A Simplified Model for Predicting Friction Factors of Laminar Blood Flow in Small-Caliber Vessels

Abstract

The aim of this study was to provide scientists with a straightforward correlation that can be applied to the prediction of the Fanning friction factor and consequently the pressure drop that arises during blood flow in small-caliber vessels. Due to the small diameter of the conduit, the Reynolds numbers are low and thus the flow is laminar. This study has been conducted using Computational Fluid Dynamics (CFD) simulations validated with relevant experimental data, acquired using an appropriate experimental setup. The experiments relate to the pressure drop measurement during the flow of a blood analogue that follows the Casson model, i.e., an aqueous Glycerol solution that contains a small amount of Xanthan gum and exhibits similar behavior to blood, in a smooth, stainless steel microtube (L = 50 mm and D = 400 μm). The interpretation of the resulting numerical data led to the proposal of a simplified model that incorporates the effect of the blood flow rate, the hematocrit value (35–55%) and the vessel diameter (300–1800 μm) and predicts, with better than ±10% accuracy, the Fanning friction factor and consequently the pressure drop during laminar blood flow in healthy small-caliber vessels.