New Course

ENGG 199  Intermediate Fluid Mechanics (Microhydrodynamics)

Instructor: Petia Vlahovska

Email: petia.vlahovska@dartmouth.edu

Offered: S08

Prerequisites: ENGS 34 and MATH 23 or equivalents

Meeting time and location: TBA. Email me if you are interested in this course.

Course Description

This is a graduate level course in fluid physics.  The course will focus on microscale flows and complex fluids, which are particularly relevant to biology and modern fluid engineering applications such as the lab-on-a-chip.

The course will survey Stokes flow, lubrication theory, free-surface flows, hydrodynamic stability and special topics.  The emphasis will be on basic physics, scaling and nondimensionalization, and approximations that can be used to obtain analytical solutions.

Learning Objectives

By the end of this course, students will be able to apply modern analytic methods for the solution of fluid mechanics problems, focusing on approximations based on scaling and asymptotic methods. In particular, student will be able to

 (1) Obtain dimensionless forms of the Navier-Stokes equations and identify relevant dimensionless parameters.

(2) Simplify the governing equations for problems involving symmetry, and negligible terms.

(3) Specify appropriate mathematical boundary conditions and obtain the exact solutions.

(4) Solve for the motion of small particles in a viscous fluid, e.g.,  flow past a sphere, (thermally driven) motion of bubbles and drops,   and leading-order inertial corrections.

(5) Apply lubrication analysis to thin film flows.

(6) Perform linear stability analysis of free-surface flows.

Text and Resources

L. Gary Leal “Advanced Transport Phenomena” (Cambridge Press, 2007)

Additional reading:

Sangtae Kim and Seppo J. Karrila “Microhydrodynamics” , 1991

P.K. Kundu and I. Cohen “Fluid Mechanics”, 2002

P. G. Drazin “Introduction to hydrodynamic stability” 2002

Grading 

40% Homework

30% Midterm (take home)

30% Final (take home)

Tentative schedule:

Week 1:

Fluid flow: Equations of motion, Boundary conditions

Geometry of curves and surfaces. Surface tension and statics of fluid-fluid interfaces

Week 2,3, 4,5:

Stokes flow: basics (linearity, reversibility, symmetries)

Fundamental solutions of the Stokes flow, integral representations, the multipole expansion.

Translating sphere, sphere in a linear flow

Lorentz reciprocal theorem, Faxen’s laws

Hydrodynamic interactions –method of reflections

Slender body theory.

Rheology of suspensions

Microfluidics.

Flow past a sphere at small but non-zero Reynolds.

Bio-topic: Swimming of microorganisms, Bioconvection

Bio-topic: Blood flow in the microcirculation, Blood rheology

Week 6,7:

Lubrication theory and thin films.

Marangoni flows.

Drop coalescence and stability of dispersions.

Bio-topic: joints and the synovial fluid

Bio-topic: tear film.

Week 8, 9:

Hydrodynamic stability: linear theory      

Capillary instability of a jet         

Rayleigh-Benard Convection      

Week 10.

Special topics:Electrokinetic flows?