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We study the active flow around isolated defects and the self-propulsion velocity of + 1 / 2 defects in an active nematic film with both viscous dissipation (with viscosity η ) and frictional damping Γ with a substrate. The interplay between these two dissipation mechanisms is controlled by the hydrodynamic dissipation length ℓ d = η / Γ that screens the flows. For an isolated defect, in the absence of screening from other defects, the size of the shear vorticity around the defect is controlled by the system size R . In the presence of friction that leads to a finite value of ℓ d , the vorticity field decays to zero on the lengthscales larger than ℓ d . We show that the self-propulsion velocity of + 1 / 2 defects grows with R in small systems where R < ℓ d , while in the infinite system limit or when R ≫ ℓ d , it approaches a constant value determined by ℓ d .
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The role of fluid flow in the dynamics of active nematic defects
Abstract We adapt the Halperin–Mazenko formalism to analyze two-dimensional active nematics coupled to a generic fluid flow. The governing hydrodynamic equations lead to evolution laws for nematic topological defects and their corresponding density fields. We find that ±1/2 defects are propelled by the local fluid flow and by the nematic orientation coupled with the flow shear rate. In the overdamped and compressible limit, we recover the previously obtained active self-propulsion of the +1/2 defects. Non-local hydrodynamic effects are primarily significant for incompressible flows, for which it is not possible to eliminate the fluid velocity in favor of the local defect polarization alone. For the case of two defects with opposite charge, the non-local hydrodynamic interaction is mediated by non-reciprocal pressure-gradient forces. Finally, we derive continuum equations for a defect gas coupled to an arbitrary (compressible or incompressible) fluid flow.
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- Award ID(s):
- 1938187
- PAR ID:
- 10310108
- Date Published:
- Journal Name:
- New Journal of Physics
- Volume:
- 23
- Issue:
- 3
- ISSN:
- 1367-2630
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript
- Journal Article:
- https://doi.org/10.1088/1367-2630/abe8a8
