Modelling foam flow through vein-like geometries

Abstract

We explore the effectiveness of using foam in its application within a minimally invasive treatment for varicose veins called foam sclerotherapy. The foam is injected into a varicose vein where it aims to displace the blood and deliver the surfactant to the veins’ endothelial cells. This leads to the collapse of the vessel. Foam is used in the treatment due to its yield stress, which allows an effective displacement of blood. The value of the yield-stress of the foam can be empirically estimated in terms of its surface tension, liquid fraction and bubble radius [Princen and Kiss, 1989]. Further investigation is carried out on the average bubble radius R32 thus the value of the yield stress τ0, allowing us to estimate the yield stress for both the Varethina® and Physician-compounded foams using the data from Carugo et al. [2016]. In order to analyse the effectiveness of the treatment, we conduct finite element simulations of yield-stress fluid through two dimensional channels of various geometries. Due to the nature of the microfluidic flows, we solve the Stokes equations in unison with the Papanastasiou model [Papanastasiou, 1987], treating the foam as a generalised Newtonian fluid with a shear rate dependent viscosity. The algorithms are validated by comparing the numerical velocities with the respective analytical velocity profile. This is done through both straight and curved channel geometries. In order to validate the latter geometry, we produce an analytical velocity profile for a pressure-driven Bingham fluid. The effect of curvature on the channel flow provides added complexity as the yield surfaces are derived as functions of yield-stress, pressure gradient and additionally channel curvature. Once the simulation has been validated, we consider more complex geometries such as a sinusoidal channel. This allows us to explore the effect of deviating from the straight channel case and increasing the channel amplitude has on the size of the rigid plug regions, which is the essential region of the foam in displacing blood.

Date of Award	2020
Original language	English
Awarding Institution	Aberystwyth University
Supervisor	Tudur Davies (Supervisor) & Simon Cox (Supervisor)