Enhanced mass transfer in electrochemical cells using turbulence promoters

Many electrochemical processes suffer in varying degrees from mass transfer limitations. These limitations may require operation at considerably less than economic optimum current densities. Mass transfer to a surface may be considerably enhanced by insertion of turbulence promoters in the fluid flow path near the affected surface.An instrument was developed to measure local current densities in the hydrodynamically very difficult region near the turbulence promoter. A general method for the relative evaluation of hydrodynamic conditions has been developed. Generalization of the data permits optimization of hydrodynamic cell design using the promoter shapes investigated.

Notation

Symbols A Coefficient for cell power costs, $ m² (As)^–1 - A _c Cell area, m² - a Constant in Equation 4 - B Coefficient for area-proportional costs, $ A (m² s)^–1 - C Coefficient for pumping power costs, $ A (m² s)^–1 - C _b Bulk concentration, kg mol m^–3 - C _bi Inlet bulk concentration, kg mol m^–3 - C _e Energy cost, $ (Ws)^–1 - C _i Interfacial concentration, kg mol m^–3 - ¯C _s Amortized area cost, $ (m² s)^–1 - D Current—density-insensitive costs, $ s^–1 - D _e Equivalent diameter, m - D Diffusion constant, m² s^–1 - e Current efficiency - F _d Cell feed rate, m³ s^–1 - F 96.5×10⁶ A s kg eq^–1 - g Channel width, m - h Channel height, m - i Current density, A m^–2 - i _opt Economic optimum current density, A m^–2 - K Total costs of running cell, $ s^–1 - (K–D)_ideal Total sensitive costs under hydrodynamically ideal conditions, $ s^–1 - k _c Convective mass transfer coefficient, m s^–1 - L Total length of flow path, m - l Promoter spacing, m - N Mass flow rate to surface due to convection, kg mol m² s^–1 - n _e Number of electrons transferred in electrode reaction - P _c Power required by cell, W - P/L Average pressure gradient in channel, N m^–3 - R _av Effective cell resistance, m² - S Open channel cross-section, m² - S ₀ Minimum channel cross-section at promoter, m² - s _i Stoichiometric coefficient of species i - t _i Transport number of species i in solution - ¯t _i Effective tranport number of species at polarized surface - V Average fluid velocity, m s^–1 - x Distance from inception of concentration disturbance, m - ₁ Electrical power conversion efficiency - ₂ Pumping power conversion efficiency - Solution viscosity, kg (m s)^–1 - Solution density, kg m^–3 Dimemionless groups Fanning friction factor - Reynolds number - R h/g Channel aspect ratio - D _e/l Promoter frequency - S/S ₀ Contraction coefficient - Sherwood number - Degree of reaction - Dimensionless total sensitive - Dimensionless current density - Energy cost ratio