Asymmetric fluid-structure dynamics in nanoscale imprint lithography

The boundary conditions are p = 0 whenLx = ± . From the boundary2conditions, C1= 0 and26µ L dh= − . Substituting for C 1 and C 2 gives4hdtC23p parallel3 dh 2 2( x) ( x − L )= µ . [2.23]2hdt34The pressure distribution is parabolic and symmetric about ( x = 0). For parallelplates the normal damping force per unit width is simplyfL2µ L= ∫ p(x)dx = −hparallel 3−L23dhdt[2.24]From equation 2.24, it is observed that the fluid layer generates large1damping forces that scale as and is directly proportional to both the approach3hvelocity of the template and the viscosity of the fluid.2.3.3 Squeeze Film Due to an Inclined Surface of Infinite WidthIn the case of a flat, inclined plate approaching a surface, the height of theplate relative to the surface it approaches varies linearly along the x direction.The template geometry and flow profile are shown in Figure 2.5. The gap height∂h2= and = hD+ xθD sec θ .∂tis h( t, x) hx = h() t + x tanθ() t29