 2, it is necessary to include shell effects in the liquid drop model if we want to get reasonable values for nuclear masses. Similarly, we must devise a way to include these same shell effects into the liquid drop model description of the effect of deforming nuclei. Strutinsky (1967) proposed such a method to calculate these shell corrections (and also corrections for nuclear pairing) to the liquid drop model. In this method, the total energy of the nucleus is taken as the sum of a liquid drop model (LDM) energy, LDM and the shell (8S) and pairing (8P) corrections to this energy,... 

Liquid drops on anisotropic solid surfaces will tend to elongate in the higher surface energy direction and the contact angle will, therefore, vary with position. 

Surface energy present in a small liquid drop at the inlet reservoir was used to pump the liquid through a PDMS microchannel [398]. 

Kitamori s group has proposed selective chemical surface modification utilizing capillarity (called the capillarity restricted modification or CARM method) (Hibara et al., 2005). In the CARM method, a microchannel structure combining shallow and deep microchannels and the principle of capillarity are utilized. The procedures are shown in Figure 19. A portion of an ODS/toluene solution (lwt%) is dropped onto the inlet hole of the shallow channel, and the solution is spontaneously drawn into this channel by capillary action. The solution is stopped at the boundary between the shallow and deep channels by the balance between the solid-liquid and gas-liquid interfacial energies. Therefore, the solution does not enter the deep channel. It remains at the boundary for several minutes and is then pushed from the deep channel side by air pressure. 

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