In this study, the effects of finger roughness on the electrostatic potential, electrostatic field, and average effective squeezing pressure between a human finger and a touchscreen are calculated by the perturbation method. This theory is an extension of an earlier work by Persson. It is found that an additional potential <ϕ⁽²⁾> will appear between the solids when the roughness effect is considered in calculating the perturbation potential. This additional potential is still proportional to the distance ū from the bottom surface. Therefore, the effect of the roughness increases the effective potential <ϕ> between the two solids. As a result, the average electrostatic field and average effective squeezing pressure increase. Using the increased effective squeezing pressure, we obtain the contact area, average surface separation, and friction between a human finger and the surface of a touchscreen. The effect of the roughness of the finger skin on the increased average effective squeezing pressure (electroadhesion) increases the contact area and reduces the average surface separation between the finger skin and touchscreen. Therefore, the finger-touchscreen friction increases. The surface topography for the forefinger skin is also measured by atomic force microscopy to obtain more realistic results. The auto spectral density function for the forefinger skin surface is calculated as well.

在这项研究中，通过摄动法计算了手指粗糙度对人的手指与触摸屏之间的静电势，静电场和平均有效挤压压力的影响。该理论是Persson早期工作的延伸。发现在计算扰动电势时考虑了粗糙度效应时，在固体之间会出现一个额外的电势ϕ ^（2） >。该附加电势仍然与距底表面的距离ü成比例。因此，粗糙度的效果增加了有效电位< φ>在两个实体之间。结果，平均静电场和平均有效挤压压力增加。使用增加的有效挤压压力，我们可以获得人的手指与触摸屏表面之间的接触面积，平均表面分离以及摩擦。手指皮肤粗糙度对增加的平均有效挤压压力（电粘附）的影响会增加接触面积，并减少手指皮肤与触摸屏之间的平均表面分离。因此，手指触摸屏的摩擦增加。食指皮肤的表面形貌也可以通过原子力显微镜进行测量以获得更真实的结果。还计算了食指皮肤表面的自动光谱密度函数。