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We report a method to predict equilibrium concentration profiles of hard ellipses in nonuniform fields, including multiphase equilibria of fluid, nematic, and crystal phases. Our model is based on a balance of osmotic pressure and field mediated forces by employing the local density approximation. Implementation of this model requires development of accurate equations of state for each phase as a function of hard ellipse aspect ratio in the range k = 1–9. The predicted density profiles display overall good agreement with Monte Carlo simulations for hard ellipse aspect ratios k = 2, 4, and 6 in gravitational and electric fields with fluid–nematic, fluid–crystal, and fluid–nematic–crystal multiphase equilibria. The profiles of local order parameters for positional and orientational order display good agreement with values expected for bulk homogeneous hard ellipses in the same density ranges. Small discrepancies between predictions and simulations are observed at crystal–nematic and crystal–fluid interfaces due to limitations of the local density approximation, finite system sizes, and uniform periodic boundary conditions. The ability of the model to capture multiphase equilibria of hard ellipses in nonuniform fields as a function of particle aspect ratio provides a basis to control anisotropic particle microstructure on interfacial energy landscapes in diverse materials and applications.
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This content will become publicly available on December 1, 2025
The fall of an ellipse in a stratified fluid
The free fall of an ellipse in an infinite linearly-stratified fluid is investigated using a linear two-dimensional, Boussinesq, diffusionless, inviscid model. The oscillations of the ellipse decay because of radiation damping, but unlike the case of a circular cylinder, the ellipse can also rotate and move horizontally. The resulting equations are solved analytically for some simple cases for which there is little or no rotation. Motions with rotation are studied numerically using a spectral method to solve for the wave field in the fluid.
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- Award ID(s):
- 0133978
- PAR ID:
- 10559312
- Publisher / Repository:
- Institute of Physics
- Date Published:
- Journal Name:
- Fluid Dynamics Research
- Volume:
- 56
- Issue:
- 6
- ISSN:
- 0169-5983
- Page Range / eLocation ID:
- 061402
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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