Deformation of a tensile membrane adjacent to a moving wall caused by viscous flow

Theoretical analysis is done for deformation of a tensile membrane caused by viscous flow between the membrane and a solid boundary (wafer) placed adjacent to the membrane. The membrane and its support are assumed to have circular shapes. The boundary is assumed to move perpendicularly to the membrane by a small fraction of the gap width. The Hele–Shaw flow theory is applied to the flow. Variation of the central gap width is obtained, and it is shown that the maximum membrane deformation depends on the membrane tension and the final gap width. The dependence agrees with experimental results.