Asymmetric fluid-structure dynamics in nanoscale imprint lithography

Assuming the liquid perfectly wets the surfaces of the plate and substrate,− 2γi.e., zero contact angle, the pressure at the boundary is given by p = whenhr =r b2− 2 γ 3µrbdh. Therefore B = − .3h h dt2 2( r − r )3µb dh − 2γp = [A.7]3h dt hThe force is given by the integration of the pressure in the r and θ directions2∫ ∫() rF = π rp drdθ. [A.8]0 0Integrating with respect to r and θ, the squeeze film force is thenr bF42⎛ − 3µr − ⎞b dh γrb= 2π ⎜⎟ .3[A.9]⎝ 4hdt h ⎠104