Journal of Colloid and Interface Science 308 (2007) 1–3 www.elsevier.com/locate/jcis Letter to the Editor Comment on “Two touching spherical drops in uniaxial extensional flow: Analytic solution to the creeping flow problem” M.B. Nemer a , X. Chen a , D.H. Papadopoulos a , J. Blawzdziewicz b , M. Loewenberg a,∗ a Department of Chemical Engineering, Yale University, New Haven, CT, USA b Department of Mechanical Engineering, Yale University, New Haven, CT, USA Received 20 August 2006; accepted 15 October 2006 Available online 19 October 2006 Abstract From an analysis of tangent spherical drops in straining flow, Baldessari and Leal conclude that the drop-scale internal circulation, driven by the ambient flow, has a negligible influence on the drainage of the thin liquid film between drops under small-deformation conditions [F. Baldessari, L.G. Leal, J. Colloid Interface Sci. 289 (2005) 262]. However, their conclusion is incorrect as explained in this letter. Published by Elsevier Inc. Keywords: Drop coalescence; Film drainage; Noncoalescence; Stokes flows Drop coalescence is often controlled by the drainage dynam- ics of the thin liquid film that forms between the flattened inter- faces of two drops pushed together by body forces or an am- bient flow. Until recently, it was believed that an ambient flow affects the near-contact motion of nearly spherical drops only through the pushing force generated by hydrodynamic stresses acting on the drop interfaces outside the near-contact region. The ambient flow was considered to have no direct influence on the film drainage, even for drops with tangentially-mobile interfaces [2]. According to this view, the near-contact motion of drops was predicted to be the same whether they are pushed together by an ambient flow or by an equivalent pair of body forces. Recently, however, it was shown [3] that for drops with tan- gentially mobile interfaces, an ambient flow can directly affect film drainage dynamics, even under small-deformation condi- tions. As a result, the near-contact motion of drops pushed together by an ambient flow is qualitatively different from the motion of drops pushed by body forces in a quiescent fluid. In their article, Baldessari and Leal [1] refute the analysis pre- sented in Ref. [3] asserting that the influence of an ambient flow on film drainage under small-deformation conditions is negligi- * Corresponding author. E-mail address: michael.loewenberg@yale.edu (M. Loewenberg). ble (as was formerly believed). In this letter we point out the flaw in their argument, and provide numerical simulations to illustrate the importance of the drop-scale internal circulation. Baldessari and Leal [1] base their argument on an analysis of the flow field in a system of two equal-size tangent spherical drops immersed in a fluid undergoing extensional flow (1) u ∞ = G  1 2 ρ e ρ − ze z  , where G is strain-rate, and (ρ,z) are cylindrical coordinates with unit vectors e ρ , e z . The z-axis coincides with the line- of-centers, and the point of tangency corresponds to z = 0. The external-phase fluid has viscosity μ, the drop-phase fluid has viscosity ˆ μ = λμ, the interfacial tension is σ , and the drops have radius R. Surface tension gradients are absent and creeping-flow conditions apply. Baldessari and Leal present an analytical solution for this tangent-sphere problem and discuss the flow field in the contact region using scaling arguments. We note that an analytical solution of the general tangent-sphere problem for drops with arbitrary size ratio is presented in [3,4]. For a pair of spherical or nearly spherical drops pushed to- gether by external flow (1), the ambient velocity field drives a drop-scale internal circulation which is absent for drops pressed together by body forces. Baldessari and Leal [1] argue that this internal circulation does not affect near-contact motion 0021-9797/$ – see front matter Published by Elsevier Inc. doi:10.1016/j.jcis.2006.10.028