Diffusion

Lab Report #1: Diffusion

Team 7: Christina DiPaul

James Thomas

Nam Nguyen

Amanda Velez

Introduction:

The human body undergoes a variety of processes throughout each and every day in order to sustain life. Tasks such as walking, breathing, and digesting what has been eaten are sometimes considered mundane, even taken for granted. One such process that is necessary to maintain life is diffusion. Diffusion is a key factor in moving ions, fuels, and other molecules into and out of the blood. It is one of the most important components in supplying oxygen to the alveoli and removing carbon dioxide. Without diffusion, substances would find it very difficult to pass through membranes and could cause detrimental effects to the human body.

The paradox scientists have drawn is related to glucose molecules and the directions in which the molecules "know" to move. No single molecule should diffuse in any particular fashion, but should diffuse randomly. This report looks at four simulations attempting to solve the problem presented, how do the molecules know which way to diffuse?

In order to understand the obtained research, it is necessary to present and identify the key components of Fick's Law of Diffusion:

F = -D * A*dC/dx

F = the flow of material across a real or imaginary plane

D = the diffusivity of the diffusing molecules

(the ease in which the molecule diffuses in the surrounding medium)

A= area of the plane

C= concentration of the molecules

X= distance

dC/dx = the concentration gradient

There will be four simulations conducted in order to apply Fick's Law and determine if molecules do in fact know which way to diffuse. The first simulation will look at a single molecule in an open area, the second looks at the movement of several molecules, the third looks at molecules diffusing in a box, and the fourth looks at molecules diffusing through a pipe between two boxes. Understanding the movements of the molecules in each of these simulations will allow the problem to be solved.

Materials/Methods:

In order to properly experience each of the simulations it is necessary to have access to Microsoft Excel and MatLab, a program designed allowing scientists to view data in a visual format.

The first simulation, as mentioned, dealt with a single molecule randomly moving in an open area. It is assumed that the molecule will move from a higher concentration to a lower concentration based on the laws of diffusion and that the molecule will move a set distance in one step before heading randomly into its next direction. The molecule will proceed randomly through several hundred steps and countless collisions with a fixed free path length, or the average distance between each collision.

The second simulation demonstrates several molecules randomly moving in a designated area. This simulation is similar to the first in that it is also a random walk with a fixed free path length and random direction after each collision.

Ten thousand molecules start at the origin to show this relationship because we are assuming that the molecules have no size, however this would not be physically possible outside of the simulation. Again the assumption is made that the molecules will move from a higher concentration (near the origin) to a lower concentration (away from the origin.) Another simplification is also made in order to allow the molecules to ignore each other and not bounce off one another like they would do in the actual environment.

The third simulation shows the diffusion of molecules in a box. This simulation is unlike the others because there is now a restriction placed on the molecules. Once again a simplification is made in which the collisions do not cause the molecules to lose their energy. The left half of the box is filled with molecules and a partition is placed so the right half has no molecules. The partition will then be removed and the molecules will once again move randomly. The main assumption for this simulation is that the collisions between molecules are perfectly elastic so researchers do not have to deal with the complicated effects of molecules that may have resorted to the edges of the walls or how rough the walls are to begin with.

The final simulation demonstrates the diffusion of molecules between two boxes that are connected by a pipe. The area is therefore reduced in this simulation yet the concentration remains constant. As before, the molecules will move randomly and they will lose no energy when bounced against another molecule. An assumption included in this simulation is in dealing with the pipe, entrance region effects are therefore ignored to allow simplicity once again.

Results:

The following graphs are representative data collected from :

Simulation #!:

Figure 1-Path of the Particle

Figure 2-Distance from Origin vs. Time

Figure 1 simulates the path of a single molecule through several hundred time steps and collisions. Figure 2 represents the random motion of a molecule from its origin.

Simulation #2:

Figure 3-Position of Molecules at the End of Simulation

Figure 4-Mean Distance From Origin vs. Time

Figure 5- Distance of Molecules of Several Groups vs.

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