RESUMEN
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.
RESUMEN
The growth of spherical drops by coalescence in simple shear and axisymmetric straining flows has been numerically investigated, and the long-time scaling behavior of the system was explored. It is shown that hydrodynamic interactions qualitatively modify the the collision kernel in the population balance equation and thus alter the evolution of the drop size distribution at long times. In the presence of hydrodynamic interactions, the number of drops in the system decays as t(-1), and the average drop size grows as e(sqrt[t]); in the absence of hydrodynamic interactions, these quantities evolve exponentially at long times. Hydrodynamic interactions lead to broader drop size distributions, and cause the influence of initial conditions to decay with time. Drops undergoing thermocapillary migration are shown to exhibit similar features. Our results are shown to be consistent with the established theory for the scaling behavior of aggregating systems. It is shown that the theory applies even in certain cases where the binary collision kernel does not have the assumed form. In the presence of hydrodynamic interactions, the scaling regime is attained slowly (logarithmically).
RESUMEN
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.
RESUMEN
A lubrication analysis is presented for near-contact axisymmetric motion of spherical drops covered with an insoluble nondiffusing surfactant. The surfactant equation of state is arbitrary; detailed results are presented for ionic surfactants. The qualitative behavior of the system is determined by the dimensionless force parameter &Fcirc;, the external force normalized by the maximum resistance force generated by Marangoni stresses. For &Fcirc; > 1 drops coalesce on a time scale commensurate with the coalescence time tau0 for drops with clean interfaces. For &Fcirc; < 1, the system evolves on the time scale tau0 until Marangoni stresses approximately balance the external force; thereafter a slow evolution occurs on the Stokes time scale. In the long-time regime a self-similar surfactant concentration profile is attained that scales with the extent of the near-contact region. The gap width decreases exponentially with time but slower than for rigid particles because of surfactant backflow. For &Fcirc; < 1, drop coalescence does not occur without van der Waals attraction. Quantitative results depend only moderately on the surfactant equation of state. Copyright 1999 Academic Press.
RESUMEN
The stability and pairwise aggregation rates of small spherical particles in a heterogeneous suspension under the collective effects of gravitational motion and electrophoretic migration are analyzed. The particles are assumed to be non-Brownian, with thin, unpolarized double layers and different zeta potentials. The gravity vector and the electric field are assumed to be oriented in either the same direction or opposite directions. The particle aggregation rates are always enhanced by the presence of an electric field for parallel alignment of the gravitational and electrophoretic velocities. For antiparallel alignment with the magnitude of the gravitational relative velocity exceeding the magnitude of the electrophoretic relative velocity between two widely separated particles, the particle aggregation rates are reduced by the presence of the electric field, and there is a "collision-forbidden" region in parameter space due to stronger hydrodynamic interactions of the particles for gravitational motion than for electrophoretic motion. For antiparallel alignment with the magnitude of the electrophoretic relative velocity exceeding the magnitude of the gravitational relative velocity between two widely separated particles, the particle aggregation rates are enhanced by the presence of the electric field.