Mass transfer effects on the fibre arrangement in the extracorporeal membrane oxygenator under extra-luminal flow

• Impact of the fibre arrangement in membrane oxygenator is crucial. • The hexagonal configuration provides maximum O 2 saturation. • Mass transport is severely affected by the blood flow path in extra-luminal flow. Oxygen enters the bloodstream through the lungs, where it binds reversibly with haemoglobin to form oxyhaemoglobin. The binding of oxygen to haemoglobin is primarily influenced by the partial pressure of oxygen. The novelty of our analysis lies in optimizing the oxygen transfer based on blood rheology and the dimensions of a micro-oxygenator. We utilize the Casson-Papanastasiou fluid model to analyse the non-Newtonian blood flow . The convection-diffusion model, incorporating chemical reactions due to the binding of oxygen to haemoglobin, is used to estimate oxyhaemoglobin and dissolved oxygen in the blood. By applying Henry's law for dissolved oxygen in plasma and Hill's equation for oxyhaemoglobin concentration, we reformulate the oxygen transport model as a function of the partial pressure of oxygen. The entire model is solved numerically using finite element methods. We estimate the partial pressure of oxygen for various fibre sets and outer radii, as well as different fibre bundle arrangements. Our analysis predicts that >90 % partial pressure of oxygen can be achieved at the device outlet with fewer fibres of a specific outer radius. The findings could be highly beneficial to the biomedical field, particularly in the design optimization of extra-corporeal membrane oxygenator devices.