# Microfluid Mechanics

## Objectives

editIn natural and constructed microsystems, unfamiliar physics of the fluid flow have been discovered and utilized. In this course, we give an theoretical basis of microfluid mechanics and show example studies from the literature and conducted at the institute of fluid mechanics(LSTM-Erlangen) at FAU Erlangen-Nuremberg. In the theoretical part, the fluid models for gases and liquids are discussed, The validity of the Navier Stokes equations is questioned by checking the continuum hypothesis. Different regimes of fluid flow are presented based on continuum considerations. Intermolecular, intramolecular, surface as well as well as particle forces dominating in micro fluid devices are discussed. An overview of modeling strategies on molecular, meso and macro scale is given. Prominent examples and studies from the literature are presented regarding the micro fluid dynamics. Example studies conducted at LSTM-Erlangen are presented.

The students are expected to to understand the multiscaling and multiphysical nature flow phenomena in microsystems. The dominating forces in those systems will be made familiar to students. They should be able to conduct basic dimensional analysis to classify the flow with respect to the different flow regimes regarding the continuum hypothesis. Ultimately, they can decide which forces can be effective under certain gas, liquid and particle laden flows in Microsystems and which numerical modeling strategy is appropriate for a given microsystem. With the given applied examples from the literature and from our institute, it expected that students can establish the bridge between theory and application of the subject matter.

## Basic components of the course

editThis course is dominnatly a theoretical one. However, examples are provided in the form of visual media, recitations and laboratory experiments in the form of experiments and computations. In the last part of the course, relevant examples of research work, which are conducted at LSTM-Erlangen, are provided.

## Chapters:

edit- Chapter 1. Introduction
- Chapter 2. Intermolecular and Surface Forces
- Chapter 3. Models for Gases and Liquids
- Chapter 4. Fluid Dynamics
- Chapter 5. Differential Analysis of Fluid Flow
- Chapter 6. Analytical Solutions of Internal Flows
- Chapter 7 Dimensional Analysis
- Chapter 8. Scaling Effects and Governing Equations in Microflows
- Chapter 9. Flow Phenomena in Microflows
- Chapter 10. Measurements of Microflows(not offered yet)
- Chapter 11. Modeling of Microflows
- Chapter 12. Microflow Devices and Systems
- Chapter 13. Example Studies Conducted at LSTM-Erlangen

## Literature

edit- Karniadakis, G., Beşkök, A., Aluru, N. R.: Microflows and nanoflows: fundamentals and simulation, Springer, New York, 2005.
- Gad-El-Hak, M.: MEMS: Introduction and Fundamentals, CRS Press Taylor & Francis Group, 2006.
- Israelachvili, J.: Intermolecular and Surface Forces, 2nd Ed., Academic Press, London, 1991.
- Encyclopedia of Microfluidics and Nanofluidics, Springer, 2008.
- Gad-el-Hak, M.: The ﬂuid mechanics of microdevices. J. Fluids Eng., 12(1):5–33, 1999.
- Tabeling, P.: Introduction to Microfluidics, Oxford University Press, ISBN 978-0-19-958816-9,2010.
- Bruus, H.: Theoretical Microfluidics, Oxford University Press, ISBN 978-0-19-923509-4,2008.
- Nguyen, N.-T., Wereley, S.: Fundamentals and Applications of Microfluidics, Artech Print on Demand, 2nd ed, ISBN 1580539726, 2006.
- Abgral, P., Nguyen, N.-T.: Nanofluidics, Artech House Publishers, ISBN 159693350X, 2009.
- Sinha, S.K. and Dey, T.K.: Molecular Physics, Alpha Science, 2006.
- Bird, G.A.: Molecular Gas Dynamics and the Direct Simulation of Gas Flows, Oxford Science Publications, 1994.
- Chapman, S. and Cowling, T.G.: The Mathematical Theory of Non-Uniform Gases, Cambridge University Press, 1970.
- Durst, F.: Fluid Mechanics: An Introduction to the Theory of Fluid Flows,Springer, 2007.