THE VOLTERRA-KOSTITZIN INTEGRAL AND DIFFERENTIAL APPLICATION TO UNSTEADY RHEOLOGICAL PROPERTIES OF BIOFLUIDS
We have found that the integral and differential equation of Volterra-Kostitzin in Mathematical Ecology (Volterra [1], Kostitzin and Volterra [3]), can be readily used to describe the unsteady rheological properties of biofluids (blood, synovial fluid ...). For this purpose, we have performed some mathematical transformations in order to obtain an explicit solution, and we have formulated some basic physical hypothesis. In this work, we have reported the result obtained from the deoxy-hemoglobin S (deoxy-HbS) gels, which have characteristic properties such as viscoelasticity, elasto-thixotropy, and a maximum on the viscosity profile (polymerization overshot).
Volterra-Kostitzin equations, deoxy-hemoglobin S aggregation, mathematical model, unsteady viscosity profiles.