1：Experimental Design and Method Selection:

The study involved FSSLM experiments to model the transport of germanium using Aliquat 336 as a carrier. The model was based on extraction equilibrium, mass transfer, and diffusion equations derived from Fick's law, with programming in Matlab for numerical solutions.

2：Sample Selection and Data Sources:

Feed solutions were prepared with germanium(IV) oxide dissolved in distilled water to achieve approximately 100 mg/L Ge concentration, with tartaric acid at 2.76 mmol/L. Aliquat 336 concentrations ranged from 2.5 to 10%v/v in kerosene and 1-decanol diluents.

3：76 mmol/L. Aliquat 336 concentrations ranged from 5 to 10%v/v in kerosene and 1-decanol diluents. List of Experimental Equipment and Materials:

3. List of Experimental Equipment and Materials: Equipment included a FSSLM system with mechanical impellers, flat sheet PTFE membranes (Millipore Durapore, 47 mm diameter, 0.45 μm pore size), a capillary U-tube viscometer for viscosity measurements, and an ICP spectrometer (Agilent 700 Series) for germanium analysis. Materials included Aliquat 336 (Alfa Aesar), germanium(IV) oxide (Sigma-Aldrich), kerosene and 1-decanol (Sigma-Aldrich and Merck), and other analytical grade chemicals.

4：45 μm pore size), a capillary U-tube viscometer for viscosity measurements, and an ICP spectrometer (Agilent 700 Series) for germanium analysis. Materials included Aliquat 336 (Alfa Aesar), germanium(IV) oxide (Sigma-Aldrich), kerosene and 1-decanol (Sigma-Aldrich and Merck), and other analytical grade chemicals. Experimental Procedures and Operational Workflow:

4. Experimental Procedures and Operational Workflow: Membranes were impregnated with Aliquat 336 solutions, rinsed, and placed in a holder between feed and strip cells (220 mL each, with 1 M HCl strip solution). Samples were taken at intervals, and germanium concentrations were measured via ICP. Viscosity was measured using ASTM D445 protocol.

5：Data Analysis Methods:

Data were analyzed using Matlab programming to solve mathematical models, with error minimization functions (e.g., fmincon) to determine extraction and mass transfer constants. Statistical parameters (RMSE, bias, SI) and correlation coefficients were used to validate the model.