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Die achsensymmetrische Strömung in einem dünnen Film zwischen einer fluid-flüssigen Grenzfläche und einer festen Kugel, die sich dieser nähert, wird unter Berücksichtigung der Strömung in der an den Film angrenzenden fluiden Phase untersucht. Die Geschwindigkeitsverteilungen im Film und in der angrenzenden Phase sind Funktionen der Zeit, des Druckgradienten im Film, der anfänglichen Strömungen in den beiden Phasen, der Krümmung des Systems und der physikalischen Eigenschaften, repräsentiert durch die Parameterη (Verhältnis der dynamischen Viskositäten) undR ( =η (νB/νA)1/2). Aus der Geschwindigkeitsverteilung im Film wird über eine Massen- und eine Kräftebilanz eine Gleichung für die Änderung der Filmdicke hergeleitet, welche unter anderem eine temporäre Zunahme der Dicke des Films vorauszusagen vermag. Ferner konnten damit aus der Literatur entnommene experimentelle Kurven der Abnahme der Filmdicke gut reproduziert werden.

A pseudospectral algorithm has been used to compute solutions u(x,t), A(x,t), B(x,t), and R(x,t) to one-dimensional equations of change incorporating the simple reaction A + B → R for statistically homogeneous random velocity and partially premixed reactant concentration fields. An initial turbulence Reynolds number of 400 has been used, together with Damköhler numbers of 10² and 10³ for fast reactions and Schmidt numbers of 10^-3, 1, and 10² to span a wide range of diffusivities. Evolving concentration profiles inform intuition in general and provide insight into the evolution of the single-point statistical measures in particular:  〈A〉, 〈B〉, 〈a²〉, 〈b²〉, 〈ab〉, 〈ab〉/〈A〉〈B〉, and 〈a²b〉. There is a pronounced effect of Da on all the statistical properties, but for a given value of Da, 〈A〉, 〈B〉, 〈ab〉/〈A〉〈B〉 (t), and 〈a²b〉 are identical for Sc = 1 and 10² and virtually so for Sc = 10^-3 as well, whereas 〈a²〉, 〈b²〉, and 〈ab〉 evolve differently for Sc = 10^-3 than for Sc = 1 and 10². Comparisons between different single-point closures for nonpremixed turbulent reactions and the present partially premixed results have been made. As was found by Leonard et al. in three dimensions for a slower nonpremixed reaction (Ind. Eng. Chem. Res. 1995, 34, 3640−3652), it is found that Toor's closure (Ind. Eng. Chem. Fundam. 1969, 8, 655−659) comes closest to agreement with our direct numerical simulations of 〈ab〉(t) in one dimension for a faster partially premixed reaction. We propose a closure for partially premixed reactions that incorporates a reaction segregation effect which yields improved agreement with our simulations of 〈ab〉(t).

Unsteady conjugate mass transfer between a spherical bubble, droplet, or particle and a surrounding fluid flow with chemical reaction in the continuous phase has been analyzed. An algorithm based on spectral methods has been developed and implemented for the simulation of the interphase mass transfer. The influence of Pe (convection) and Da (rate of external reaction), but in particular of D (diffusivity ratio) and H (distribution coefficient), which characterize the coupling features of the conjugate mass transfer, is studied in a wider range of parameters than earlier investigations. The asymptotic regime of mass transfer is investigated for long times, and an upper limit for the corresponding dimensionless mass transfer coefficient is established. A method for decoupling the conjugate problem is proposed that results in a modified version of the addition rule, which is a higher level of approximation than the original one. As measured against the results of our numerical simulations, the modified addition rule yields results in the asymptotic regime that are superior to those obtained using the customary addition rule.