Departmental Papers (MEAM)

Document Type

Journal Article

Date of this Version



Suggested Citation:
Gogos, George S., et. al. (1986) Thin-flame theory for the combustion of a moving liquid drop: effects due to variable density. Journal of Fluid Mechanics, Volume 171, p. 121-144.

Copyright 1986 Cambridge University Press. This article is also available at


The combustion of a moving liquid fuel drop has been investigated. The drop

experiences a strong evaporation-induced radial velocity while undergoing slow

translation. In view of the high evaporation velocity, the flow field is not in the

Stokes regime. The combustion process is modelled by an indefinitely fast chemical

reaction rate.

While the flow and the transport in the continuous phase and the drop internal

circulation are treated as quasisteady, the drop heat-up is regarded as a transient

process. The transport equations of the continuous phase require analysis by a

singular perturbation technique. The transient heat-up of the drop interior is solved

by a series-truncation numerical method. The solution for the total problem is

obtained by coupling the results for the continuous and dispersed phases.

The enhancement in the mass burning rate and the deformation of the flame shape

due to drop translation have been predicted. The initial temperature of the drop and

the subsequent heating influence the temporal variations of the flamefront standoff

ratio and the flame distance. The friction drag, the pressure drag and the drag due

to interfacial momentum flux are individually predicted, and the total drag behaviour

is discussed. The circulation inside the drop decreases with evaporation rate. A

sufficiently large non-uniform evaporation velocity causes the circulation to reverse.



Date Posted: 17 August 2010

This document has been peer reviewed.