In the present paper, we propose new equations describing the fluid behavior in nanochannels with its molecular structure. We consider the Poiseuille flow and the flow throw the channel with vibrating walls. The obtained results show that it is possible to describe the structural transformations in thin layers by using the continuum mechanics methods. We introduce new degrees of freedom of the material by introducing the second continuum, which plays the role of the arising new phase of state. In the models considered here, the properties of the new phase are determined by the influence of rigid boundaries with a different structure.
Indeitsev, D. A., Abramyan, A. K., & Semenov, B. N. (2012). Vibration Control of a Fluid in Micro- and Nanotubes. In Advanved Dynamics and Model-Based Control of Structures and Machines (pp. 119-126). Springer. https://doi.org/10.1007|978-3-7091-0797-3_2