The Flow of Blood through Narrow Tubes

IN a recent letter, one of us¹ has shown that the flow of the blood of several species in a single capillary tube of radius R and length L follows an equation recently proposed by Casson² for varnishes and inks. where P is pressure, V is volume flow/see, k ₀, and k ₁ are constants. When k ₀ becomes zero, this equation reduces to the well-known equation of Poiseuille, since the terms in parenthesis represent the stress and shear rate respectively, at the wall of the tube. When k ₀ has finite values, however, it is a measure of a yield-value or critical shearing stress which, as pressure is raised, will be first reached at the capillary wall. As pressure still further increases, the critical distance (r ₀) from the centre at which this occurs, will steadily diminish. A similar phenomenon was studied many years ago for the Bingham equation, which differs from Casson's equation only in the absence of square roots; when Buckingham³ and, independently, Reiner⁴ evaluated the correct equation of flow for such a system where p is the pressure corresponding to the yield-value given by p = 2Lk ₀ ²/R.