Diffusion-limited currents at hemitoroidal microelectrodes

Steady-State Currents at Sphere-Cap Microelectrodes and Electrodes of Related Geometry

“…The Laplacian operator in toroidal coordinates, when there is axial symmetry, is , where h , defined by is the scale factor.…”

“…when η f 0 and ξ f 0 (3.8) ∂c/∂ξ ) 0 at ξ ) 0 and all η (4.1) where ∇ 2 c is set to 0. In (4.5), the local concentration c is a function of both ξ and η, but we shall now assume 21 that c may be written as where f is a function of ξ only and g is a function of η only. Substitution of this assumption into (4.5) leads eventually to…”

Microfluidic Analyte Transport to Nanorods for Photonic and Electrochemical Sensing Applications

“…Analytical solutions derived from fundamentals often involvep ure diffusive transport in infinite domains (void of convection)t os imple shapes having convenient symmetry, including embedded disks and strips, hemispheres, [7] hemispheroids, [8] embedded rings, [9] ellipsoids, [10] sphere caps, [11] and hemitoroids. [12] Predictiono ft ransport to more complicated shapes requiresthe use of numerical methods, where several approaches (e.g.,f inite difference, volume, element) have been used to simulatet ransport to (among others) embedded squares and bands, [13] cylinders, [14] cones, [15] and heptodes. [16] Resultsf rom simulation are often used to constructa nalyticala pproximationsf or rates of transport.…”

“…Solutions for steady‐state diffusion‐limited rates of transport have been found for a variety of surfaces pertinent to micro‐ and nanoparticle‐based sensors. Analytical solutions derived from fundamentals often involve pure diffusive transport in infinite domains (void of convection) to simple shapes having convenient symmetry, including embedded disks and strips, hemispheres, hemispheroids, embedded rings, ellipsoids, sphere caps, and hemitoroids . Prediction of transport to more complicated shapes requires the use of numerical methods, where several approaches (e.g., finite difference, volume, element) have been used to simulate transport to (among others) embedded squares and bands, cylinders, cones, and heptodes .…”