Estimation of critical number of hydrogen bubbles for critical current density using the dry spot model

•A critical current density (CCD) model is proposed, which envisages the CCD mechanism.•Resemblance of CCD to critical heat flux (CHF) was revealed by nucleation characteristics.•Critical number of bubbles is estimated by utilizing the dry spot model for the CHF.•The critical number is six and thus, hexagonal bubble packing is envisaged at the CCD.•The CCD can be considered as the mini-CHF due to small bubbles and rich nucleation sites. The hydrogen evolving system has an upper operation limit called critical current density (CCD), where electrochemically generated hydrogen bubbles form hydrogen film on the surface just like the critical heat flux (CHF) in the boiling system. With aim of proposing a model envisaging the hydrogen bubble configuration, ‘insulated spot model’ is proposed by applying the dry spot model for the CHF using 1.5 M of sulfuric acid electrolysis system. Critical number of bubbles at the CCD is estimated by the insulated spot model. Nucleation characteristics of the present electrolysis system are applied and then the critical number of bubbles is calculated as 6, which predicts measured CCD with error of 7.4%. Accordingly, a hexagonal packing structure is envisaged for the hydrogen bubble configuration. It is concluded that the CCD phenomenon is dominated by the hydrodynamic behavior, similar to the CHF and it can be regarded as a miniature CHF.