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Abstract: Extensive experimental investigations have shown some of the differences between the behaviours of the barrel and the clamshell shapes of droplets on filter fibres in flow fields. Realistic flow velocities (such as those used in many industrial filter systems) were utilised. The forces acting are air drag, interfacial tension and gravity. The properties of the interfacial restoring force are modelled, and show agreement with the experimental results, at least in the linear extension region before the onset of oscillatory behaviour of the droplets (induced by instability of the flow field). The model for the oscillatory behaviour is explored, and the natural frequencies of oscillation in the radial and transverse directions are shown to be the same, for the barrel shape. The clamshell shape also has the same natural frequencies, but they are different to those of the barrel shape. The coupling of the radial and transverse oscillation modes is explored for both the barrel and clamshell shape. Some contact angle results are given, both without airflow acting on the droplet and with increasing airflow. [Copyright &y& Elsevier]