Journal of Fluid Mechanics

Marangoni effects of trace impurities on the motion of long gas bubbles in capillaries

J.  Ratulowski a1 and H.-C.  Chang a1
a1 Department of Chemical Engineering, University of Notre Dame, Notre Dame, IN 46556, USA

Article author query
ratulowski j   [Google Scholar] 
chang h   [Google Scholar] 


When a viscous liquid is displaced by a long air bubble in a capillary, it leaves behind a wetting liquid film. A lubrication analysis by Bretherton (1961), which assumes a mobile surface, underpredicts the film thickness at low bubble speeds. In this investigation, the Marangoni effect of small amounts of impurities is shown to be capable of explaining this discrepancy. We carry out an asymptotic analysis for different convective, diffusive and kinetic timescales and show that, if transport in the film is mass-transfer limited such that a bulk concentration gradient exists in the film, the film thickness increases by a maximum factor of 4 2/3; over Bretherton's mobile result at low bubble speeds. Moreover, at large bubble speeds, Bretherton's mobile prediction is approached for all ranges of timescales. For intermediate bubble speeds, the film thickness varies with respect to the bubble speed with an exponent smaller than 2/3 of the mobile theory. These results are favourably compared to literature data on film thickness.

(Published Online April 26 2006)
(Received November 16 1988)
(Revised June 22 1989)