*Article* **Simulation of an Adaptive Fluid-Membrane Piezoelectric Lens**

#### **Hitesh Gowda Bettaswamy Gowda and Ulrike Wallrabe \***

Laboratory for Microactuators, IMTEK - Department of Microsystems Engineering, University of Freiburg, Georges-Koehler-Allee 102, Room 02-081, 79110 Freiburg, Germany; hitesh.gowda@imtek.uni-freiburg.de **\***Correspondence:wallrabe@imtek.uni-freiburg.de;Tel.:+49-(0)-761203-7580

 

Received: 16 October 2019; Accepted: 16 November 2019; Published: 20 November 2019

**Abstract:** In this paper, we present a finite-element simulation of an adaptive piezoelectric fluid-membrane lens for which we modelled the fluid-structure interaction and resulting membrane deformation in COMSOL Multiphysics-R . Our model shows the explicit coupling of the piezoelectric physics with the fluid dynamics physics to simulate the interaction between the piezoelectric and the fluid forces that contribute to the deformation of a flexible membrane in the adaptive lens. Furthermore, the simulation model is extended to describe the membrane deformation by additional fluid forces from the fluid thermal expansion. Subsequently, the simulation model is used to study the refractive power of the adaptive lens as a function of internal fluid pressure and analyze the effect of the fluid thermal expansion on the refractive power. Finally, the simulation results of the refractive power are compared to the experimental results at different actuation levels and temperatures validating the coupled COMSOL model very well. This is explicitly proven by explaining an observed positive drift of the refractive power at higher temperatures.

**Keywords:** adaptive lens; piezoelectric devices; fluid-structure interaction; moving mesh; thermal expansion; COMSOL
