• Biomedical Engineering, Semester 3, position 5
• Zavarivanje i zavarene konstrukcije, Semester 3, position 5
• Industry Engineering, Semester 3, position 5
• Hidroenergetika, Semester 3, position 5
• Mechanics, Semester 3, position 5

The aim of this subject is getting academic knowledge about fluid dynamical processes in micro and nano flows and introducing with scientific methods for predicting, analyzing and studying gas and liquid flow in structures of micrometer and nanometer characteristic dimensions.

Students are trained to: -apply the basic equations of fluid mechanics ie. equations of continuity, momentum and energy to describe the compressible and incompressible fluid flow in micro and nano channels; -determine the velocity and pressure field for isothermal compressible and incompressible fluid flow in micro and nano channels, pipes and bearings for continuuma boundary conditions; - calculate the velocity and pressure field for isothermal compressible gas flow in micro channels, pipes and bearings for the slip flow regime; - calculate the velocity, pressure and temperature field for non-isothermal compressible gas flow in micro channels, for the slip flow regime; -calculate the pressure and velocity field for electroosmotic flow in micro and nano channels and pipes; - applie the law of diffusion equation and obtained analytical solutions which enables determination the change of a substance concentration in the micro channel with no fluid stream, as well as in the fluid stream; -determine the equilibrium height in the capillaries and the time required for its achievement, as well as the change in the liquids position with time in the capillary pump.

Theoretical lessons contains fundamental fluid mechanics equations applied on fluid flow modeling in the micro and nano structures, rarefaction effect, slip and temperature jump boundary conditions, the behavior, manipulation and control of fluids that are confined to structures of nano and micrometer characteristic dimensions, electric double layer and Debye length, electrokinetic effects such as electrophoresis and electroosmosis which are often present in the micro-and nanofluidics, basic diffusion equations and some exact analytical solutions for the substance concentration in the fluid, the ability to use the process of diffusion for mixing and separation in micro and nanosystems, capillary phenomena that are important for micro and nanosystems, micro-pumps.

Practical lessons contains: application of the basic fluid mechanics equations, exact solutions for modeling fluid flow in the micro and nano structures which include different effects as rarefaction, slip and temperature jump at the wall,calculation of electro-osmotic flow for different channel geometries taking into account the presence of the double layer and Debye-Huckel approximation for the distribution of charge density in the electric double layer , calculation of electro-osmotic pumps of various structures, calculation of the propagation of the substance due to diffusion and advection for different conditions, calculation of capillary motion of fluids and capillary pump.

Third semestar of Master study

Books related to the field of microfluidics written by professors from the department Department of Fluid Mechanics, lecture presentations (Stevanović N.).

Total assigned hours: 75

New material: 25
Elaboration and examples (recapitulation): 5

Auditory exercises: 0
Laboratory exercises: 0
Calculation tasks: 25
Seminar paper: 5
Project: 0
Consultations: 0
Discussion/workshop: 0
Research study work: 0

Review and grading of calculation tasks: 10
Review and grading of lab reports: 0
Review and grading of seminar papers: 0
Review and grading of the project: 0
Test: 0
Test: 0
Final exam: 5

Activity during lectures: 5
Test/test: 0
Laboratory practice: 0
Calculation tasks: 50
Seminar paper: 0
Project: 0
Final exam: 45
Requirement for taking the exam (required number of points): 30

Stevanovic N., Fundamentals of microfluidics and nanofluidics (in Serbian), 2014, Faculty of Mechanical Engineering, University of Belgrade, ISBN: 978-86-7083-847-5.; Karniadakis G., Beskok A., Aluru N., Microflows and Nanoflows Fundamentals and Simulations, 2005, Springer, ISBN: 978-0387-22197-7; Bruus H., Theoretical Microfluidics, 2008, Oxford University Press, ISBN: 978–0–19–923509–4; Stevanović, N., Rarefied gas flow in microchannels (in Serbian), 2010, Faculty of Mechanical Engineering, University of Belgrade, ISBN: 978-86-7083-686-0