A molecular-dynamics study of sliding liquid nanodrops: Dynamic contact angles and the pearling transition.

HYPOTHESIS: That the behavior of sliding drops at the nanoscale mirrors that seen in macroscopic experiments, that the local microscopic contact angle is velocity dependent in a way that is consistent with the molecular-kinetic theory (MKT), and that observations at this scale shed light on the pearling transition seen with larger drops. METHODS: We use large-scale molecular dynamics (MD) to model a nanodrop of liquid sliding across a solid surface under the influence of an external force. The simulations enable us to extract the shape of the drop, details of flow within the drop and the local dynamic contact angle at all points around its periphery. FINDINGS: Our results confirm the macroscopic observation that the dynamic contact angle at all points around the drop is a function of the velocity of the contact line normal to itself, Ucmsinϕ, where Ucm is the velocity of the drop's center of mass and ϕ is the slope of the contact line with respect to the direction of travel. Flow within the drop agrees with that observed on the surface of macroscopic drops. If slip between the first layer of liquid molecules and the solid surface is accounted for, the velocity-dependence of the dynamic contact angle is identical with that found previous MD simulations of spreading drops, and consistent with the MKT. If the external force is increased beyond a certain point, the drop elongates and a neck appears between the front and rear of the drop, which separate into two distinct zones. This appears to be the onset of the pearling transition at the tip of a macroscopic drop. The receding contact angle at the tip of the drop is far removed from its equilibrium value but non-zero and approaches a more-or-less constant critical value as the transition progresses.

Viscoelasticity breaks the symmetry of impacting jets.

A jet of a Newtonian liquid impacting on a wall at right angle spreads as a thin liquid sheet which preserves the radial symmetry of the jet. We report that for a viscoelastic jet (solution of polyethylene glycol in water) this symmetry can break; close to the wall, the jet cross section becomes faceted and radial steady liquid films (wings) form, which connect the cross-section vertices to the sheet. The number of wings increases with increasing the viscoelastic relaxation time of the solution, but also with increasing jet velocity and decreasing distance from the jet nozzle to the wall. We propose a mechanism for this surprising destabilization of the jet shape, which develops perpendicularly to the direction expected for a buckling mechanism, and explain these dependencies. We also discuss the large-scale consequences of the jet destabilization on the sheet spreading and fragmentation, which show through the faceting of hydraulic jumps and of suspended (Savart) sheets.

General mechanism for the meandering instability of rivulets of Newtonian fluids.

A rivulet flowing down an inclined plane often does not follow a straight path, but starts to meander spontaneously. Here we show that this instability is the result of two key ingredients: fluid inertia and anisotropy of the friction between rivulet and substrate. Meandering only occurs if the motion normal to the instantaneous flow direction is more difficult than parallel to it. We give a quantitative criterion for the onset of meandering and confirm it by comparing to the flow of a rivulet between two glass plates which are wetted completely. Above the threshold, the rivulet follows an irregular pattern with a typical wavelength of a few cm.

Propagating wave pattern on a falling liquid curtain.

A regular pattern of surface waves is observed on a liquid curtain falling from a horizontal, wetted tube, maintained between two vertical wires. Since the upper boundary is not constrained in the transverse direction, the top of the curtain enters a pendulum-like motion, when the flow rate is progressively reduced, coupled to the propagation of curtain undulations, structured as a checkerboard. This structure is formed by two patterns of propagating waves. In some sense, these propagating patterns replace the stationary pattern of liquid columns observed at a lower flow rate. Measurements of phase velocity, frequency, and wavelength are reported. The data are in agreement with a simple dimensional argument suggesting that the wave velocity is proportional to the surface tension divided by the mass flux of liquid per unit length. This scaling is also that followed by the fluid velocity at the so-called transonic point, i.e., the point where the fluid velocity equals that of sinuous waves. We finally discuss the implications of these results for the global stability of liquid curtains.

Moving contact lines of a colloidal suspension in the presence of drying.

This article presents the first experimental study of an advancing contact line for a colloidal suspension. A competition between the hydrodynamic flow due to the drop velocity and the drying is exhibited: drying accounts for particle agglomeration that pins the contact line whereas the liquid flow dilutes the agglomerated particles and allows the contact line to advance continuously. The dilution dominates at low concentration and high velocity, but at high concentration and low velocity, the contact line can be pinned by the particle agglomeration, which leads to a stick-slip motion of the contact line. The calculation of the critical speed splitting both regimes gives an order of magnitude comparable to that of experiments. Moreover, a model of agglomeration gives an estimation of both the size of the wrinkles formed during stick-slip and the force exerted by the wrinkle on the contact line.

Boundary conditions in the vicinity of a dynamic contact line: experimental investigation of viscous drops sliding down an inclined plane.

To probe the microscopic balance of forces close to a moving contact line, the boundary conditions around viscous drops sliding down an inclined plane are investigated. At first, the variation of the contact angle as a function of the scale of analysis is discussed. The dynamic contact angle is measured at a scale of 6 mum all around sliding drops for different volumes and speeds. We show that it depends only on the capillary number based on the local liquid velocity, measured by particle tracking. This velocity turns out to be normal to the contact line everywhere. It indirectly proves that, in comparison with the divergence involved in the normal direction, the viscous stress is not balanced by intermolecular forces in the direction tangential to the contact line, so that any motion in this last direction gets damped.

Probing with a laser sheet the contact angle distribution along a contact line.

An optical method for probing contact angle distribution along contact lines of any shape using a laser sheet is proposed. This method is applied to a dry patch formed inside a film flowing along an inclined plane, both liquid and solid being transparent. Falling normally to the plane, a laser sheet cuts the contact line and is moved along this line. Distortions of the sheet trace observed on a screen put below the plane allow us to extract the contact angle distribution and the local line inclination along the line. Our results show that the contact angle around a dry patch is nearly constant and equal to the static advancing angle, at least when the evolution of its shape is followed for increasing flow rates. This supports a model of dry patch shape recently proposed by Podgorski and co-workers. Preliminary results obtained for decreasing flow are also qualitatively observed.

Corners, cusps, and pearls in running drops.

Small drops sliding down a partially wetting substrate bifurcate between different shapes depending on their capillary number Ca. At low Ca, they are delimited by a rounded, smooth contact line. At intermediate values they develop a corner at the trailing edge, the angle of which evolves from flat to 60 degrees with increasing velocity. Further up, they exhibit a cusped tail that emits smaller drops ("pearls"). These bifurcations may be qualitatively and quantitatively recovered by considering the dynamic contact angle along the contact line.

Control of electrohydrodynamic distortion of sample streams in continuous flow electrophoresis using oscillating fields.

Continuous flow electrophoresis is a method to separate ions contained in a sample continuously injected into a laminar flow of electrolyte as a cylindrical stream. Usually, the sample is more conductive than the electrolyte, and the charges created at the sample-electrolyte interface lead to electrohydrodynamic distortions which reduce the separation power of this technique. We demonstrate theoretically that the rate of electrohydrodynamic distortion of a cylindrical sample stream can be reduced to zero, by superimposing to the AC field responsible for the separation of a DC field transverse to it and to the flow direction, with an appropriate frequency, and an effective strength equal to that of the DC field. Using a continuous flow electrophoresis chamber, in which such a field is produced using capacitive electrodes, the major predictions of the theory are confirmed. In particular, it is shown that a sample stream more conductive than the carrying electrolyte, which was seriously deformed in the absence of a transverse AC field, recovers its cylindrical shape in presence of the field. The implications of this discovery for the separating power of continuous-flow electrophoresis are discussed.