Hydrodynamic Singularities

We give a brief overview of the physical significance of singularities in fluid mechanics

Singularities in droplet pinching with vanishing viscosity

A slender-jet model for the pinching of a liquid column is considered in the limit of vanishing viscosity. We find the model to develop a singularity in the gradients of the local radius and the velocity at a finite thread radius, so it does not describe breakup. However, the observed steepening of the profile corresponds to experiments and simulations with fluids at low viscosity. The singularity has similarity form, which we compute analytically. The result agrees well with numerical simulations of the model equations.Comment: 18 pages including 4 eps figures, revte

Epiphyllous Lejeuneaceae in Costa Rica : contributions to the altitudinal distribution of selected species

The altitudina l distribution of selected species of epiphyllous Lejeuneaceae shows 6 groups (table 1 and 2): I (only lower than 500 m) Cololejeunea setiloba; II (1-1600m) Aphanolejeunea costaricensis, A. moralesiae, Cololejeunea cardiocarpa, C. guadelupensis, C. linopteroides, C. obliqua, C. papillifera, C. standleyi, Colura verdoornii, Cyclolejeunea chitonia, C. peruviana, Diplasiolejeunea brunnea, Microlejeunea epiphylla, Rectolejeunea berteroana, R. cf. emarginuliflora, Stictolejeunea squamata; III (1-3000m) Aphanolejeunea angustissima, Colura tortifolia, Diplasiolejeunea cavifolia, D. pellucida, Drepanolejeunea inchoata, Dr. lichenicola, Lejeunea laetevirens, Odontolejeunea lunulata; IV (only 500-1600m) Aphanolejeunea cingens, A. longifolia, A. pustulosa, Cyclolejeunea accedens, C. convexistipa, Diplasiolejeunea grolleana, D. unidentata, Harpalejeunea uncinata, Lejeunea filipes, Odontolejeunea decemdentata; V (500-3000m) Anoplolejeunea conferta, Aphanolejeunea crenata, A. ephemeroides, Colura tenuicornis, Diplasiolejeunea alata, Drepanolejeunea infundibulata, Dr. mosenii, Lejeunea flava, Omphalanthus filiformis; VI (only above 1600-3000m) Aphanolejeunea camillii, Cololejeunea fefeana, Diplasiolejeunea costaricensis sp.nov., D. involuta

A brief history of drop formation

Surface-tension-related phenomena have fascinated researchers for a long time, and the mathematical description pioneered by Young and Laplace opened the door to their systematic study. The time scale on which surface-tension-driven motion takes place is usually quite short, making experimental investigation quite demanding. Accordingly, most theoretical and experimental work has focused on static phenomena, and in particular the measurement of surface tension, by physicists like E\"otv\"os, Lenard, and Bohr. Here we will review some of the work that has eventually lead to a closer scrutiny of time-dependent flows, highly non-linear in nature. Often this motion is self-similar in nature, such that it can in fact be mapped onto a pseudo-stationary problem, amenable to mathematical analysis.Comment: book chapter for "Colloque Jean Jacques Moreau

Toward a description of contact line motion at higher capillary numbers

The surface of a liquid near a moving contact line is highly curved owing to diverging viscous forces. Thus, microscopic physics must be invoked at the contact line and matched to the hydrodynamic solution farther away. This matching has already been done for a variety of models, but always assuming the limit of vanishing speed. This excludes phenomena of the greatest current interest, in particular the stability of contact lines. Here we extend perturbation theory to arbitrary order and compute finite speed corrections to existing results. We also investigate the impact of the microscopic physics on the large-scale shape of the interface

Comment on "Dynamic Wetting by liquids of different viscosity", by T.D. Blake and Y.D. Shikhmurzaev

We comment on a recent theory of dynamic wetting, that is based directly upon a model for interface formation, introduced by Shikhmurzaev. We argue that the treatment of surface tension and its relaxation, inherent in the original model, is physically flawed.Comment: comment submitted to Journal of Colloid and Interface Scienc