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Recent work by Lee et al. [Phys. Rev. E, 65 (2002) 051602] on self-propulsion of liquid via adsorption showed that droplet length has an adverse effect on droplet velocity in reactive wetting experiments. A similar study by Dos Santos and Ondarcuhu [Phys. Rev. Lett, 75 (1995) 2972], however, correlated a positive effect of length-to-velocity. We present an analysis of the forces involved and examine whether kinetic or equilibrium approaches should be used for reactive wetting systems. We found that suitable treatment for droplet adsorption progress can be inferred from the relative length of the droplet. Increased adsorption reaction and the increased drag force associated with a longer droplet compete with each other, resulting in an overall length effect on droplet velocity. We also propose the existence of a transition zone in the overall relationship which consider the contributions from both of the two reaction regimes. By comparison with experimental data, we also found that capillary length of the carrier liquid could be a good indication to where this transition is likely to occur. |
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