First vs. second gradient of strain theory for capillarity effects in an elastic fluid at small length scales

Mindlin [22] wrote a milestone paper claiming that a second strain gradient theory is required for a continuum description of volume cohesion and surface tension in isotropic elastic media. The objective of the present work is to compare Mindlin’s approach to more standard capillarity models based on a first strain gradient theory and Korteweg’s equation. A general micromorphic model is then proposed as a numerical method to implement Mindlin’s theory in a finite element code.