Energy conversion efficiency in electro-hydrodynamic transport of viscoelastic fluids through hydrophobic surfaces in soft nanofluidic channels

The present article deals with the electro-hydrodynamic energy conversion efficiencies of a viscoelastic fluid through a charge-dependent hydrophobic surface in a soft nano-fluidic channel under combined effects of an applied harmonic pressure gradient and a uniform heat flux boundary. The ion partitioning effect appears due to the dissimilarity in the dielectric constant between the electrolyte and the polyelectrolyte layer (PEL) region, which influences the reshaping of ion distribution by integrating the Born energy. Using the induced potential distribution for the situation of low surface charge density, analytical expressions for the streaming potential and corresponding energy conversion efficiency are established in this study. The semi-analytic solution for the temperature distribution is presented, and the corresponding Nusselt number is calculated in this study. The energy conversion efficiency is found to be strongly influenced by both the ionic Peclet number and the permittivity ratio among the PEL and electrolyte regions. An increase in the permittivity variation between the PEL and the electrolyte layer leads to an enhancement in the energy conversion efficiency. The energy conversion efficiency increases with the bare slip length for a soft charged nanochannel under fully absorbed surface conditions and reaches a constant value at higher bare slip lengths. Our analysis demonstrates how ion partitioning and charge-dependent hydrophobic surfaces influence the energy conversion efficiency due to their critical interplay between fluid rheology and ion transport phenomena.