Authors: R.H. Nilson, S.K. Griffiths
Affilation: Sandia National Laboratories, United States
Pages: 257 - 260
Keywords: nanoporous, hierarchical, transport, nanofluidics, optimization, multiscale
Hierarchical nanoporous materials afford the opportunity to combine the high surface area and functionality of nanopores with the superior charge/discharge characteristics of wider transport channels. In the present paper we optimize the apertures and spacing of a family of transport channels that provide access to a surrounding nanoporous matrix during recharge/discharge cycles of materials intended for storage of gas or electric charge. A diffusive transport model is used to describe alternative processes of viscous gas flow, Knudsen gas flow, and ion diffusion. The coupled transport equations for the matrix and transport channels are linearized and solved analytically for a periodic variation in external gas pressure or ion density using a separation-of-variables approach in the complex domain. Based on these solutions, channel apertures and spacing are optimized to achieve maximum inflow/outflow from the functional matrix material for a fixed system volume. Results are strongly influenced by the relationship between channel aperture and effective transport diffusivity. For a weak dependence, optimal apertures and spacing increase more rapidly with system scale, reducing the maximum attainable transport efficiency. In all cases considered, optimized Fourier numbers associated with matrix and channel transport are of comparable magnitude, providing a basis for formulating simplified material design rules.