Dear All,
Coagulating (aggregating, coalescing) systems surround us. Gravitational accretion of matter, blood coagualtion, traffic jams, food processing, cloud formation - these are all examples of coagulation and we use the effects of these processes every day.
From a statistical physics point of view, to have full information on aggregating system, we shall have information on its cluster size distribution (number of clusters of given size) for any moment in time. However, surprisingly, having such information for most of the (real) aggregating systems is very hard.
An example of the aggregating system for which observing (counting) cluster size distribution is feasible is the so-called electrorheological fluid (see https://www.youtube.com/watch?v=ybyeMw1b0L4 ). Here, we can simply observe clusters under the microscope and count the statistics for subsequent points in time.
However, simple observing and counting fails for other real systems, for instance:
- Milk curdling into cream - system is dense and not transparent, maybe infra-red observation could be effective?
- Blood coagulation - the same problem, moreover, difficulties with accessing living tissue, maybe X-ray could be used but I suppose that resolution could be low; also observation shall be (at least semi-) continuous;
- Water vapor condensation and formation of clouds - this looks like an easy laboratory problem but I suppose is not really the case. Spectroscopic methods allow to observe particles (and so estimate their number) of given size but I do not know the spectroscopic system that could observe particles of different (namely, very different: 1, 10, 10^2, ..., 10^5, ...) sizes at the same time (?);
- There are other difficulties for giant systems like cars aggregating into jams on a motorway (maybe data from google maps or other navigation system but not all of the drivers use it) or matter aggregating to form discs or planets (can we observe such matter with so high resolution to really observe clustering?).
I am curious what do you think of the above issues.
Do you know any other systems where cluster size distributions are easily observed?
Best regards,
Michal
I would do much of the problems you have pointed out by doing angularly resolved laser/X-ray scattering ( I am not talking about cars or planetary clusters here - this is an image processing issue/problem, maybe coupled to AI software). For physical (micron, nanometer systems), from the angular distribution, you can determine the statistical distribution of scatterers (clusters, aggregations, droplets) in the scattering volume. You can do it yourself in Matlab, or using available software. i.e. Mie. Another possibility they do is X-ray diffraction for single particles/molecules, etc, where you have information about single scatterers, not necessarily symmetrical, with nanometer resolution, but I guess you are interested in statistical processes. Hope this helps.
Dynamic Light Scattering (DLS) measures particle size in solution from below 1 nm to 10 µm, providing a size distribution as output.
Ultrasound attenuation spectroscopy can measure the cluster size distribution in colloidal suspensions, and this technique should be able to measure cluster size distribution during processes such as blood coagulation and milk curdling. In the article Article Use of Ultrasound Attenuation Spectroscopy to Determine the ...
authors have used this technique to measure the equivalent spherical diameter of tectoids in aqueous clay suspensions and used this information to produce a distribution of aggregates as a function of aggregate size.
Dear Michal!
I want to recommend you papers of my husband)) He study aggregation of blood particals by scanning flow cytometry and also produced (I think, new and fruitfull) kinetic model for this processes. It is his profile https://www.researchgate.net/profile/Vyacheslav-Nekrasov
As I understand, key papers is
1 Brownian aggregation rate of colloid particles with several active sites
2 Kinetic turbidimetry of patchy colloids aggregation: latex particles immunoagglutination
3 Mathematical modeling the kinetics of cell distribution in the process of ligand–receptor binding
4 Kinetics of the initial stage of immunoagglutionation studied with the scanning flow cytometer
But you can write him directly))
Best wishes, Anna
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