Hydrodynamics transformation properties

In a case of a general transformation, relations (1.16) and (1.17) are not valid and ought to be replaced by other relations. A non-orthonormal transformation matrix was used at investigation of non-equilibrium properties of the macromolecule in a liquid when so-called hydrodynamic interaction was taking into account (Zimm 1956). 

It is apparent, from Eq. (1), that the primary sample property measured by flow FFF is the diffusion coefficient. Secondary information includes the hydrodynamic diameter which can be obtained via the Stokes-Einstein equation and the molecular weight if the molecule shape factor is constant. Unlike other FFF techniques, the retention time in flow FFF is determined solely by the diffusion coefficient rather than a combination of sample properties. As a consequence, flow FFF is well suited for analyses of complex sample mixtures and the transformation of the fractogram to a diffusion or size distribution is straightforward. In addition, flow FFF is applicable to a wide range of samples regardless of their charge, size, density, and so forth. 

Druet, Cz., Hupfer, P., Shadrin, I. (Eds.), 1976a. In Druet, Cz., Hupfer, P., Shadrin, 1. (Eds.). Properties and Transformation of Hydrodynamical Processes in Coastal Zone of Nontidal Sea. Raporty Morski Instytut Rybacki Seria R, No. 2a, edited by Gdynia, 253 pp. 

Druet C., Massel S., Bittern, B., 1976b. Transformation of wind waves in the surf zone. In Properties and transformation of hydrodynamical processes in coastal zone of nontidal sea. Gdynia, Morski Instytut Rybacki, pp. 107-120. 

Fluctuations of such extent involve collective motion of a great number of molecules and therefore can be described by the laws of macroscopic physics, namely, thermodynamics and hydrodynamics. Thus, small parts of the system where fluctuations of the macroscopic values manifest themselves in the properties of scattered light (the Fourier transform) contain rather many molecules that enables one to speak of local values of such macroscopic terms as entropy, enthalpy, and pressure. Every point f corresponding to a small space element in liquid at an instant i can be ascribed some values of entropy density a(r,i), of molecule number density p(r,l), of energy e(f,l), of pressure P(r,i), and of the dielectric constant e(f,t). 

Kadanoff s transformation, besides static properties, provides for including the effect of hydrodynamic interactions between chain points separated by a contour length less than a into the redefinition of a. 

POE, added to water at homeopathic dose levels, completely transforms its hydrodynamic properties (take, for example, the experiment devised by James in Toronto). We see here another aspect of soft matter the fact that an additive, in very small quantities, can change everything. A whole practical area of science, called formulation, is based on the study of such additives, whether it be an ink, a paint, a medicine, or a product for treating vines. In this sense, soft matter physics is directly concerned with industrial problems. 

---