Numerical simulation for unsteady motions of the human vitreous humor as a viscoelastic substance in linear and non-linear regimes

Abstract

The main goal of this research is to find a reliable numerical procedure for evaluation of the human vitreous humor as a viscoelastic substance. For this purpose, different 2D and 3D geometries were filled with the vitreous humor and they were subjected to sinusoidal oscillations; meanwhile, the flow in this gel-like material was assessed. In order to model this substance accurately, a 2-mode viscoelastic model has been introduced in this research which can cover both linear and non-linear regimes. In the numerical procedure, the dynamic mesh technique was performed to enhance the numerical stability. The amplitudes and frequencies of oscillations were selected in order to cover both linear and non-linear viscoelastic regimes. The numerical model was validated by comparing the results with the analytical solutions for velocity and boundary shear stress in linear regime and excellent agreements were observed. Additionally, the effects of different numerical schemes and stabilizers were assessed for the vitreous humor. Moreover, the numerical results for various amplitudes and frequencies in nonlinear regime were presented and discussed. Finally, the proposed method was applied for the real shape of vitreous chamber of the human eye filled with this gel-like substance and the results were compared with the similar geometry filled with the liquefied vitreous humor.