A simple model of fuel spray burning I: Random sprays☆

Ligand binding in a spherical region randomly crowded by receptors

“…It follows from formula (10) and especially clearly from (12) that λ is the characteristic penetration length for the ligand concentration field (characteristic spatial scale where the function c (r) drops rapidly to zero) [34,35]. Note in passing that the obtained general results have been applied to describe the diffusion burning of a spherical array of fuel droplets [35] and are even currently in use [36].…”

“…The volume fraction of sinks is assumed to be small enough; otherwise, for an overcrowded system of sinks, reaction occurs only on its boundary. As far as we know, Deutch et al considered the posed problem for the first time [34,35] and proposed the following mean-field equation with respect to the average (coarse-grained) concentration c (r) of diffusing reactants:…”

“…where r is the radial coordinate connected with the spherical domain L center. The solution of equations ( 8) and ( 9) under continuity conditions on the boundary of the array yields [34,35]…”

Competitive effects between stationary chemical reaction centres: A theory based on off-center monopoles

“…, N } are N identical spheres of radius a centred at locations ⃗ r i . Equation (3) represents the case of fully absorbing boundaries. Local angle coordinates are introduced on each sphere so that the position vector on the surface of a sphere is given by ⃗ r = ⃗ r i + ar i (θ, ϕ),…”

“…An interesting special case is the evaporation and subsequent combustion of a spray of finely dispersed liquid fuel droplets, a process in which the transfer of both heat and mass is involved. [1][2][3][4] In systems where multiple stationary reaction centres are in close proximity to each other, the reactive centres compete for the diffusing molecular agent. As a result, the reaction rate per site is lower than in the case of single sites.…”