Metallic zinc-based alloys are being extensively investigated for potential use in medicine for the fabrication of implants via additive manufacturing technologies. A mathematical model for zinc electro-extraction from a 20% sodium hydroxide solution is proposed. The initial–boundary–value problems for charged-particle transport that describe the electrolysis processes possess several features that complicate their numerical solution. Was developed and proposed a modification of the streamline-sweep method, suitable for the charged-particle transport problem in an electrolyte when a convective term and variable coefficients are present. This method computes the charged-particle flux at the same time as the primary solution. This approach avoids the large errors that occur when flux is obtained by numerically differentiating the solution. The algorithm was verified by comparison with experimental data and with the results of solving a one-dimensional kinetic problem at the electrode. The one-dimensional model treats both diffusive and drift fluxes more accurately than the kinetic model. As a result, the initial-stage discrepancy between experimental data and computed results was cut by 50%.