Exam 4 Review

Diffusion with Convection

100

The Navier-Stokes equation represents the conservation of linear momentum under what two assumptions about the fluid solute? A. incompressible fluid B. weakly compressible fluid C. compressible fluid D. Newtonian fluid E. non-Newtonian fluid

What is A,D?

200

For a dilute solution, density can be considered constant. T/F

What is True?

300

If v_ f L is much greater than D_e f f, there is a short convection time as compared to the diffusion time. T/F

T

400

Which of the two terms below equals zero when the fluid is incompressible?

v dot grad Ci  or Ci grad dot v

Ci grad dot v

500

Assume you have steady, 1-D diffusion and convection through a membrane (L=1.5 cm) in the z-direction with no chemical reactions.  At z=0, Ci=5 mmol/mL, and at z=L, Ci=0.  The z-component velocity is 3 cm/s, the partition coefficient is 0.8.  If the Pe number illustrates a really long diffusion time compared to convection time, then what is the flux through the membrane?

Report answer to 1 decimal place.

Answer (mmol-cm-2 s-1): ____

11.8|12.3

Peclet

100

If the Peclet number is zero, transport is limited by convection. T/F

False

200

The concentration profile is ____ through the membrane if the Pe number is very, very small.

linear

300

What does v_f represent?

filtration velocity

400

Which relationship is independent of the assumption of dilute solutions? A. conservative relationship B. constitutive relationship

A

500

The oxygen diffusion coefficient in tissue is about 1.1 x 10 to the power of negative 5 c m squared divided by s. The fluid filtration velocity is 1 mu m divided by s. The distance between capillaries is 0.01 cm. What Peclet number describes the transport involved in the oxygenation of the tissue?

What is .04|.05

Diffusion in Heterogeneous Medium

100

The boundary condition at the edge of the tissue space surrounding the capillary (r=rT) is ______ because ________.

(a)  dCi/dr = 0, of the plane of symmetry between the tissue cylinders

(b) Ci = 0, all the solute is consumed in the tissue space

(c)  Ni = Ri, the flux is balanced by the consumption rate

A

200

Given that the permeability of oxygen through capillary pores is 1.75x10-4 cm/s, the filtration velocity is 5x10-9 cm/s, and the average oxygen concentration in the capillary is 90 nmol/mL.  Oxygen is transported through capillary pores _________. 

A. primarily by convectionB. primarily by diffusionC. by roughly equal contributions of convection and diffusion

B

300

Use the following information to determine the mass transfer coefficient of a molecule within a blood vessel.  The diameter of the vessel is 0.1 mm.  The molecule's diffusion coefficient in water at 37°C is 5x10-5 cm2/s.  The average velocity of the blood flowing through the vessel is 0.5 cm/s.  Assume blood is a Newtonian fluid and that its flow is steady, laminar, and fully-developed within this vessel.    

Report your answer to 3 decimal places.

0.007|0.009

400

What is the Schmidt number?

Sc = v / Dij = momentum transport / Diffusive transport

500

What are the two types of hemodialysis units?

flat plate and hollow fiber

Dilue Solutions

100

Consider steady-state, 1D diffusion and convection across a membrane of thickness L. There are no chemical reactions occurring. At z=0, C= phi Co, and at z=L, C=phi CL, where phi is the partition coefficient of the solute in the membrane. To determine the concentration profile and flux across the membrane, what conservation relations would you use?

(A) rectangular

(B) cylindrical

(C) spherical

(A)

200

Consider steady-state, 1D diffusion and convection across a membrane of thickness L. There are no chemical reactions occurring. At z=0, C= phi Co, and at z=L, C=phi CL, where phi is the partition coefficient of the solute in the membrane. To determine the concentration profile and flux across the membrane, what can you simplify the conservation relation to?

vf dCi/dz = Deff d^2Ci/dz^2

300

Consider steady-state, 1D diffusion and convection across a membrane of thickness L. There are no chemical reactions occurring. At z=0, C= phi Co, and at z=L, C=phi CL, where phi is the partition coefficient of the solute in the membrane. What is the concentration profile?

Ci = A exp (vf / Deff z) + B

Ci = phi Co - phi (Co-CL) [(1-exp(Pe(z/L)) / (1 - exp(Pe))  ]

Pe = vfL/Deff

400

Consider steady-state, 1D diffusion and convection across a membrane of thickness L. There are no chemical reactions occurring. At z=0, C= phi Co, and at z=L, C=phi CL, where phi is the partition coefficient of the solute in the membrane. What is the flux?

Niz = -Dij dCi/dz + Civf

= phi Dij/L  Pe  [ Co - (Co-Cl)/(1-exp(Pe)] 

(example 7.1 in book)

500

As Peclet goes to zero, what limit is approached?

Diffusion limit.

Miscellaneous

100

10. For short-contact-time analysis, which of the following assumptions are true?

(a) curvature can be neglected

(b) parabolic velocity can be assumed

(c) linear velocity can be assumed

(d) concentration change appears to be semi-infinite

(e) zDij/vmaxR^22 < 0.03

ACD

200

Which flow setup for a hemodialysis machine has a higher extraction ratio and why?

counter-current. (1) The explanation should talk about the clearance or

extraction of the drug or toxins from the blood. The extraction ratio  is higher for counter-current. They don’t need to have the equations but the

logic should follow these lines.

300

The permeability across a thin rectangular region is defined by : Pi = Nix/(Co-CL). Co is the solute concentration in the blood, CL is the concentration in the lymph, and L is the thickness of the tissue between the blood and lymph.

Use the equation and flux across a membraPne (when fluid flows across a membrane) ( phi = 1) to find an expression for the permeability in the presence of convective transport across the membrane.

Pi= Dij/L Pe Co/(Co-CL) - Dij/L Pe 1/(1 - exp(Pe)) 

400

The permeability across a thin rectangular region is defined by : Pi = Nix/(Co-CL). Co is the solute concentration in the blood, CL is the concentration in the lymph, and L is the thickness of the tissue between the blood and lymph. Show that for diffusion limited transport, Pe -> 0 Pi = Dij/L.

Note: exp(x) = 1+x for x<.01

Pi = 0 - Dij/L Pe 1/(1 - (1+ Pe))

Pi = -Dij/L Pe  1/(1-1-Pe)

Pe = Dij/L

500

For steady laminar flow through a cylindrical blood vessel with radius 1.0cm, you want to determine if fluid convection enhances solute transport to the vessel wall for < v >= 10cm/s and Dij = 1x10^-6cm2/s. Use  = 0.03cm2/s.  

What dimensionless numbers do you need and what are their values?

Sc = 3 x 10^4

Re = 333.33

Sh = 504.9 if L = 1, if L = 2 , 1055