The Physics of a Centrifuge

 

Clay Adams Sero-Fuge II

Photo Courtesy of Katie Knupp

 

Regina Rumley

John Whichard

Rachel Rosenberg

Katie Knupp

 

Introduction

 

Human blood is a unique fluid tissue that is classified as one of the largest organs in the body.2  At a microscopic level, blood is composed of both cellular and liquid components, which include red blood cells, white blood cells, and platelets, all suspended in a yellow-colored substance called plasma.3  The red blood cells (erythrocytes) help carry oxygen throughout the body, the white blood cells (leucocytes) help fight against infections and viruses, while platelets help with the blood clotting process.2,5  In general, the liquid portion of blood, plasma, constitutes for 50-55% of the total blood volume.  Additionally, the cellular components, such as red and white blood cells and platelets, combine to count for 40-45% of total blood volume.3,6  When a blood sample is spun in a centrifuge, the components of the blood separate into layers based on their individual weights.  Since the heaviest particles are the red blood cells (erythrocytes), they sink at the bottom of the test tube, while the least dense constituent, plasma, proceeds to move to the top of the test tube.1,2  After the constituents have separated according to their individual weights, a percentage that represents a count of the erythrocytes, leucocytes, or the platelets per unit of blood, also known as a hematocrit, can be taken.2 

 

 

 

          A blood centrifuge utilizes the abundant, consistent, reproducible, and manageable force of gravity to separate the components of blood.4  As the blood spins in a centrifuge, the constituents are subject to g-forces that allow the blood to separate on their particular densities.1  With technology advancing, ultracentrifuges have been constructed which utilize density gradients and extremely high g-forces to separate compounds with similar properties and densities.4   

 

Analysis of Forces in a Centrifuge

           

            In an ultracentrifuge, there are only two forces acting on the blood particles being rotated in the tube.  An analysis of the forces using Newton’s second law, which states that the acceleration of the tube is directly proportional to the forces acting on it, but indirectly proportional to the mass of the tube and blood system.  The forces that act on this system include simply the weight of the tube and blood added together, and the tension force of the attachment point of the tube to the centrifuge.  This tension is often called the centripetal acceleration when it is holding the tube in place during the machine’s rotation. 

 

Figure 1: The Forces Acting in a Centrifuge

 

          These two forces can be resolved into x and y vectors with the up and down direction taken as y and the side-to-side direction as x.  With these assumptions, the force of the tension in the y direction is equal and opposite to the force of the weight.  Since these forces cancel each other, there is no change in velocity in the y direction while the centrifuge is in motion.  The x component of the tension, however, reveals that the tube is accelerating towards the left, or in this case towards the center of the rotational motion.  This acceleration is called the centripetal acceleration.

 

Calculation of Forces in a Centrifuge

 

Clay Adams Sero-Fuge II

Photo Courtesy of Katie Knupp

 

The centripetal force is the force acting towards the center of a rotating object.  On the centrifuge, the tubes are being rotated and have a centripetal acceleration, acceleration towards the center because the velocity is constantly changing direction.  This acceleration can be greater than gravity, and is used to separate the different types of particles in blood.

 

The blood is filled to half of the tube, which is about 3 mL.

 

Mass of the tube = .00357 kg

Mass of blood  = density of blood * volume of tube filled = 1.1 g/mL * 3 mL = 3.3 g = .0033 kg

Mass combined = mass tube + mass blood = .00357 kg + .0033 kg = .00687 kg

 

The centrifuge is normally run on high with an angular speed of 3,400 revolutions per minute.

 

ω = 3400 rev/min =356 rad/sec

 

r = midpoint of test tube = ½ L = ½ (.075m) = 0.0375m

 

ac = ω^2r = (356)^2 * (.0375) = 4752.6 m / s^2

 

centripetal acceleration = (4752.6 m / s^2) / (9.8 m/s^2) = 485 g

 

The centripetal acceleration is about 485 times greater than that of gravity.  This large acceleration facilitates the separation of red blood cells, white blood cells, and plasma.

 

Fc = mac = (.00687 kg) * (4752.6 m / s^2) = 32.6 N

 

This large force requires a sturdy tube to withstand the force without breaking.

 

How sedimentation rate is affected by the angular speed of the Centrifuge

Clay Adams Sero-Fuge II

Photo Courtesy of Katie Knupp

 

            A body normally reaches its normal speed when the downward force of gravity is balanced by the net upward force, or w = B +Fr.  Since B is equal to rfgV, and V is equal to m/r, then B=rfmg/r.  This all means that vt, or the sedimentation rate of the particle is equal follows the equation

           

When the centrifuge is used, however, the acceleration is no longer gravity, but it is ac, where ac=w2r.  This change in acceleration alters the value of vt.  It becomes

           

Where k is the experimentally found coefficient of frictional resistance.  (this information was found in the text book on page 292)

 

The centrifuge studied by this group has a high speed of 3,400 rpm, and a low speed of 2,800 rpm.  From the above equation for sedimentation rate, the difference in sedimentation rate for each of these speeds can be found.  This is done through substitution.

 

 

 

(1)            

 

(2)

 

Substitute equation (2) into equation (1)

 

              

 

The density, mass and radius all cancel out and all that is left is

 

           

 

This means that the sedimentation rate at the high speed is 0.54 times that of the low speed.

 

Special Links

 

http://www.physics.unc.edu/classes/spring2003/phys024-001/

http://www.tiscali.co.uk/reference/encyclopaedia/hutchinson/m0009940.html

http://www.coe.tamu.edu/~alliance/p-bloodvol_lab.html

 

References

 

Babior B, Stossel T. Hematology: A Pathophysiological Approach. New York: Churchill

Livingstone; 1994. 213p.

 

1Centrifuge. Tiscali Reference: Hutchinson Encyclopedia. Available from:

http://www.tiscali.co.uk/reference/encyclopaedia/hutchinson/m0009940.html via

the World Wide Web.  Accessed 2003 March 28.

 

Harmening D, editor. Clinical Hematology and Fundamentals of Hemostasis.

Philadelphia: Davis; 2002.

 

2Marieb, E. Human Anatomy & Physiology. San Fransisco: Benjamin Cummings; 2001.

651-663 p.

 

McKenzie S. Textbook of Hematology. Baltimore: Williams & Wilkins; 1996.

 

3Pallister, C. Blood: Physiology and Pathophysiology. Oxford: Butterworth-

Heinemann; 1994. 1-3p.

 

4Pamukcu M. The Many Faces of the Centrifuge. International Scientific

Communications. 2000 Feb.  Available from:

www.iscpubs.com/articles/abl/b0002pam.pdf via the World Wide Web. Accessed

2003 March 28.

 

5Robins M, Burn-Murdoch R. Major Points on the Physics of the Cardiovascular System.

GKT School of Biomedical Sciences. Available from:

http://www.umds.ac.uk/physiology/BDS1B/1B6.htm via the World Wide Web. 

Accessed 2003 March 28.

 

6Rodriguez L, Cameron T. Blood Volume Lab. . 2001 April 10.  Available from:

http://www.coe.tamu.edu/~alliance/p-bloodvol_lab.html via the World Wide

Web.  Accessed 2003 March 28.