BME/ME 476 - BIOFLUID MECHANICS
James B. Grotberg, Ph.D., M.D.
Department of Biomedical Engineering
Class time: 4:30-6:30pm M,W
Class location: 1123 LBME
Text: Class notes, posted at end of each section
Website: Canvas
Email:
Course grading:
Exams
Distribution: 1 midterm, 1 final.
Format: Take-home. Problems selected from exam-eligible homework problems (see below).
Homeworks
Skill HWs:assigned with solutions, collected and graded check+, check, check-
Exam-eligible HWs: assigned, not collected, exams will be a subset of these.
Final grade based on Exams, 50% each, assuming Skill HWs satisfactory.
Office Hours:
Time: Monday 3-4pm, Wednesday 11am-12pm
Location: 1100 Gerstacker
Historically there is a strong correlation between the final grade and participation in office hours where HW problems are discussed.
Outline of Class Notes
ChapterTopic
1Introduction
2Variables, Parameters, Scalings
2.1 The Dropped Ball
2.2 Impact Time: Theory and Experiments
2.3 Scalings and Dimensionless Variables
2.4 The Thrown Ball: A Dimensionless Parameter
2.5 Scaling a Mechanical System: The Buckingham Pi Theorum
2.6 Thrown Ball Revisited: Scaling the Governing Equations First
2.7 Viscous and Buoyancy Effects of a Dropped Particle: Erythrocyte Sedimentation Rate
2.8 Microfluidic Cell Sorting
3Kinematics, Lagrangian &Eulerian Frames
3.1 Lagrangian and Eulerian Variables
3.2 Mappings and Inverse Mappings
3.3 Functions in Lagrangian and Eulerian Reference Frames
3.4 Partial derivatives in Eulerian and Lagrangian frames
3.5 Mapping Example: Stagnation Point Flow
3.6 Streamlines
3.7 Streaklines
3.8 Timelines
3.9 Aerosol Particle Deposition in the Lung
3.10 Numerical Methods
4Conservation of Mass
4.1 Mass Conservation from an Eulerian Control Volume
4.2 Incompressible Fluids
4.3 The Stream Function
4.4 Streamlines and Stream tubes
4.5 Conservation of Mass for a Soluble Species
4.6 Different Coordinate Systems
4.7 Kinematics of Fluid Deformation
4.8 The Reynolds Transport Theorum
4.9 Mass Conservation from a Lagrangian Control Volume
5Conservation of Momentum
5.1 Linear Momentum Conservation from an Eulerian Control Volume
5.2 Cauchy Momentum Equation
5.3 The Stress Tensor
5.4 Angular Momentum Conservation
5.5 Fluid Pressure
5.6 Stress Tensor and Momentum Conservation in Other Coordinate Systems
6Constitutive Equations I: Inviscid and Newtonian Fluids
6.1 Inviscid Fluid: Euler Equations
6.2 Bernoulli Equation
6.3 Newtonian Viscous Fluid
6.4 Constitutive Equation in Other Coordinate Systems
6.5 Navier-Stokes Equations
6.6 Scaling the Navier-Stokes Equations
6.7 Kinematics of a Fluid Element
6.8 Navier-Stokes Equations in other Coordinate Systems
7Steady Newtonian Viscous Flow
7.1 Hagen-Poiseuille Flow in a Circular Tube
7.2 Applying Poiseuille Law: Vascular Hemodynamics
7.3 Gravity and Boundary Driven Flow: Respiratory Mucociliary Clearance
7.4 Core-Annular Two-Phase Flow in a Circular Cylinder:Vascular and Respiratory Applications
7.5 Flow and Anatomical Evolution: Murray’s Law
7.6 Murray’s Law with Variable Length and Branch Angle
7.7 Flow in a Rectangular Duct: Microfluidic Channels
8Unsteady Newtonian Viscous Flow
8.1 Stokes First Problem
8.2 Stokes Second Problem
8.3 Oscillatory Flow in a Channel
8.4 High Frequency Ventilation
8.5 Oscillatory Flow in a Tube
8.6 Pulsatile Flow in a Tube
8.7 Mucus Transport from Cough
9Flow in Flexible Tubes
9.1 Steady Viscous Flow in a Flexible Tube
9.2 The Nonlinear Tube Law
9.3 Viscous Flow Limitation
9.4 Wave Speed and Inviscid Flow Limitation
9.5 Pulse Propagation in a Flexible Tube
9.6 Pulsatile Flow and Wave Propagation
9.7 Solutions to the Wave Equation
9.8 Waves at a Bifurcation: Transmission and Reflection
9.9 Flow Induced Oscillations
10Constitutive Equations II: Generalized Newtonian Fluids
10.1 Rheology and Constitutive Equations
10.2 Cauchy Equation for Generalized Newtonian Fluids
10.3 Power-Law Fluids
10.4 Herschel-Bulkley Fluids
10.5 Casson Fluid Model for Blood
10.6 Casson Fluid Flow in a Tube
10.7 More Constitutive Models
10.8 Viscometers and Viscometric Flows
11Lubrication Theory
11.1 The Slide Block
11.2 Slide Block Forces and Flows
11.3 A Model RBC in a Capillary
11.4 RBC Model Forces and Flow
11.5 Microcirculation and Apparent Blood Viscosity
11.6 Filtration Flow in a Capillary
11.7 Squeeze Film: Flow in Joints
11.8 Non-Newtonian Squeeze Film
12Laminar Boundary Layers
12.1 Boundary Layer Flow over a Flat Plate
12.2 Polynomial Approximations to Boundary Layer Flow
12.3 Entrance Flow in a Tube: Airways and Blood Vessels
12.4 Inspiratory Flow in the Tracheobronchial Tree
12.5 Flow in a Curved Tube
12.6 Flow Through a Bifurcation
12.7 Viscous Stagnation Point Flow
13Turbulence
13.1 Examples of Turbulent Flows in Biofluid Mechanics
13.2 Analysis of Turbulence
13.3 Fully Developed Turbulent Pipe Flow: The Moody Diagram
13.4 Turbulent Flow Near a Boundary
13.5 Turbulent Entrance Flow
13.6 Turbulent Boundary Layer on a Flat Plate
13.7 Integral Balances for Boundary Layer Flow over a Flat Plate
13.8 Solutions to the Momentum Integral Equation
14Constitutive Equations III: Viscoelastic Fluids
14.1 Viscoelastic Materials: Mucus and Blood
14.2 Maxwell Fluid Response to Step Inputs
14.3 Kelvin-Voigt Viscoelastic Solid: Biological Tissues
14.4 Maxwell Fluid - Oscillatory Forcing
14.5 Complex Fluid Viscosity
14.6 Kelvin-Voigt Solid - Oscillatory Forcing
14.7. Maxwell Constitutive Model in the Cauchy Equation
14.8 The Equivalent Approach for Fading Memory Fluid
14.9 Oscillating Flow over a Mucus Film: Respiratory Clearance
14.10 Oscillatory Squeeze Film with a Maxwell Fluid: Synovial Fluid
15Flow from Boundary Motion
16.Flow in Poroelastic Media:
17.Surface Tension & Stability: