Wave model for longitudinal dispersion: Application to the laminar‐flow tubular reactor
The wave model for longitudinal dispersion, published elsewhere as an alternative to the commonly used dispersed plug-flow model, is applied to the classic case of the laminar-flow tubular reactor. The results are compared in a wide range of situations to predictions by the dispersed plug-flow model as well as to exact numerical calculations with the 2-D model of the reactor and to other available methods. In many practical cases, the solutions of the wave model agree closely with the exact data. The wave model has a much wider region of validity than the dispersed plug-flow model, has a distinct physical background, and is easier to use for reactor calculations. This provides additional support to the theory developed elsewhere. The properties and the applicability of the wave model to situations with rapidly changing concentration fields are discussed. Constraints to be satisfied are established to use the new theory with confidence for arbitrary initial and boundary conditions.
Laminar dispersion in capillaries: Part I. Mathematical analysis
Since 1953, when G. I. Taylor first considered the problem, numerous studies of the miscible displacement of fluids in capillaries have produced several approximate mathematical solutions which are purported to be valid under different conditions. Their form and ranges of applicability have been in conflict to some extent, since no exact solution is available to check these expressions. 
 
This study has resulted in exact numerical solutions to this problem with both axial and radial molecular diffusion accounted for. The range of parameters investigated is wide enough for comparison with all known analytical and empirical results and covers τ from 0.01 to 30 and NPe from 1 to 23,000. It is shown that for sufficiently large values of τ the Taylor-Aris theory is valid and thus results for all τ and NPe of any practical interest are now known. 
 
Axial molecular diffusion is significant at lower values of the Peclet number but the magnitude of NPe at which this occurs depends on the value of τ. In general, axial molecular diffusion is important for Peclet numbers less than about 100. 
 
Present results show that there is no justification for Bailey and Gogarty's empirical modification which yields an exponent of 0.541 rather than 0.50 for τ in Equations (35) and (36). Also, for the system studied here, no justification was found for the conjecture of Bournia et al. that Aris' low NPe modification may not account for axial diffusion properly. 
 
Simple expressions given by Equations (48) and (50) were developed empirically and they give with good accuracy the average concentration distribution over wider ranges of NPe and τ than previously reported expressions.
THE PERFORMANCE OF STEADY DETONATION ENGINES
Propulsion systems driven by steady normal detonations are studied. The practical di‐culties associated with stabilizing a detonation wave are highlighted. The requirement on the freestream total enthalpy is considered in parallel with efiects such as condensation or auto-ignition of the fuel-air mixture and limitations associated with fuel sensitivity to detonation. A criterion for detonation stabilization is formulated and applied to an analytical treatment of a detonation ramjet and a detonation turbojet, which are the respective analogs of the ramjet and the turbojet using detonative combustion. The performance of these engines is evaluated and compared to the ideal ramjet and turbojet models for hydrogen and JP10. A limitation is placed on the maximum total temperature allowed in the combustor, based on material considerations. The results show that steady detonation engines have a small thrust-producing range, due to the requirements for detonation stabilization. Their performance is always lower than that of the conventional ramjet and turbojet because of the total pressure loss across the detonation.