Downloadable COMSOL (.mph) files

The microdroplet is a half-circle with a flattened bottom that is flush with a flat electrode surface. Typical microdroplet radii range from 100 nm - 2 um and the contact is usually set to 1/200th of the contact radius. 

Electroanalysis physics module was used to assign the Butler-Volmer equation to the electrode|microdroplet interface. For mass transfer limited potentials, one can instead set the concentration of the electrochemical reactant (Fo) to 0 at the surface, and the redox product (Fi) to the bulk, initial concentration of the reactant.

The follow-up enzymatic reaction is modeled by Michaelis-Menten kinetics, which is applied to the microdroplet domain. 

Please see https://doi.org/10.1073/pnas.2025726118 for the experimental system and analysis of the results.

Please see the Supporting Information file www.pnas.org/doi/suppl/10.1073/pnas.2025726118/suppl_file/pnas.2025726118.sapp.pdf for the full explanation of the model. 

A square domain represents the continuous (organic) phase. The electrode is a segment along the bottom edge of the domain that meets the left edge of the domain (the axis of symmetry). The aqueous droplet is modeled by a curve that joins the axis of symmetry and electrode surface, where the droplet geometry is easily tunable. 

The Butler-Volmer equation was input as a flux boundary condition at the electrode|aqueous surface and the electrode|organic surface.

The partitioning of the redox species at the liquid|liquid interface was described by  a net flux equation based on the measured partition coefficients. 

Please see  DOI:10.1021/acs.jpcc.2c03973 for the experimental data and analysis. 

The Supporting Information file https://pubs.acs.org/doi/suppl/10.1021/acs.jpcc.2c03973/suppl_file/jp2c03973_si_001.pdf includes a detailed description of the model.