The basic equation for the coagulation of milk and blood compared with the Maxwell (relaxation) and Kelvin (retardation) equations

Article type: Research Article

Authors: Scott Blair, G.W.

Affiliations: Oxford Haemophilia Centre, Churchill Hospital, Oxford, England

Abstract: The concept of “basic equations” is discussed. Maxwell proposed a basic equation for the relaxation of stress in a material depicted as an elastic and a viscous element in series; and Lord Kelvin proposed a similar equation for these elements in parallel. Although some materials obey these equations, their proposers were quite clear that further modifications would be needed for many real systems. The Maxwell equation for relaxation at constant strain and the Kelvin equation for the build-up of strain at constant stress give simple logarithmic relations between two dimensionless ratios, one rheological and the other temporal. Some years ago, an empirical equation was found to relate the complex modulus of coagulating milk and also blood, to the time following the first signs of coagulation. In the present paper, it is shown that, making the three most probable assumptions about the limits and form of the coagulation curve, this hitherto empirical equation is immediately derived. It shows a striking parallelism with the Maxwell and Kelvin equations. In the latest stages of normal blood coagulation, however, the equation does not hold. This “ceiling effect” is doubtless due to the rapidly increasing shortage of unattached possible junction-points on the long-chain molecules but its quantitative nature is still obscure.

DOI: 10.3233/BIR-1969-6209

Journal: Biorheology, vol. 6, no. 2, pp. 143-150, 1969