Indian Institute of Technology (Banaras Hindu University), Varanasi
"Oesophageal catheterisation under the influence of dilating amplitude with peristaltically driven Newtonian fluid: A mathematical model"
We presented a mathematical model of swallowing in a catheterized oesophageal tube by duly considering the peripheral and core layers. We adequately account for the fluid mass conservation in both these layers. According to Kahrilas et al. (1995) and Pandey et al. (2017), peristaltic waves that govern the flow are thought to have gradually dilating amplitudes so that the distal oesophagus experiences higher pressure to ensure smooth delivery of gradually globular getting bolus into the abdomen through the cardiac sphincter. The technique of long wavelength and low Reynolds number is used to get the solutions in terms of stream function. Mass conservation in the two layers is taken care of by resolving the interface as a streamline from a fourth-order algebraic equation. The previous researchers' attempt to uniform wave amplitude had ignored mass conservation identically in the two layers by a wrong assumption of a fixed ratio between the layers. Due to unrealistic assumptions, those results cannot be accepted. Pressure, flow rate, and forces expressions are obtained for the tube with the catheter. The findings are accepted, and the interface between the two layers is explored. One wavelength's worth of pressure variation with flow rate is investigated. It is found that pressure and flow rate have a linear relationship even when the tube is catheterized. With pressure, the flow rate rises. It has been discovered that pressure rises as the peripheral layer viscosity does. Moreover, it has been found that when peripheral viscosity increases, the flow rate rises. Additionally, it has been found that as the flow rate in a catheterized oesophagus increases for a given difference in pressure, the peripheral layer thins down.
Additional authors: Prof. Sanjay Kumar Pandey Department of Mathematical Sciences Indian Insitute of Technology (BHU), Varanasi Uttar Pradesh, 221005 INDIA