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• Multi-field modeling on simultaneously removing mercury and particulate matter. • The mass transfer module shows relatively higher accuracy than previous models. • Sorbent particle size predominates over simultaneous removal efficiency. • The influences of other typical operating parameters are carefully discussed. • EHD conditions have complex effects on capture of mercury and particulate matter. A computational fluid dynamics (CFD) model coupled with gas-particle mass transfer, electrohydrodynamic (EHD) effect, electric field, particle motion and particle charging is established to advance the understanding of combined particulate matter precipitation and mercury capture within industrial electrostatic precipitators (ESPs). The comparisons between experimental data and numerical results demonstrate that this model can reasonably predict the mercury removal efficiency by powdered sorbent injection (PSI). The mechanism of simultaneous removal of mercury and particulate matter is then discussed in detail by considering the complex interactions among multi-physics. The influences of particle size, mercury concentration, particle injection rate and the EHD effect are investigated. The simulation results indicate that the mercury removal process is primarily controlled by the sorbent particle residence time, surface area and mass transfer rate. Accordingly, reducing the size of sorbent particles (activated carbon) can promote mercury removal efficiency while decreasing the particle collection efficiency. Increasing the initial mercury concentration and adsorbent mass loading also benefit mercury adsorption by influencing the mass transfer rate and the surface area. The EHD effect plays important roles in mercury removal and particle collection by means of altering the flow patterns and particle migration. The two mechanisms of in-flight and wall-bounded mercury adsorption affected by ionic wind are also evaluated and some interesting phenomena are observed. [ABSTRACT FROM AUTHOR]