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The rigorous optimization of the geometry of a glass cell with computational fluid dynamics (CFD) is performed. The cell will be used for non-invasive nuclear magnetic resonance (NMR) measurements on a single droplet levitated in a counter current of liquid in a conical tube. The objective function of the optimization describes the stability of the droplet position required for long-period NMR measurements.The direct problem and even more the optimization problem require an efficient method to handle the high numerical complexity implied. Here, the flow equations are solved two-dimensionally and in steady state with the finite-element code SEPRAN for a spherical droplet with ideally mobile interface. The optimization is performed by embedding the CFD solver SEPRAN in the optimization environment EFCOSS. The underlying derivatives are computed using the automatic differentiation software ADIFOR. An overall concept for the optimization process is developed, requiring a robust scheme for the discretization of the geometries as well as a model for horizontal stability in the axially symmetric case. The numerical results show that the previously employed measuring cell described by Schröter is less suitable to maintain a stable droplet position than the new cell.

The flow dynamics inside a single liquid droplet of toluene levitated by a countercurrent of deuterated water (D 2 O) is investigated noninvasively and quantitatively by nuclear magnetic resonance (NMR) imaging techniques for the first time and compared with computational fluid-dynamics (CFD) calculations. For this purpose, a unique device is developed meeting the requirements for long period measurements (namely, a permanently stable droplet position and shape) and for measurements on series of droplets (namely, a high reproducibility of generation and position of droplets). The measurement cell of this device is manufactured with low tolerances regarding axial symmetry and positioned vertical and central in the NMR magnet with high precision enabling axially symmetric flow dynamics. The measured flow field shows good agreement with 2D axially symmetric CFD calculations with the finite element (FEM) code SEPRAN. A simple interface model with one free parameter accounts for the rigid cap encountered in the measurements. This free parameter is estimated by matching the velocity fields of the simulation with those determined experimentally.

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