Mechanics of active surfaces.

Area of Science:

• Physics
• Materials Science
• Biophysics

Background:

• Active processes at surfaces are crucial in biological systems (e.g., cell cortex, epithelial tissues) and engineered materials.
• Existing theories often lack a fully covariant framework to describe these dynamic surface phenomena.

Purpose of the Study:

• To establish a covariant theory for the mechanics of active surfaces.
• To provide a framework for studying active biological and chemical surface phenomena.
• To identify and characterize active terms and their influence on surface properties and instabilities.

Main Methods:

• Derivation of force balance conditions for surfaces under active forces and torques.
• Analysis of symmetry breaking in surfaces with in-plane rotational symmetry.
• Formulation of linear constitutive relations satisfying Onsager relations.
• Renormalization of passive surface properties (bending modulus, spontaneous curvature, surface tension) by active terms.

Main Results:

• Introduced forces and torques acting on surfaces within a covariant framework.
• Demonstrated that surfaces can exhibit broken up-down, chiral, or planar-chiral symmetries.
• Showed active terms renormalize passive surface properties.
• Identified novel active terms not present in passive theories.
• Discussed shape instabilities driven by active surface processes.

Conclusions:

• The derived theory offers a comprehensive framework for active surface mechanics.
• Active processes significantly renormalize passive surface properties and can induce shape instabilities.
• The theory is applicable to diverse systems, from biological tissues to reconstituted active matter.