Analytical solutions of the lattice Boltzmann BGK model

Analytical solutions of the two-dimensional triangular and square lattice Boltzmann BGK models have been obtained for the plane Poiseuille flow and the plane Couette flow. The analytical solutions are written in terms of the characteristic velocity of the flow, the single relaxation time , and the lattice spacing. The analytic solutions are the exact representation of these two flows without any approximation. Using the analytical solution, it is shown that in Poiseuille flow the bounce-back boundary condition introduces an error of first order in the lattice spacing. The boundary condition used by Kadanoffet al. in lattice gas automata to simulate Poiseuille flow is also considered for the triangular lattice Boltzmann BGK model. An analytical solution is obtained and used to show that the boundary condition introduces an error of second order in the lattice spacing.     

Flow injection analysis methods for determination of diffusion coefficients

Two flow injection analyses (FIA) methods for the determination of diffusion coefficients in a straight single tube FIA system were developed. Based on the analytical solution of the convection-diffusion equation, linear relationships of the logarithmic values of the dispersion coefficient (D) and the half-peak width (W_1/2) with the diffusion coefficient (D_m) were obtained. Experiments were designed to verify these methods. For example, for potassium hexacyanoferrate (III) a D_m value of 0.72 × 10⁵ cm² s⁻¹ was found versus a literature value of 0.76 × 10⁵ cm² s⁻¹ (error, 5%). For potassium hexacyanoferrate (II) a D_m value of 0.67 × 10⁵ cm² s⁻¹ was obtained versus a literature value of 0.63 × 10⁵ cm² s⁻¹ (error, 6%). The diffusion coefficients of some important biomedical compounds, such as dopamine, epinephrine, norepinephrine and ascorbic acid, were then determined. The values of 10⁵ D_m/cm² s⁻¹ are 0.60 ± 0.03, 0.44 ± 0.02, 0.60 ± 0.01 and 0.68 ± 0.06, respectively.