Fig. 1. One-dimensional Fickian diffusion model. (a) Schematic diagram of Fickian diffusion process; (b) concentration distribution calculated by Fickian diffusion model with diffusion coefficient of 6.86×10^-10 m²/s

Fig. 2. Diaphragm cell method and Taylor dispersion method for measuring liquid‒liquid diffusion coefficient^[8,17]. (a) Schematic diagram of diaphragm cell method; (b) schematic diagram of experimental setup for diaphragm cell method; (c) schematic diagram of Taylor dispersion method; (d) schematic diagram of experimental device for Taylor dispersion method

Fig. 3. Light beam deflection method for measuring liquid‒liquid diffusion coefficient^[25-26]. (a)(b) Schematic diagram of the light beam deflection method; (c) schematic diagram of experimental setup for the light beam deflection method; (d)(e) light beam diagrams of experimental observation; (f) fitting the light deflection amount with Gaussian curves

Fig. 4. Interferometry method for measuring liquid‒liquid diffusion coefficient. (a) Gouy interference experiment^[32]; (b) schematic diagram of the interferometry method^[33]; (c) schematic diagram of experimental setup for the interferometry method^[34]

Fig. 5. Liquid-core cylindrical lens method for measuring liquid‒liquid diffusion coefficient^[43-45]. (a)‒(c) Schematic diagram of the liquid-core cylindrical lens method; (d) imaging of the parallel light beam through liquid-core lens filled with solutions of different refractive indices; (e) visual observation of diffusion process by the liquid-core cylindrical lens method

Fig. 6. Microfluidic methods for measuring liquid‒liquid diffusion coefficient. (a) Microfluidic devices using microvalves^[49]; (b) Y-type microfluidic tube^[55]; (c) schematic diagram of the measurement method of Y-type microfluidic tube combined with Raman imaging^[55]; (d) concentration distribution data measured by the method of Y-type microfluidic tube combined with Raman imaging^[56]

Fig. 7. Non-Fickian phenomena in liquid‒liquid diffusion observed experimentally. (a) Non-Fickian diffusion phenomenon of saturated IBA solution and water observed by the light beam deflection method^[30]; (b) non-Fickian diffusion phenomenon of water and glycerol observed in a transverse capillary tube^[58]; (c) non-Fickian diffusion phenomenon of fluorescent colloid solution and water observed by the microfluidic method^[49]; (d) non-Fickian diffusion phenomenon of water and glycerol solution observed by the microfluidic method combined with Raman imaging method^[55]

Fig. 8. Optical fiber micro-sensor. (a)‒(c) Schematic diagram of structure and principle of the micro-sensor^[59]; (d)(e) refractive index (RI) sensitivity of the micro-sensor^[59]; (f)(g) the monitoring of the rapid RI change process with the micro-sensor^[62]; (h)(i) the measurement of the gradient RI distribution with the micro-sensor^[62]

Fig. 9. In-situ measurement of the diffusion process of water‒50% glycerol solution system by the micro-sensor^[59]. (a) Schematic diagram of the experimental setup; (b)(c) glycerol concentration distribution data measured by in-situ scanning with the micro-sensor; (d)‒(f) fitting of experimental data by the non-Fickian diffusion model; (g) space-time diagram of glycerol concentration calculated by the non-Fickian diffusion model