Advanced Continuum Physics

• Explain the theory of hydrostatic equilibrium, including pressure, buoyancy, stability of a floating object, hydrostatic shapes and surface tension.
• Explain the concepts of strain and stress in elastic materials and explain the derivation of and apply the Cauchy equation and Hooke’s law.
• Explain the derivation of and apply the Euler, the Bernouilli, the Navier-Stokes, and the continuity equation for incompressible fluid flows.
• Describe flows at low Reynolds number.
• Derive the wave equation and the dispersion relation for linear surface waves and sound waves in fluid- and elastodynamic systems
• Apply linear stability theory and explain the Rayleigh-Plateau instability.
• Explain and apply Prandtl’s boundary layer equations.
• Apply dimensional analysis to make estimates in continuum physics.
• Solve analytic problems from selected models in continuum physics.
• Apply vector and tensor analysis with the index notation on models in continuum physics

Introduction of velocity field and pressure field. Hydrostatic problems with special focus on surface tension. Strain and stress in elastic media. The equations for linear elasticity. Bending and buckling. Ideal, incompressible fluid motion (the Euler equation). Viscosity, Navier-Stokes equation, and boundary layers. Potential flow theory, surface waves and sound waves in fluid- and elastodynamic materials. Index notation in vector and tensor analysis.

01001/01002/02002/10033/10034, especially central material from classical physics and mathematics, i.e., knowledge of mechanics, thermodynamics, electromagnetism, vector analysis, and ordinary as well as partial differential equations.

The weekly block of four hours will consist of a mixture of lectures, work with problems and computer exercises. Central in the course are two larger homework problems, which are graded and count as part of the final grade. The homework problems are new from year to year and each assignment focuses on a selected problem of current research interest.

Continuum Physics (10346) and Theoretical Microfluidics (10337) are independent. The courses only overlap in the introduction to the fundamental fluid dynamics equations.