Characteristics absolute dimensionless characteristic

The dimensionless retention parameter X of all FFF techniques, if operated on an absolute basis, is a function of the molecular characteristics of the compounds separated. These include the size of macromolecules and particles, molar mass, diffusion coefficient, thermal diffusion coefficient, electrophoretic mobility, electrical charge, and density (see Table 1, Sect. 1.4.1.) reflecting the wide variablity of the applicable forces [77]. For detailed theoretical descriptions see Sects. 1.4.1. and 2. For the majority of operation modes, X is influenced by the size of the retained macromolecules or particles, and FFF can be used to determine absolute particle sizes and their distributions. For an overview, the accessible quantities for the three main FFF techniques are given (for the analytical expressions see Table l,Sect. 1.4.1) ... 

Natural convection occurs when a fluid is in contact with a solid surface of different temperature. Temperature differences create the density gradients that drive natural or free convection. In addition to the Nusselt number mentioned above, the key dimensionless parameters for natural convection include the Rayleigh number Ra = p AT gx3/ va and the Prandtl number Pr = v/a. The properties appearing in Ra and Pr include the volumetric coefficient of expansion p (K-1) the difference AT between the surface (Ts) and free stream (Te) temperatures (K or °C) the acceleration of gravity g(m/s2) a characteristic dimension x of the surface (m) the kinematic viscosity v(m2/s) and the thermal diffusivity a(m2/s). The volumetric coefficient of expansion for an ideal gas is p = 1/T, where T is absolute temperature. For a given geometry,... 

Here A is the pre-exponential factor, E is an effective activation energy or temperature coefficient for the overall reaction, R = 8.314 JK moP is the Gas Constant and T is the local absolute temperature. The quotient E/R has units of temperature and is sometimes known as the Arrhenius temperature It is a characteristic feature of combustion processes that if Ta is the ambient temperature, then Tatt> so that the group RTJE and, more generally, the scaled or dimensionless temperature RTIE are typically (very) small quantities in the systems of interest. 

In both the Flory and LF theories, the cohesive energy density of a fluid at absolute zero equals its characteristic pressure, P. It is, therefore, convenient to define a dimensionless parameter Ag in terms of the characteristic pressures of the pure components ... 

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