Lab 8

Lab 8: Diffusion and Brownian Motion (Makeup) Part 1: Diffusion Methods My goal was to observe the diffusion of dye in water and assess the behavior and causes of different motions of the dye within the water. To do so I filled a large beaker about 2/3 full of water and dropped three drops of dye and observed its motion. My expectation was for the dye to drift downward to the bottom of the beaker and then disperse upward after bouncing off the bottom and take several minutes to diffuse. I observed for two minutes and witnessed all the categories of motion, I saw the motion of dye caused by gravitational force downward, the motion resulting from the initial velocity imparted when squeezed out of the dropper, and from random currents in the fluid. Data Image 1 shows the first motion present due to initial velocity which was found to have a magnitude on the order of 1 second. Image 2 shows the second motion present due to gravity which was found to have a magnitude on the order of 10 seconds. Image 3 shows the final motion present due to random currents in the fluid which was found to have a magnitude on the order of 100 seconds. I observed a quick descent of the dye due to the initial velocity shortly followed by a longer period allowing gravity to act on the dye until gravity had acted upon it and the dye started to drift randomly through the fluid for quite some time. Conclusion Overall, I found that the diffusion of the dye in the water is dominated by random motion, and then it is followed by gravitational force and initial velocity. What was observed differed from what I predicted; the dye started to drift randomly before all the dye reached the bottom. Ultimately, the diffusion of the dye inside the container is based mostly upon the random motion inside the matter. For future iterations, I will repeat this experiment with more trials to determine if these findings hold. Part 2: Brownian Motion Methods My goal for this portion of the lab was to view particles at a microscopic level and discern if the particle motions are random. I predicted that it would be most closely associated with random motion. To do so I prepared a microscope slide by using a plastic pipette and the water provided

in a beaker, I placed the drop in the middle of the slide, then carefully picked up a needle, dipped the tip of the needle into the evaporated milk and pulled it out, leaving a very tiny droplet of milk. I touched the needle to the droplet of water on the slide so that the milk disperses into the droplet. Then carefully dropped a microscope slide on top. I then observed the slide on the microscope platform, turned the light on, and toggled the lenses to the magnification of 40x and focused the image. With the help of the microscope camera, I used “Swift Imaging” to see the collection of milk globules bouncing around in the water. Before I began collecting and analyzing the data, I predicted the movement of the particle would have random motion. I then collected data by using the “draw arrow annotation” button to measure the displacement of the globule I focused on and timing each increment with a stopwatch in my hand. Image 4 shows the Swift Imaging with the measured displacement. Data The stopwatch had an analog systematic uncertainty of +/- 0.01 seconds. I measured the globule for a total of 51.03 +/- 0.01 seconds and found it to have a displacement of 1286.86 +/- 0.01 pixels while using seven different data points. To determine which motion, random, constant velocity, or accelerated, the particles were most closely associated with I graphed my data and compared the data to the equations. The equation for Brownian motion is x = c √ t . The equation for velocity motion is x = v average t . The equation for accelerated motion is x = 1 2 at 2 . Chart 1 shows the graph for constant velocity motion. Chart 2 shows the graph for Brownian motion. Chart 3 shows the graph for accelerated motion. I formed linear regression lines by using the time variable to be used as t, t2, or √ t to find out which motion I was most likely viewing. Once I was able to plot the linear regressions and observe its R 2 value, I found that constant velocity motion produced the R 2 value closest to 1. Conclusion I found that the particles motion most closely reflected that of constant velocity motion. This proved my prediction false.

Image 4 Chart 1 4 5 6 7 8 9 10 11 0 50 100 150 200 250 300 350 400 f(x) = 25.72 x R² = 0.95 Constant Velocity Motion T (seconds) Displacement (Pixels)

Chart 2 2 2.2 2.4 2.6 2.8 3 3.2 3.4 0 50 100 150 200 250 300 350 400 f(x) = 70.7 x R² = 0.92 Random Motion √? (seconds) Displacement(pixels) Chart 3 0 20 40 60 80 100 120 0 50 100 150 200 250 300 350 400 f(x) = 2.98 x R² = 0.94 Accelerated Motion T2 (seconds) Displacement (Pixels)