Surface integration approach: a new technique for evaluating geometry dependent forces between objects of various...

Area of Science:

• Physics
• Physical Chemistry
• Materials Science

Background:

• Calculating interaction forces between macroscopic bodies and surfaces is crucial in fields like colloid science and nanotechnology.
• Existing approximations, such as the Derjaguin approximation, have limitations in scope and accuracy for complex geometries.

Purpose of the Study:

• To develop a generalized method for exact calculation of interaction forces between arbitrary 3D bodies and a half-space.
• To derive specific force expressions for various interaction potentials and object shapes, including biologically relevant ones.

Main Methods:

• Generalization of the Derjaguin approximation to provide exact force calculations.
• Application of the method to Lennard-Jones, standard van der Waals, and retarded (Casimir) interactions.
• Derivation of analytical expressions for forces involving ellipsoids, tori, and generalized Cassini ovals interacting with half-spaces or slabs.

Main Results:

• Exact analytical expressions for interaction forces were derived for a range of potentials and geometries.
• The method accommodates complex shapes, including a red blood cell mimic, and various separation media (gas, liquid, vacuum).
• Demonstrated applicability to interactions between biological objects and plate-like substrates.

Conclusions:

• The presented generalized approach offers a powerful and exact tool for calculating inter-body forces.
• This method expands the capabilities for modeling interactions involving complex shapes in diverse physical and biological systems.
• The derived formulas provide precise quantitative insights into nanoscale and macroscopic interactions.