Second order radial force

V,e define the second order radial force constant 6.- as ... 

Hydrodynamic mechanisms are those which produce particle interactions through the surrounding fluid due to hydrodynamic forces and the asymmetry of the flow field around each particle. These mechanisms, which are not dependent on the relative differences in acoustic particle entrainments, can act from distances larger than the acoustic displacement and have to be considered as the main mechanism in the agglomeration of monodispersed aerosols, where particles are equally entrained. There are two main types of hydrodynamic mechanisms, namely mutual radiation pressure [50] and the acoustic wake effect [51,52]. The radiation pressure is a second-order effect which produces a force on a particle immersed in an acoustic field due to the transfer of momentum from the acoustic wave to the particle. This force moves the particles towards the pressure node or antinode planes of the applied standing wave, depending on the size and density of the particles. The mutual radial pressure can be computed from the primary wave as well as from other wave fields of nearby scatters. In fact, it gives rise to particle interactions as the result of forces produced on two adjacent particles by a non-linear combination of incident and scattered waves. 

Across the actinide series from Pu to Lr, the solution properties of the ttipositive actinide ions vary only slowly and in a regular manner. Thus, much of the behavior described in prior chapters for trivalent actinide ions can be safely extrapolated to estimate that of Es. Bonding with ligands is almost entirely attributed to electrostatic forces, but with some second-order contribution from covalent sharing of electrons due to the relatively large radial extension of the Sf orbitals. The ionic radius of Es has been calculated from the six-coordinated... 

The term m = 0.74048 Vm°/Vm = 1/6 7rN0cJm/Vm> where Vm° is the close-packed volume, N0 is the Avogadro number, and Vm is the molar volume of the system. V° is a simple function of the temperature (T) (10) with a characteristic value V°° at T = 0 K. The last term in Equation 12 was introduced by Alder et al. (II). Dnm are 24 universal constants common for all substances whose radial and higher distribution functions are the same functions of u/kT and the reduced density p = V°/V. As shown by Chen and Kreglewski (10) and Simnick, Lin, and Chao (12), Equation 12 is the most accurate known equation with four characteristic constants a, V°° (V° at T = 0 K), u°/k, and rj/k (see Equations 13 and 14). They also have shown (10) that in order to obtain agreement with second virial coefficient data of the gas and the internal energy or the enthalpy of the liquid, it is necessary to assume that u(r) is a function of T as required by the theory of noncentral forces between nonspherical molecules (13)... 

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