ME 537
Multiphase Flows
Class time: Mon Wed 9:30-10:50 MEB Annex Design Studio


Professor Alberto Aliseda
office: MEB 306
tel: 543-4910
office hours: TuTh 9:00-10:00 or by appointment

Course description Lecture Notes
Syllabus Textbook Grading Homework Exams

Course Description

  This course is designed to provide students with a strong background on 
fundamental fluid mechanics the necessary understanding of the dynamics
of multiphase flow to carry out research in their area of interest. Particular
emphasis will be placed on bubble and particle dynamics, including
sediment transport, cavitation, atomization and other environmental and
industrial processes. 
Although we will cover both Eulerian-Eulerian (two fluid) models and
Eulerian-Lagragian (discrete particles) models, most of the material
concentrates on the study of a discrete phase (particles, droplets or
bubbles) in a continuous phase. Topics will include Basset-Boussinesq-
Oseen equation of motion for a particle in a non-uniform flow, particle
interactions with turbulence, inertial clustering, cavitation and bubble
dynamics, droplet breakup, collisions and coalescence,  and surface tension

Lecture Notes

Two Fluid Formulation: Conservation of Mass, Momentum and Energy for multiple immiscible phases.

Flow around a spherical particle. Terminal Velocity of a settling or rising heavy or light sphere. Stokes Flow, Oseen correction for non-zero Reynolds numbers.

Dynamics of Particles in an inhomogeneous flow: a model for interactions between spherical particles and turbulence.

Equation of Motion of a small rigid sphere in a nonuniform flow: Maxey and Riley PoF 1983.

Particle-Turbulence Interaction. Turbulence Modification by Particles.

Bubble/Drop Deformation Induced by External Flows.

Aerodynamic Break Up of Liquid Drops.

Bubble Dynamics.


Assigned Homework Sets

Homework #1. Motion of a spherical particle starting from rest, in a uniform flow under the effect of gravity. Non-dimensional parameters, effect of the Reynolds number, ...

Homework #2. Motion of spherical particles in a cellular flows. Inertial Particles and Bubbles. Influence of Inertia and Gravity.

"The motion of small spherical particles in a cellular flow field" M. Maxey, 1987, Physics of Fluids, 30, 7, pp 1915-1928.


Midterm Exam. Evolution of a Dust Storm as a particle-laden turbulent boundary layer flow.

Final Exam. Propagation of Sound in a Bubbly Liquid: bubble-liquid two-fluid mixture and mechanism for sound propagation from an individual bubble dynamics.


Introductions, syllabus, course administration.                                       Week 0
Two Fluid Models.                                                                                       Week 1
Stokes flow around a spherical particle and Oseen correction.              Week 2
Equation of motion for a small spherical particle in a
non-uniform flow, the Basset-Boussinesq-Oseen equation.      
              Week 3

Other forces exerted by the carrier flow on a bubble/droplet/particle
immersed in it. Saffman Lift, Bjerknes force, thermophoresis, etc.      
Week 4    

Particle dynamics. Inertial effects.                                                            Week 5

Turbulence modulation by particles.                                                       
Week 6
Droplet/bubble deformation and breakup.                                              Week 7
Bubble dynamics.                                                                                       Week 8    

Cavitation.                                                                                                   Week 9

Droplet collisions and coalescence.                                                           Week 10


The required texts for this course are:

        1. Crowe, C.T. “Multiphase Flow Handbook”. Taylor & Francis, Boca Raton, Fl. 2006.
        2. Brennen, C.E.”Fundamentals of Multiphase Flow”, Cambridge University Press, New York, 2005.
        3. Crowe, C.T., Sommerfeld, M. and Yutaka, T.  “Multiphase Flows with Droplets and Particles”, CRC Press, Boca Raton, FL. 1998.


Homework               20%        
Personal Project       40%
Midterm                  15%
         Final                        25%

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