Can surface-attached bubbles serve as effective thermal insulators?

Surface-attached air bubbles are known to provide lubricating (i.e., drag reducing) benefits but their contribution to inhibiting heat transfer, whether at the size of lab-on-a-chip devices or at larger scales, is not as well understood. Here, we ask whether surface-attached air bubbles may prove useful as thermal insulators for internal and external flow. In the former case, we apply theory and numerics to study pipe/channel flow and explore scenarios where the bounding surface supplies a uniform surface heat flux (USF) vs. is maintained at a uniform surface temperature (UST). Thus do we identify a remarkable connection between the drag reduction problem and the USF thermal insulation problem, i.e. the proportional change of water temperature with bubble thickness is identical to the proportional change of drag. Also, and although our analysis is conducted in the 'perfect plastron limit', we can, e.g. by evaluating hydrodynamic and thermal slip lengths, contrast our work against related studies where heat transfer occurs through the ridges or pillars that affix the air layer in place. This comparison indicates that the oft-applied adiabatic interface assumption may prove overly restrictive in some regions of the parameter space.

The external flow problem is more delicate, mathematically-speaking, and so we limit attention to Stokes flow around an air-enveloped solid sphere of constant temperature. Key to our (matched asymptotic) analysis is to derive an expression for the Nusselt number in terms of the air layer thickness and the Peclet number of the surrounding liquid, here assumed to be water. From the resulting equation, we critically assess the solution validity, i.e. by defining the parametric range over which model predictions are consistent and reasonable.