Measurement and verification of concentration-dependent diffusion coefficient: Ray tracing imagery of diffusion process*

Abstract

Ray tracing method is used to study the propagation of collimated beams in a liquid–core cylindrical lens (LCL), which has dual functions of diffusion cell and image formation. The diffusion images on the focal plane of the used LCL are simulated by establishing and solving both linear and nonlinear ray equations, the calculated results indicate that the complex imaging results of LCL in inhomogeneous media can be treated by the law of ray propagation in homogeneous media under the condition of small refractive index gradient of diffusion solution. Guided by the calculation conditions, the diffusion process of triethylene glycol aqueous solution is experimentally studied at room temperature by using the LCL in this paper. The spatial and temporal concentration profile C e(z, t) of diffusion solution is obtained by analyzing diffusion image appearing on the focal plane of the LCL; Then, the concentration-dependent diffusion coefficient is assumed to be a polynomial D(C) = D 0 × (1 + α 1 C + α 2 C 2 + α 3 C 3 + ⋅). The finite difference method is used to solve the Fick diffusion equation for calculating numerically the concentration profiles Cn (z, t). The D(C)of triethylene glycol aqueous solution is obtained by comparing the Cn (z, t) with C e(z,t). Finally, the obtained polynomial D(C) is used to calculate the refractive index profiles nn (z,t)s of diffusion solution in the used LCL. Based on the ray propagation law in inhomogeneous media and the calculated n(z,t), the ray tracing method is used again to simulate the dynamic images of the whole experimental diffusion process to varify the correctness of the calculated D(C). The method presented in this work opens up a new way for both measuring and verifying the concentration-dependent liquid diffusion coefficients.