We derive a fully covariant theory of the mechanics of active surfaces. This theory provides a framework for the study of active biological or chemical processes at surfaces, such as the cell cortex, the mechanics of epithelial tissues, or reconstituted active systems on surfaces. We introduce forces and torques acting on a surface, and derive the associated force balance conditions. We show that surfaces with in-plane rotational symmetry can have broken up-down, chiral, or planar-chiral symmetry. We discuss the rate of entropy production in the surface and write linear constitutive relations that satisfy the Onsager relations. We show that the bending modulus, the spontaneous curvature, and the surface tension of a passive surface are renormalized by active terms. Finally, we identify active terms which are not found in a passive theory and discuss examples of shape instabilities that are related to active processes in the surface.
ABSTRACT
PUBLICATION RECORD
- Publication year
2017
- Venue
Physical Review E
- Publication date
2017-01-31
- Fields of study
Medicine, Physics
- Identifiers
- External record
- Source metadata
Semantic Scholar, PubMed
CITATION MAP
EXTRACTION MAP
CLAIMS
CONCEPTS
- active surfaces
Surfaces on which active biological or chemical processes generate mechanical effects and are treated within the surface theory.
Aliases: surface activity
- active terms
Contributions to the surface equations that arise from active processes rather than passive elasticity alone.
Aliases: activity terms
- bending modulus
The elastic parameter controlling resistance to bending of the surface.
Aliases: bending rigidity
- chiral symmetry
A handedness-related symmetry class describing structures that are not superimposable on their mirror image.
Aliases: chirality
- covariant theory
A formulation written so that the mechanical laws retain their form under surface-coordinate changes.
Aliases: fully covariant framework
- entropy production
The rate at which irreversible processes generate entropy in the active-surface description.
Aliases: rate of entropy production
- force balance conditions
Equations expressing mechanical equilibrium of forces acting on the surface.
Aliases: force balance
- in-plane rotational symmetry
Symmetry of the surface under rotations within the tangent plane.
Aliases: rotational symmetry in the surface plane
- linear constitutive relations
Linear relations connecting thermodynamic fluxes and forces in the surface mechanics model.
Aliases: constitutive relations
- onsager relations
Reciprocity constraints on the coefficients appearing in linear irreversible thermodynamics.
Aliases: Onsager reciprocity
- planar-chiral symmetry
A mirror-asymmetric symmetry class for structures that are chiral within the surface plane.
Aliases: planar chirality
- shape instabilities
Instabilities in which the surface shape becomes unstable to deformation modes.
Aliases: morphological instabilities
- spontaneous curvature
The preferred curvature encoded by the surface's local elastic description.
Aliases: preferred curvature
- surface tension
The in-surface tension parameter governing isotropic stretching or contraction.
Aliases: tension
- torque balance conditions
Equations expressing mechanical equilibrium of torques acting on the surface.
Aliases: torque balance
- up-down symmetry
Symmetry under reversal of the surface normal or exchange of the two sides of the surface.
Aliases: top-bottom symmetry
REFERENCES
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