Maximum size of drops levitated by an air cushion

Liquid drops can be kept from touching a plane solid surface by a gas stream entering from underneath, as it is observed for water drops on a heated plate, kept aloft by a stream of water vapor. We investigate the limit of small flow rates, for which the size of the gap between the drop and the substrate becomes very small. Above a critical drop radius no stationary drops can exist, below the critical radius two solutions coexist. However, only the solution with the smaller gap width is stable, the other is unstable. We compare to experimental data and use boundary integral simulations to show that unstable drops develop a gas "chimney" which breaks the drop in its middle.Comment: 13 pages, 11 figure

Coalescence Dynamics

The merging of two fluid drops is one of the fundamental topologi- cal transitions occurring in free surface flow. Its description has many applications, for example in the chemical industry (emulsions, sprays etc.), in natural flows driving our climate, and for the sintering of mate- rials. After reconnection of two drops, strongly localized surface tension forces drive a singular flow, characterized by a connecting liquid bridge that grows according to scaling laws. We review theory, experiment, and simulation of the coalescence of two spherical drops for different parameters, and in the presence of an outer fluid. We then general- ize to other geometries, such as drops spreading on a substrate and in Hele-Shaw flow, and discuss other types of mass transport, apart from viscous flow. Our focus is on times immediately after reconnection, and on the limit of initially undeformed drops at rest relative to one another

The relationship between viscoelasticity and elasticity

Soft materials that are subjected to large deformations exhibit an extremely rich phenomenology, with properties lying in between those of simple fluids and those of elastic solids. In the continuum description of these systems, one typically follows either the route of solid mechanics (Lagrangian description) or the route of fluid mechanics (Eulerian description). The purpose of this review is to highlight the relationship between the theories of viscoelasticity and of elasticity, and to leverage this connection in contemporary soft matter problems. We review the principles governing models for viscoelastic liquids, for example solutions of flexible polymers. Such materials are characterized by a relaxation time λ, over which stresses relax. We recall the kinematics and elastic response of large deformations, and show which polymer models do (and which do not) correspond to a nonlinear elastic solid in the limit λ → ∞. With this insight, we split the work done by elastic stresses into reversible and dissipative parts, and establish the general form of the conservation law for the total energy. The elastic correspondence can offer an insightful tool for a broad class of problems; as an illustration, we show how the presence or absence of an elastic limit determines the fate of an elastic thread during capillary instability

Dynamic drying transition via free-surface cusps

We study air entrainment by a solid plate plunging into a viscous liquid, theoretically and numerically. At dimensionless speeds of order unity, a near-cusp forms due to the presence of a moving contact line. The radius of curvature of the cusp's tip scales with the slip length multiplied by an exponential of. The pressure from the air flow drawn inside the cusp leads to a bifurcation, at which air is entrained, i.e. there is 'wetting failure'. We develop an analytical theory of the threshold to air entrainment, which predicts the critical capillary number to depend logarithmically on the viscosity ratio, with corrections coming from the slip in the gas phase.</p

Viscoelastic wetting: Cox-Voinov theory with normal stress effects

The classical Cox-Voinov theory of contact line motion provides a relation between the macroscopically observable contact angle, and the microscopic wetting angle as a function of contact line velocity. Here we investigate how viscoelasticity, specifically the normal stress effect, modifies wetting dynamics. Using the thin film equation for the second-order fluid, it is found that the normal stress effect is dominant at small scales. We show that the effect can be incorporated in the Cox-Voinov theory through an apparent microscopic angle, which differs from the true microscopic angle. The theory is applied to the classical problems of drop spreading and dip-coating, which shows how normal stress facilitates (inhibits) the motion of advancing (receding) contact lines. For rapid advancing motion, the apparent microscopic angle can tend to zero in which case the dynamics is described by a new regime that was already anticipated in Boudaoud (2007)

Viscoelastic wetting:Cox-Voinov theory with normal stress effects

The classical Cox-Voinov theory of contact line motion provides a relation between the macroscopically observable contact angle, and the microscopic wetting angle as a function of contact-line velocity. Here, we investigate how viscoelasticity, specifically the normal stress effect, modifies the wetting dynamics. Using the thin film equation for the second-order fluid, it is found that the normal stress effect is dominant at small scales yet can significantly affect macroscopic motion. We show that the effect can be incorporated in the Cox-Voinov theory through an apparent microscopic angle, which differs from the true microscopic angle. The theory is applied to the classical problems of drop spreading and dip coating, which shows how normal stress facilitates (inhibits) the motion of advancing (receding) contact lines. For rapid advancing motion, the apparent microscopic angle can tend to zero, in which case the dynamics is described by a regime that was already anticipated in Boudaoud (Eur. Phys. J. E, vol. 22, 2007, pp. 107-109).</p

Self-similar breakup of polymeric threads as described by the Oldroyd-B model

When a drop of fluid containing long, flexible polymers breaks up, it forms threads of almost constant thickness, whose size decreases exponentially in time. Using an Oldroyd-B fluid as a model, we show that the thread profile, rescaled by the thread thickness, converges to a similarity solution. Using the correspondence between viscoelastic fluids and non-linear elasticity, we derive similarity equations for the full three-dimensional axisymmetric flow field in the limit that the viscosity of the solvent fluid can be neglected. A conservation law balancing pressure and elastic energy permits to calculate the thread thickness exactly. The explicit form of the velocity and stress fields can be deduced from a solution of the similarity equations. Results are validated by detailed comparison with numerical simulations

Cusp-Shaped Elastic Creases and Furrows

The surfaces of growing biological tissues, swelling gels, and compressed rubbers do not remain smooth, but frequently exhibit highly localized inward folds. We reveal the morphology of this surface folding in a novel experimental setup, which permits us to deform the surface of a soft gel in a controlled fashion. The interface first forms a sharp furrow, whose tip size decreases rapidly with deformation. Above a critical deformation, the furrow bifurcates to an inward folded crease of vanishing tip size. We show experimentally and numerically that both creases and furrows exhibit a universal cusp shape, whose width scales like y3/2 at a distance y from the tip. We provide a similarity theory that captures the singular profiles before and after the self-folding bifurcation, and derive the length of the fold from finite deformation elasticity.publishe

Cox–Voinov theory with slip

Most of our understanding of moving contact lines relies on the limit of small capillary number Ca . This means the contact line speed is small compared to the capillary speed γ/η , where γ is the surface tension and η the viscosity, so that the interface is only weakly curved. The majority of recent analytical work has assumed in addition that the angle between the free surface and the substrate is also small, so that lubrication theory can be used. Here, we calculate the shape of the interface near a slip surface for arbitrary angles, and for two phases of arbitrary viscosities, thereby removing a key restriction in being able to apply small capillary number theory. Comparing with full numerical simulations of the viscous flow equation, we show that the resulting theory provides an accurate description up to Ca≈0.1 in the dip coating geometry, and a major improvement over theories proposed previously