X. Chen

Yale University, New Haven, Connecticut, United States

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Publications (4)13.19 Total impact

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    ABSTRACT: A study on the axisymmetric near-contact motion of drops with tangentially mobile interfaces under the action of a body force in a quiescent fluid is described. A long-time asymptotic analysis is presented for small-deformation conditions. Under these conditions the drops are nearly spherical, except in the near-contact region, where a flattened thin film forms. According to our analysis, a hydrostatic dome does not form in the near-contact region at long times, in contrast to the assumption underlying all previous analyses of this problem. Instead, the shape of the film in the near-contact region results from the absence of tangential stresses acting on it. As a result, the long-time behaviour of the system is qualitatively different than previously predicted. According to the theory presented herein, the minimum film thickness (rim region) decays with time as \${h}_{m} \sim {t}^{- 4/ 5} \$, and the thickness at the centre of the film decays as \${h}_{0} \sim {t}^{- 3/ 5} \$, which is a faster decay than predicted by prior analyses based on a hydrostatic dome. Numerical thin-film simulations quantitatively confirm the predictions of our small-deformation theory. Boundary-integral simulations of the full two-drop problem suggest that the theory also describes qualitatively the long-time evolution under finite-deformation conditions.
    Journal of Fluid Mechanics 08/2013; 728. · 2.29 Impact Factor
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    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.
    Journal of Colloid and Interface Science 05/2007; 308(1):1-3. · 3.55 Impact Factor
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    ABSTRACT: We analyze axisymmetric near-contact motion of two drops under the action of an external force or imposed flow. It is shown that hydrodynamic stresses in the near-contact region that are associated with the outer (drop-scale) flow can qualitatively affect the drainage of the thin fluid film separating the drops. If this far-field stress acts radially inward, film drainage is arrested at long times; exponential film drainage occurs if this stress acts outward. An asymptotic analysis of the stationary long-time film profile is presented for small-deformation conditions, and the critical strength of van der Waals attraction for film rupture is calculated. The effect of an insoluble surfactant is also considered. Hindered and enhanced drop coalescence are not predicted by the current theories, because the influence of the outer flow on film drainage is ignored.
    Physical Review Letters 04/2004; 92(11):114501. · 7.73 Impact Factor
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    ABSTRACT: At long times, a thin liquid film between two deformable drops forms a central dimpled region which is separated from an outer hydrostatic region by a narrow rim region where the film thickness is minimal. We present a long-time asymptotic analysis of this problem. Previous scaling analyses were based on the assumption that the dimple assumes a hydrostatic shape at long times. Matching of the hydrostatic dimple to the inner rim solution requires that the film thickness in the matching region varies linearly with the distance x from the minimal gap. However, our solution of the integro-differential equation describing the rim indicates that nonlocal contributions give rise to a film thickness that varies as x^1/2. The dimple shape is governed by another integro-differential equation that minimizes the stresses due to the flow inside the drops. Based on the new matching conditions, we find that the central gap decreases as t-3/5 and the minimum gap as t-4/5, in contrast to the results of earlier studies. Evidence from thin film numerical simulations supports our assertions.
    11/2001;