BMED 3300 Biotransport
Homework 2
January 19, 2010.
Professor Julie Babensee
1.
One way to deliver a timed doscage of a drug within the human body is to ingest a capsule and allow it to
settle in the gastrointestinal system. Once inside the body, the caps
BMED3300 (C-F) - Biotransport Phenomena
Problem Set #2 - Due: Thursday January 24, 2013
Solutions
Please note that mark breakdown shown for some
questions is not for purposes of this problem set.
Instead, these were questions given on previous exams
and t
BMED 3300 Biotransport
Homework 7
October 24, 2011.
Professor Julie Babensee
1.
The simplest patient infusion system is that of gravity flow from an intravenous (IV) bag. A 500-mL IV
bag containing an aqueous solution is connected to a vein in the forearm
BMED3300 (C-F) - Biotransport
Problem Set #8 - Due: Thursday March 28
NOTE: PLEASE PROMINENTLY INDICATE YOUR RECITATION SECTION NEXT TO YOUR
NAME ON THE FIRST PAGE OF YOUR SUBMITTED PROBLEM SHEET.
1. Consider steady 1-D diffusion through a funnel of varyi
BMED3300 Biotransport Lecture Notes
C. Ross Ethier 2004, 2013
Lecture 5: Fluid statics. Buoyancy. Fluid rheology.
Fluid Statics: Hydrostatics refers to the behaviour of fluids at rest.
From the definition of a fluid, there can be no shearing forces in a
4/7/14
Delivery of oxygen to tissue is a
geometric problem
August Krogh (Nobel prize, 1920) realized that in
order for all cells to receive enough oxygen by the
microvasculature, capillaries must be spaced in
such a way to account for diffusion lengths of
BMED3300 Biotransport Lecture Notes
C. Ross Ethier 2004, 2013
Lecture 17: Introduction. Diffusion vs convection. Concentrations
and mass fluxes.
In this unit, we will consider systems in which there are two (or more)
components. In general, their concent
4/21/14
2
Hemodialysis
Filtering of the blood
Goal: to provide limited kidney function by the removal of
toxic solutes accumulating in the blood
Without one functioning kidney, death can occur within a
few days due to toxin accumulation
Associated with en
BMED3300 Biotransport Lecture Notes
C. Ross Ethier 2004, 2013
Lecture 1: What is biotransport? Generate Ideas Model (GIM).
Units.
What is biotransport?: This course is concerned with fluid mechanics,
mass transfer and heat transfer.
Fluid mechanics is th
3/26/14
Mass or molar flux at boundary
Weve already broached this topic
before
Reactions that occur uniformly through a given phase
are considered to be homogeneous
c A
RA 0
t
c
DA2 c A A R A 0
t
N A
Reactions that take place only at a boundary (surfac
3/31/2014
Unsteady-state diffusion
In real-life, often things are diffusing with changes
in t,x,y,z
If more than one variable is changing, and
concentration is a function of (t,x,y,z) then solving
for changes in concentration results in a partial
differen
4/2/14
Use of charts
The book provides solutions in the appendix for plate, spherical, and
cylindrical geometry
Although for 1D transfer, they may be combined for 2D,3D
The use of these charts must follow the following conditions:
1)
Ficks 2nd law assumed
3/10/14
Relation between concentration gradient and flux by Ficks 1st Law
Ficks 2nd Law: the Diffusion Equation
J ( x, t )
c( x, t )
x
t
c( x, t )
J ( x, t ) D
x
Ficks 1st Law
Continuity Equation
J
c
D
x
x x
D c
J
2c
x x D x 2
x
0
1D:
3D:
c
2c
D
3/4/14
Definitions : Mass (ch. 24)
Molecule of species A
Density
A
Molecular weight
mass A M A
volume V
n
i
i
1
Volume of multicomponent
mixture
Mass fraction
A
n
i
1
n
i
1
i
M
A A
M
A
1
i
Molecular concentration
n
cA A A
MA V
n
c ci
i
1
# moles
Mole
3/12/14
Concentration gradients give cells positional
information
Unlike the propagation of light or sound waves, diffusion is not a constant-rate
phenomenona diffusing front gets slower as it spreadsmaking computation of
distance from arrival time tricky
3/24/14
Membrane Transport
8
80-100
Cell membranes are 80100 thick
The lipid bilayer has
pores roughly 8 in
size
Integral membrane proteins are bound tightly to the membrane and are not
readily dislodged without the use of detergents that disrupt the memb
BMED3300 Biotransport Lecture Notes
C. Ross Ethier 2004, 2011
Lecture 2 (continued): Systems vs Control Volumes. Fluxes.
Reynolds Transport Theorem.
System vs. Control Volume: In analyzing fluid flow, the idea of a control
volume is very useful. Students
4/16/14
Two laws of heat transfer:
1.
2.
The rate of energy transfer into a system
has to equal to the rate of energy
increase of the system
Heat must be transferred in the direction
of decreasing temperature
Heat thermal energy. Therefore rule 1 is conse
4/23/14
Wanted: undergraduate TA
Drs. Luke Timmins and David Molony will
be teaching BMED 3300 this summer
If you are
excelling in the course
available for the entire summer term
interested in this experience
email lucas.timmins@bme.gatech.edu
A reminder
4/14/2014
Relative contributions of convection vs. diffusion
We have defined a new dimensionless value to compare diffusion
versus convection transport, the Peclet number
Pe = mass transport by convection
mass transport by diffusion
L2 L
D L D
AB
AB
W
BMED3300 Biotransport (Ethier/Kemp)
Problem Set #4 Contributes to Quiz 2
1. The cooling system for a piece of medical
Tube 1
Tubes 2 and 3
equipment has a flow distributor formed of 3
20 cm
30 cm
cylindrical tubes (see diagram), with the Length L
Diameter
BMED3300 Biotransport (Ethier/Kemp)
Problem Set #3 Contributes to Quiz 2
1. Blood flow in small vessels has a Poiseuille velocity profile:
2
() = 2 [1 ( ) ]
where R is the vessel radius and r is any radial location. For vessel diameters less than a few
h
BMED 3300 (Ethier/Kemp) - Problem Set 4 solutions
Problem 1
Initial Considerations: This problem is steady state. We are looking at the original pressure drop over
the tubes and comparing it to the pressure drop if only one of the two identical tubes is o
BMED3300 PS2 - Solutions. (GIM shown in red.)
Pol 1
rb m :
e
IiaC ni r i sT bg t s rb m w fsne tudrad hths ays apn
n i os e t n: o ei h pol , eitedo ne t w apyi l ihpetl
d ao
n i
e
r
sn
cl
i . o t s rb m a w t m vs ut og t nzl t riar s r f oi n l o
n F rh
BMED3300 Biotransport (Ethier/Kemp)
Problem Set #2 Contributes to Quiz 1
1. A large cylindrical tank of diameter is filled to a depth
by fluid of density . A small nozzle of diameter is
located at the bottom of the tank, as shown, with
. The tank sits o
IiaC ni r i sI t s rb m t Fhau e eted tb aa zd T e ec p
n i os e t n:nh pol , e ar s f cneso e nl e. h dsr tl
d ao
i
e h
e f
y
i
t n a b v w dnh pol s t etT iit a d s s ay te rb m
i cn e i e it rb m te n h sr t a a t d s tpol .
o
e
e
e am . s ee
e
a
e
A a
BMED3300 - Biotransport (Ethier/Kemp)
Problem Set #1 Contributes to Quiz 1
1.
Using the data in the table, and a renal
artery flow rate of 1.25 L/min, determine
(a) The fraction of water filtered across
the glomerulus;
(b) The renal vein flow rate; and
(c
BME 3310:
Fluid Properties
Dr. Harley
What is a fluid?
A substance that tends to flow under applied forces (shear
stress) or that conforms to the outline of its container.
Fluid Statics
Ex. Hoover Dam
Fluid Dynamics
Ex. Alaskan Pipeline
Stress and the St
BME 3310:
Fluid Statics
Dr. Harley
Pressure Field
Asume
you have a
stationary beaker of
water that sits on top of
the table.
The temperature of the
water is room
temperature.
Now let us consider a
small square of fluid of
unit depth into the page.
Sin
BME 3310:
Biostransport
Dr. Harley
Introductions
Roll Call
Syllabus and Schedule
What is biotransport?
Mass Transfer
Heat Transfer
Fluid Mechanics
What is a fluid?
o A substance that tends to flow under applied forces or that conforms to
the outline of i
BMED3300 - Biotransport (Ethier)
Problem Set #1 Solutions
Question 1
Use GIM
Initial considerations: For this to make sense, we need to remember kidney
anatomy/physiology - water and solutes filter out of blood in glomerulus, are
partially resorbed into b