friction presentation march
- 1. Hydrodynamic Damping of Collective Motion in a Quasi-Two-Dimensional Dense Colloidal Particle Suspension Michael Ryan Undergraduate Student West Chester University Kevin Aptowicz West Chester University Arjun Yodh Tim Still University of Pennsylvania
- 2. Background Hydrodynamic properties of colloidal system are not the same as atomic crystal “Colloidal Crystal” Atomic Crystal Hydrodynamic forces Shared electrons Friction of surrounding water No analogous form A.M. Alsayed, M.F. Islam, J. Zhang, P.J. Collings, and A.G. Yodh, “Premelting at defects within bulk colloidal crystals,” Science 309, 1207-1210, (2005)
- 3. System: 2D Colloidal Crystal Densely packed PNIPAm particles sandwiched between two coverslips 5 μm Spheres are soft (deformable)
- 4. Video Microscopy (Sped up 30x) 5 μm • 1500-3000 particles • 1770 normal modes • 1000 fps Low frequency mode High frequency mode We analyze video and compute eigenvectors Previous work using this method: Chen et al., PRL, 2010; Kyay et al., Science, 2010; A. Ghosh et al., PRL, 2010
- 5. Mode Dynamics Displacement(Pixels) Time (s) Histogram of mode: Displacement (Pixels) m k T, γ Lag time (s) AutocorrelationofDisplacement We know: k, m, T. We can find: γ
- 6. Mode Number Displacement Histogram Autocorrelation 14 1000 1500 Dynamics of Multiple Modes Lag Time (s) Lag Time (s) Lag Time (s) Displacement (px) Displacement (px) Displacement (px)
- 7. qa Springconstant(kBT/μm2) qa DecayTime(s) qa Frictioncoff.(kBTs/μm2) Longitudinal Still et al., Phys. Rev. E, 2014 Main Result Transverse (Averaged over all q-vector directions)
- 8. A Similar System Baumgartl et al., Soft Matter, 2008 Baumgartl et al. Our System Sphere Type Polystyrene PNIPAm Interaction Method Charged spheres Mechanical
- 9. Experimental Stokes Law Friction* (~15.5 kBTs/μm2) Conclusions qa Frictioncoff.(kBTs/μm2) P(D) = 1 2ps 2 e -D2 2s 2 s = 2kBTt g Plot by Baumgartl et al: Longitudinal Transverse * Nakroshis et al., American Journal of Physics, 2003 Longitudinal Transverse Unlike Baumgartl et al., our friction coefficient does not appear to vanish.
Editor's Notes
- #2: Hi, my name is Michael Ryan, I’m an undergraduate at West Chester University working on finding the friction coefficient of a dense 2D colloidal crystal.
- #4: The kind of colloidal crystal I am working with is PNIPAM particles sandwiched between two coverslips. Observed through a microscope, one of mine looks like this picture. I take pretty long video of 1500-3000 particles, about 100 seconds at 1000 frames per second.
- #5: The motion of the colloidal crystal is dependent on the temperature of the system; as it increases, the particles shrink and move with thermal motion. Using particle tracking and IDL, I can create a covariance matrix and use it to find eigenmodes and eigenvectors of the system.
- #6: 3rd mode
- #7: i=12, 999,1699 These are three modes out of the 2248 for the section of the video I analyzed. Lower modes look fairly Gaussian, but curve fitting seems to default to overdamped for even the lowest modes. The reason for this is unclear, but it remains possible that all modes may be overdamped.
- #9: A paper in Soft Matter also created a crystal, but with an interference pattern to hold them in their lattice and with charged spheres. The paper determined the friction coefficient of these spheres and approximated that the dynamics of normal modes would be overdamped; in other words, the expected shape of the autocorrelation function should decay exponentially for all modes.
- #10: Black is longitudinal