Two Phase Flow by Level Set Method

ii Preface This report is written at the Technological University of Denmark. The Department of Micro and Nanotechnology offers the three week course 33443 Microfluidics Theory and Simulation, which sorts under the Microfluidics Theory and Simulation (MIFTS) group [4], headed by Professor Henrik Bruus. The motivation for the present report is built on a contact from the Swedish company HemoCue [3], who requests theoretical calculations on their blood analysis products. Development of the HemoCue products has until now based on a trial and error approach and further progress now demands a more theoretical and analytical treatment. The main problem is air bubbles that get stuck in the central analysis chamber, which is filled using the capillary forces. Optical measurements on the blood are very sensitive to these bubbles that give rise to incorrect outcomes. It is therefore decided that this report shall act as a preliminary treatment of the problem. During the three weeks the authors and their supervisors has visited the R&D department of HemoCue in¨Angelholm, Sweden. It has been an interesting meeting, which first of all has given an introduction to the company and their visions, but has also clarified the specific problem of trapped bubbles. This report focuses on following a two phase flow interface by using a level set method, which can simulate complex flows. It does not give the specific answer for the HemoCue problem, but provides a tool, which together with analytical treatments of the problem, can provide HemoCue with the necessary guidelines when developing new micro cuvettes. Throughout the report the Einstein summation rule will be used when appropriate. The reader is assumed to be familiar with this notation. For notational simplicity ∂ x will be used instead of ∂ ∂ x etc. We hope the reader will enjoy reading the report.