Supplemental Materials_HYENG-14634

The file includes:Figures S1–S6:S1: Influence of TSKAM parameters S2–S4: Complete experimental and simulated zinc BTCs for 35‑mesh, 60‑mesh and 100‑mesh sand columns under four flow regimes (Uniform, T60, T40, T20), each with three injection cycles.S5: Comparison of equivalent dispersion coefficient (EDC) vs. velocity‑dependent dispersion (VarD) for bromide transport.S6: Mesh‑independence test results (three grid resolutions).Tables S1–S2:S1: Simulation accuracy (R², RMSE) of the velocity‑dependent dispersion model for Br⁻.S2: Fitted TSKAM parameters and goodness‑of‑fit metrics for all zinc breakthrough experiments.Text sections (within the PDF):Numerical implementation of the variable‑velocity TSKAM: spatial discretization (upwind for advection, central difference for dispersion), time discretization (implicit backward Euler + operator splitting with RK4 for reaction terms), and order of accuracy (first‑order in time, second‑order in space).Mesh‑ and time‑step independence test: quantitative convergence analysis (peak concentration errors <1%).Model calibration and evaluation metrics: definition of R² and RMSE, parameter determination procedure, boundary and initial conditions.Justification for using an equivalent dispersion coefficient instead of a velocity‑dependent formula under transient flow.Data generationExperimental data: Column breakthrough experiments were conducted using quartz sand of three particle sizes (35‑mesh, 60‑mesh, 100‑mesh).

Four flow regimes were tested: steady‑state (Uniform) and sinusoidal flow with periods of 20, 40, and 60 min (T20, T40, T60), all at the same mean flow rate (1 mL/min). Bromide was used as a conservative tracer, and Zn²⁺ solutions (100 mg/L) were injected in three sequential cycles. Effluent concentrations were measured by ICP‑OES (Zn) and UV‑Vis spectrophotometry (Br⁻).Numerical data: The variable‑flow advection‑dispersion equation (ADE) was used to simulate bromide BTCs, and the Two‑Site Kinetic Attachment Model (TSKAM) was used for Zn²⁺ transport.