A model for the linear stability of the interface between aqueous humor and vitreous substitutes after vitreoretinal surgery

• Published in: Physics of fluids (1994) 2014-12, Vol.26 (12)
• Main Authors: Isakova, Krystyna, Pralits, Jan O., Repetto, Rodolfo, Romano, Mario R.
• Format: Article
• Language: English
• Subjects: Computational fluid dynamics; Dimensional stability; Fluids; Interface stability; Kelvin-Helmholtz instability; Mathematical models; Miscibility; Retina; Solid surfaces; Stability analysis; Steady flow; Substitutes; Two dimensional analysis; Viscous fluids
• ISSN: 1070-6631; 1089-7666
• DOI: 10.1063/1.4902163

We consider the motion of two immiscible viscous fluids induced by periodic oscillations of a flat solid surface along its plane. The interface between the two fluids is parallel to the solid wall; one fluid occupies the region between the wall and the interface and the other extends from the interface to infinity. We study numerically the linear stability of the interface with respect to two-dimensional perturbations using the normal mode analysis and assuming quasi-steady flow conditions. The analysis is motivated by the need of understanding the behavior of vitreous substitutes inserted in the vitreous chamber of the eye after vitrectomy. This is a common surgical procedure adopted to treat retinal detachments, whereby the vitreous humor is removed from the eye and replaced by fluids immiscible with water. Owing to their hydrophobic nature, vitreous substitutes coexist in the vitreous chamber with a certain amount of aqueous humor (the fluid produced in the anterior part of the eye) and, typically, a thin layer of aqueous separates the tamponade fluid from the retina. A common problem with this treatment is that, in some cases, the interface between the two fluids breaks down and this might eventually lead to the generation of an emulsion. It is believed that mechanics plays an important role in this process but the problem remains very poorly understood. We find that instability of the interface is possible in a range of parameters that is relevant for the problem that motivated the present analysis. This suggests that shear instability is likely a possible mechanism triggering the onset of vitreous substitutes–aqueous interface instability.