|1||Started reading up on confocal microscopy. The following page was particularly useful: http://www.physics.emory.edu/faculty/weeks//confocal/.|
Made new (more concentrated) microsphere solutions to collect better data and got more accurate results. As far as the new direction of this work is concerned, I narowed down my work to two fundamental problems that I must solve. Firstly, I need to develop a proper treatment of bidisperse solutions. Secondly, I need to develop a treatment for drifting particles. This second problem involves two approaches according to my current understanding. I need to see whether I have to fit the curve to the appropriate function to find the velocity or if I can extract enough information from the decorrelation time of the process.
|2||Did a thorough literature review while looking for details about particles drifting in the liquid, and about bidisperse suspensions. The following paper helped understand what I should expect from the analysis of a bidisperse colloidal solution: "Differential dynamic microscopy of bidisperse colloidal suspensions" by Mohammad S. Safari, Ryan Poling-Skutvik, Peter G. Vekilov and Jacinta C. Conrad. If I want to clearly observe two distinct plateau, the size of the larger particles must be atleast ten times greater than the smaller ones.The following paper has turned out to be very useful in two different ways: "Differential Dynamic Microscopy: A High-Throughput Method for|
Characterizing the Motility of Microorganisms" by Vincent A. Martinez, Rut Besseling, Ottavio A. Croze, Julien Tailleur, Mathias Reufer, Jana Schwarz-Linek, Laurence G. Wilson, Martin A. Bees, and Wilson C. K. Poon. Firstly, it includes diagrama and descriptions that illustrate the difference in the curves for diffusing and drifting particles. Secondly, it neatly describes a method to estimate the fitting paramters, A(q) and B(q), allowing us to isolate and plot f(q, delta t), which then allows us to study how it decays as a function of lag time. The number of decays in this plot tells us how many decorrelation mechanisms are at play (for example a drifting and diffusing system would show two decay mechanisms).
|3||Following the method used to estimate A(q) and B(q) by finding D at low and high delta t, I isolated the decorrelation functions. Although the decorrelation drifting spheres did show faster decorrelation than the diffusiing spheres, neither of the functions were decaying to zero. I believe that because the low frame rate of the video results in there being no plateau in D at low t, our estimation of B(q) is very poor, therefore, the estimation of A(q) must also be poor. I have returned to fitting the functions and calculating the paraemters. After this, when I plot the decorrelation functions, the show the trend that I expect, and they decay all the way to zero. |
|4||I have been working on fitting the curves for drifting spheres to the appropriate function, and the task turned out to be more difficult than I had imagined. I am now trying to fit using Mathematica, since MATLAB has been difficult to use for a complicating fitting model. Apart from that, I wrote a small program that will help me simulate the correlation functions fro diffusing and drifitng spheres, allowing me to see how the function should behave according to the percentage of spheres that are moving with a certain velocity. Update: The fitting program finally worked. I will now look at the fitting parameters to extract the velocity distribution of the particles. Update: Despite the fact that the fitting seemed to be pretty decent, the parameters are not making much sense. Most of the values for the decay time of the diffusive motion are negative. The constants related to the velocity distribution of the particles are varying a lot, while we expect them to remain constant. Wilberforce Analysis: I have made a program that simulates the motion of both coupled pendulums using the initial conditions. I will generalize it to 4 degrees of freedom on Monday morning.|
|5||It turns out that although MATLAB was fitting the curves, the fitting wasnt good enough. I removed the data that seemed to be unnesecary from the extended regions of the curves, and retained only the region uptil the beginning of the plateaus. The fitting drastically imporved and the parameters started to make sense. The percentage of drifting particles, alpha, varied close to 1, which is correct since the entire system was flowing. The camera noise term is still not constant (this has been a problem since this work started). The average velocity came out to be around 2.9um/s. I opened the video in ImageJ and manually estimated the velocity of several randomly chosen particles. These velocities varied between 2.3 and 3.1um/s, which makes me think that the estimate was pretty decent. I will now repeat the experiment with particles moving at a different velocity in order to make sure that these results really are the result of a proper implementation of this technique, and that I wasn't simply lucky. Moreover, i analyzed a video i had recorded a few months ago. I kept the relolution very low in order to get to 50 fps. The problem is that the curves were not smooth. My guess is that the small number of particles is the problem. I will now repeat this with a much more concentrated solution and try to see how much results could improve if i could work with a 50 fps video insetad of a 20 fps one. |
|6||I have realized how the fitting routine should work: 1. I identify the range of accessible frequencies. I am currently sticking to curves 60 to 160 since these curves gave time constants for Brownian motion that agreed well with the theoretical values. 2. Next, I move on to the batch-fitting program. In order to give it a good initial guess for the parameters, I open the first curve (curve 60) in Mathematica, and attempt to manually fit it to the appropriate function. I then use those parameters as the guess for my batch-fitting program on MATLAB. The program automatically updates the guess parameter as it moves on to the next curve. It turns out that this fitting routine works well for curves 60 to 110. I use the fitting parameters to estimate the average velocity of the particles. I then open the video in ImageJ, and manually track random particles over a few seconds in order to estuimate their velocities. I estimate the average velocity and compare it to the one obtained using fitting in MATLAB. The latest data I collected showed these results: Fitting -> 1.7 um/s, Manual estimation -> 1.66 um/s. Remaining issues: The value of alpha (the fraction of particles in motion) turned out to be 1.45 for the data set mentioned above, which is certainly not good enough. The variation in the velocity that the fitting parameters give is way too small. Next steps: 1. These remaining fitting issues need to be fixed so that all the parameters make physical sense. 2. I should try DDM with different sized particles. |
|7||I spent some time going over the work I had been doing before the lockdown. I regenerated the curves that I was working on to get familiar with the fitting routine again. I listed down the important points that I will mention in the report. Unfortunately, there are not too many conclusions I can make from the current analysis. However, I will describe in great detail the process that I brought me to this point and the next immediate problems that need to be solved. Although there is a major issue with one of the three fitting parameters of the velocity autocorelation function, I am confident that the parameter that gives us the average velocity is pretty close to the actual average velocity of the particles. However, before including this conclusion in the report, I need to look into one more decent data set that I have and see if I can also estimate its velocity upto a reasonable accuracy. |