Nanoscale and Microscale Phenomena by Yogesh M. Joshi & Sameer Khandekar

Author:Yogesh M. Joshi & Sameer Khandekar
Language: eng
Format: epub
Publisher: Springer India, New Delhi

3.1.2 Single Newtonian Falling Film: Neo-Hookean Solid

In the preceding section, we presented the long-wave asymptotic analysis considering the deformable solid layer as a linear viscoelastic medium. In this section, we represent the dynamics of deformable solid medium by a more accurate nonlinear neo-Hookean model. The governing equations are reported in Sect. 2.1.5 (Eqs. 35–37) and conditions at LS interface are Eqs. 41–44. The underlined terms in these equations are the additional coupling terms between the base state and perturbations which are present because of nonlinear neo-Hookean constitutive relation. We demonstrate that these additional terms remain absent in the long-wave limit and hence, the instability suppression predicted by the linear model in low-k limit holds for a more accurate neo-Hookean model as well. The scalings for fluid variables, governing equations for the liquid layer and conditions at GL interface, remain identical as presented in the previous section. Thus, , and and expansions 57–59 holds. Similarly, we set , and this implies that and according to solid continuity (Eq. (35)) and x–momentum balance (Eq. 36), respectively. If we expand the solid variables according to the scalings mentioned above, the following equations govern the leading-order continuity and momentum balance for neo-Hookean viscoelastic solid:

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