Gradient, chemically modified, flat surfaces enable directed transport of droplets. Calculation of apparent contact angles inherent for gradient surfaces is challenging even for atomically flat ones. Wetting of gradient, flat solid surfaces is treated within the variational approach, under which the contact line is free to move along the substrate. Transversality conditions of the variational problem give rise to the generalized Young equation valid for gradient solid surfaces. The apparent (equilibrium) contact angle of a droplet, placed on a gradient surface depends on the radius of the contact line and the values of derivatives of interfacial tensions. The linear approximation of the problem is considered. It is demonstrated that the contact angle hysteresis is inevitable on gradient surfaces. Electrowetting of gradient surfaces is discussed.

经过梯度化学修饰的平坦表面可实现液滴的定向运输。即使对于原子平面的表面，梯度表面固有的视在接触角的计算也具有挑战性。在变型方法中处理倾斜的平坦固体表面的润湿，在该方法下，接触线可沿基材自由移动。变分问题的横向条件产生了适用于梯度固体表面的广义杨氏方程。放置在倾斜表面上的液滴的视在（平衡）接触角取决于接触线的半径和界面张力的导数的值。考虑问题的线性近似。证明了在倾斜表面上不可避免的接触角滞后。讨论了梯度表面的电润湿。