With improvements in measuring techniques such as AFM, confocal microscopy and SEM, researchers were able to produce and image droplets at ever smaller scales. With the reduction in droplet size came new experimental observations of wetting. These observations confirm that the modified Young’s equation does not hold at the micro-nano scales. In addition the sign of the line tension is not maintained through the modified Young’s equation.
For a sessile droplet, the free energy of the three phase system can be expressed as:
At constant volume in thermodynamic equilibrium, this reduces to:
Usually, the VdP term has been neglected for large droplets, however, VdP work becomes significant at small scales. The variation in pressure at constant volume at the free liquid-vapor boundary is due to the Laplace pressure, which is proportional to the mean curvature of the droplet, and is non zero. Solving the above equation for both convex and concave surfaces yields:
Where the constant parameters A, B, and C are defined as:
:,  and 
This equation relates the contact angle , a geometric property of a sessile droplet to the bulk thermodynamics, the energy at the three phase contact boundary, and the curvature of the surface α.  For the special case of a sessile droplet on a flat surface (α=0),
The first two terms are the modified Young’s equation, while the third term is due to the Laplace pressure.  This nonlinear equation correctly predicts the sign and magnitude of κ, the flattening of the contact angle at very small scales, and contact angle hysteresis.