%0 Generic
%A Staack, Karsten
%C Heidelberg
%D 2013
%F heidok:15706
%R 10.11588/heidok.00015706
%T Image Analysis of Microfluidic Flows Using Partial Differential Equations
%U https://archiv.ub.uni-heidelberg.de/volltextserver/15706/
%X This thesis deals with advanced models to characterize microfluidic flows from image sequences. The governing equations and boundary conditions for viscous flows are introduced as a global model in order to impose physically sound motion results. The connection between the computational fluid simulations and experimental measurement data is established by using constrained optimization. This framework also allows to introduce control variables, which are determined in agreement with the underlying data.  In this context, the thesis focuses on the study of the influence of i) the image data, ii) the underlying motion and iii) the boundary conditions on the estimation of the control variables and the corresponding physical quantities. These questions are assessed by the application to synthetic images that allow to measure the induced errors. It is shown that the application of physically motivated differential equations as global motion models increase the robustness and accuracy of the motion estimation. Control variables are used to change the equations in a modeled manner, so that the solution describes the processes that are inherent in the images. The strength of global models lies in the combination with sparsely distributed information in the images, where common state-of- the-art methods have extreme difficulties to obtain reasonable results. It is demonstrated that the optimal control framework allows to relax the governing equations in order to model uncertainty of the measurement setting parameters, such as wall-slip. And finally, such a parameter model is extended to three dimensions and allows to estimate the pressure drop of the flow and the diffusion coefficient of the trace substance caged Q-rhodamine dextran in water.