User:Brian P. Josey/Notebook/2010/06/03

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Needles and Droplets

I had a good talk with Koch yesterday about my salad dressing project, and he pointed me in the direction of some good ideas. I'm hoping to work through all of them today and tomorrow to let them gel over the weekend. He pointed out that one lab group, Weitz over at Harvard, where able to isolate enzymes and essentially run a PCR in a droplet. Really cool stuff, so I'm going to look up what they did to see if I can apply their idea to the ferritin. Another idea was one that he was working on while at Sandia, using vitrotubes with microtubules, and see if it would work. I'm also going to look into what I can expect if I magnetize a piece of wire, or a needle and put it directly into a flow cell.

Non-Spherical Droplets

The first paper that I found and my spring board is "Droplet Microfluidics for Fabrication of Non-Spherical Particle" by Shum et al out of the Weitz lab. The paper was motivated by the desire to find a way to create colloidal scale droplets that did not have a spherical shape, which is the most common due to surface tension's strong tendency to form spheres. By adjusting the chemicals on a surface of the droplets, the authors were able to create zigzag and boat shaped structures composed out of the single droplets.

The authors then continue to outline and explain several different approaches to creating non-spherical particles, many of which are creative, and have obvious uses. They did mention how the packing density can be modified from the flow rate of the microfluidics tube that they used, which I found the most interesting. For me, I am interested in modifying the density of ferritin in a droplet, and the most sophisticated idea I have is simply altering the density by either evaporation on dilution. They did not expand on it.

A Keeper

Looking through the Weitz lab publication page I manage to find another paper that has helped me out a great deal. It is Magneto-mechanical mixing and manipulation of picoliter volumes in vesicles by Franke et al. In it, they describe a process where they use superparamagnetic beads to stir the contents of a vacuole. While their approach is simple, it does confirm some of my own ideas.

They use a similar equation to measure the force and balance it with Stoke's equation, without altering it for any change in shape of the vacuole. Their modified equation for the force is:

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle F = \frac {V \Delta \chi} {\mu_0} (\vec B \cdot \nabla )\vec B\, }

Where:

  • V is the volume
  • Δχ is the change in suseptability between the bead and water
  • μ0 is the magnetic constant
  • B is of course the magnetic field

They then showed that the potential energy, U, can be expressed as:

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle U = \frac {m^{2}} {2 \pi \mu_0} \frac {1} {l^{3}} = \frac {\mu_0} {2 \pi} V^{2} M^{2} \frac {1} {l^{3}} \, }

Where:

  • m is the magnetic moment of a single bead
  • l is the distance between the two beads
  • M is the net magnetization

From that the force can be calculated as:

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle F = - \frac {\partial U} {\partial l} }

The most interesting part however is the structure that the superparamagnetic beads create when they are under a magnetic field. The arrange themselves in lines, so that their magnetic moments are aligned, but there is spacing between adjacent lines. Intuitively, this was how I imagined it preparing my calculations, but it is gratifying to see someone else doing the something similar and getting the same results.