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c dissolved species concentration [mol m−3] D diffusion coefficient [m2 s−1] m Co 2 + SLM $$ {m}_{{\mathrm{Co}}^{2+}\ \mathrm{SLM}} $$ mass transfer rate of Co2+ at lumen–SLM interface [mol m−2 s−1] pKa molar logarithmic dissociation constant Re Reynolds number S source term for convection–diffusion equation [mol m−3 s−1] u fluid velocity [m s−1] INTRODUCTION Given the high value of key lithium-ion battery components cobalt and nickel, it is becoming apparent that after all possible use as...

DATA AVAILABILITY STATEMENT The data supporting the findings of this study are included within the manuscript and are available only in this version. No additional data are available beyond what is presented.

Ceramic membranes offer considerable promise for future industrial applications due to their superior chemical, mechanical, and thermal stabilities, resistance to harsh operating conditions, and long-term operating processes. However, several bottlenecks still limit their commercial scale-up in filtration and separation applications, including brittleness, the high costs of conventional ceramic materials, and fouling.