Following the usual approach in contact mechanics [21], we assume that the contact pair is formed by the deformed boundary γl and its projection on the rigid surface denoted by Pðγl Þ. Now, there is some freedom in choosing the domain on which the Reynolds equation is formulated. One can assume S ¼ γl , or S ¼ Pðγl Þ, or more generally S ¼ Pα ðγl Þ, where Pα ðγl Þ is an inter- mediate surface with parameter α defining its position between γl and Pðγl Þ, such that