Y. Pawar et Kj. Stebe, MARANGONI EFFECTS ON DROP DEFORMATION IN AN EXTENSIONAL FLOW - THE ROLE OF SURFACTANT PHYSICAL-CHEMISTRY .1. INSOLUBLE SURFACTANTS, Physics of fluids, 8(7), 1996, pp. 1738-1751
The shape of a drop centered in an axisymmetric extensional flow is de
termined by the viscous stresses that deform the drop and surface tens
ion gamma' that resists the deformation. The ratio of these stresses i
s given by the capillary number, Ca. When Ca is small enough, the drop
attains a steady shape. However, above a threshold value, Ca-cr, the
drop elongates continuously, and no steady shape is attained. When sur
factants are present on the drop interface, the surface tension is det
ermined by the surface concentration profile, which varies throughout
the deformation process. Initially, the surface tension is given by ga
mma(eq), in equilibrium with the uniform surface concentration Gamma'(
eq). When the flow is initiated, surfactant is swept toward the drop t
ips, reducing the surface tension there, and altering the interfacial
stress balance tangentially through Marangoni stresses and normally th
rough the Laplace pressure. In this paper, the effects of an insoluble
surfactant on drop deformation are studied. In previous work, either
a surface equation of state for the surface tension gamma' that is lin
ear in the surface concentration Gamma' was used, an approximation tha
t is valid only for dilute Gamma', or Gamma' sufficiently dilute for t
he linear approximation to be valid were studied. In this paper, a non
linear surface equation of state that accounts for surface saturation
and nonideal interactions among the surfactant molecules is adopted. T
he linear framework results are recovered for Gamma' that are sufficie
ntly dilute. As Gamma' is increased, the effects of saturation and sur
factant interactions are probed at constant initial Gamma'(eq) and at
constant initial gamma'(eq). Finally, the case of strong intersurfacta
nt cohesion is treated with a first-order surface phase transformation
model. At moderate surface concentrations, these nonlinear phenomena
strongly alter the steady drop deformations and Ca-cr relative to the
uniform surface tension and linear equation of state results. (C) 1996
American Institute of Physics.