Interrelations Involving Solutions of Equations of Equalizing Processes and Oscillating Processes

• Published in: The Journal of chemical physics 1958-01, Vol.29 (4), p.689-696
• Main Author: O'Sullivan, D. G.
• Format: Article
• Language: English
• ISSN: 0021-9606; 1089-7690
• DOI: 10.1063/1.1744576

Assessment of the velocity of a fast chemical reaction can be made by studying the way the reaction interferes with other rapid processes. Both equalizing processes, such as diffusion, and oscillating processes, such as the passage of sound waves, can be employed. Solution of the differential equations of these processes, under a variety of conditions, is a necessary part of the background investigation of these methods and is also of importance in the study of many other physical and chemical problems. This paper shows how a wide range of these solutions can easily be obtained from simpler existing solutions. Among other results, complete resolutions of the ``age equation'' ∂v(r,t)/∂t=D(r)·∇2v(r,t)+A(r,t)+B(t)·v(r,t) and the vibration equation ∂2ξ(r,τ)/∂τ2+b∂ξ(r,τ)/∂τ=κ(r)·∇2ξ(r,τ)+A(r,τ)+B(r)·ξ(r,τ) have been effected for arbitrary initial conditions and a range of important boundary conditions (including those of Dirichlet and Neumann as special cases).