Saddle-splay elasticity and interfacial nematostatics.

Area of Science:

• Physics
• Materials Science
• Soft Matter Physics

Background:

• Classical liquid crystal physics provides foundational equations for interfacial phenomena.
• Interfacial statics equations like Laplace-Young and Marangoni force equations lack explicit static saddle-splay terms.
• Saddle-splay elasticity is a key gradient surface elasticity in liquid crystals.

Purpose of the Study:

• To derive generalized force balance equations for nematic liquid crystal (NLC) and isotropic fluid (I) interfaces.
• To elucidate the specific contributions of saddle-splay elasticity to interfacial force balance equations.
• To provide exact expressions for static saddle-splay terms in the Laplace-Young and Marangoni force equations.

Main Methods:

• Utilizing classical liquid crystal physics equations.
• Applying gradient surface elasticity principles, specifically saddle-splay elasticity.
• Deriving generalized static and dynamic force balance equations for NLC/I interfaces.

Main Results:

• Identified congruent tensorial order and functional forms for saddle-splay and interfacial tension contributions.
• Established that interfacial tension must be renormalized by saddle-splay energy.
• Derived exact expressions for pressure jumps and tangential Marangoni force, including saddle-splay induced distortion stresses.

Conclusions:

• Generalized interfacial equations for nematostatics by including saddle-splay energy.
• Saddle-splay elasticity introduces distortion stresses affecting tangential Marangoni force.
• Results are applicable to nematocapillarity phenomena like wetting, spreading, and thin film mechanics.