Jacobus Hendrikus Snoeijer

Order-to-disorder transition in ring-shaped colloidal stains.

A colloidal dispersion droplet evaporating from a surface, such as a drying coffee drop, leaves a distinct ring-shaped stain. Although this mechanism is frequently used for particle self-assembly, the conditions for crystallization have remained unclear. Our experiments with monodisperse colloidal particles reveal a structural transition in the stain, from ordered crystals to disordered packings. We show that this sharp transition originates from a temporal singularity of the flow velocity inside the evaporating droplet at the end of its life. When the deposition speed is low, particles have time to arrange by Brownian motion, while at the end, high-speed particles are jammed into a disordered phase.

Short time dynamics of viscous drop spreading

Liquid drops start spreading directly after coming into contact with a solid substrate. Although this phenomenon involves a three-phase contact line, the spreading motion can be very fast. We experimentally study the initial spreading dynamics, characterized by the radius of the wetted area, for viscous drops. Using high-speed imaging with synchronized bottom and side views gives access to 6 decades of time resolution. We show that short time spreading does not exhibit a pure power-law growth. Instead, we find a spreading velocity that decreases logarithmically in time, with a dynamics identical to that of coalescing viscous drops. Remarkably, the contact line dissipation and wetting effects turn out to be unimportant during the initial stages of drop spreading.

Elastic deformation due to tangential capillary forces

A sessile liquid drop can deform the substrate on which it rests if the solid is sufficiently “soft.” In this paper we compute the detailed spatial structure of the capillary forces exerted by the drop on the solid substrate using a model based on Density Functional Theory. We show that, in addition to the normal forces, the drop exerts a previously unaccounted tangential force. The resultant effect on the solid is a pulling force near the contact line directed towards the interior of the drop, i.e., not along the interface. The resulting elastic deformations of the solid are worked out and illustrate the importance of the tangential forces

Pointy ice-drops: How water freezes into a singular shape

A water drop that is gently deposited on a very cold surface freezes into a pointy ice-drop with a very sharp tip. The formation of this singular shape originates from the reduction of mass density during the freezing process and can be explained using a simplified model for which the universal structure of the singularity is revealed in full detail. The combination of a relatively simple, static experiment, and the accessible asymptotic analysis makes this system an ideal introduction to the topic of singularities

Stokes flow near the contact line of an evaporating drop

The evaporation of sessile drops in quiescent air is usually governed by vapour diffusion. For contact angles below , the evaporative flux from the droplet tends to diverge in the vicinity of the contact line. Therefore, the description of the flow inside an evaporating drop has remained a challenge. Here, we focus on the asymptotic behaviour near the pinned contact line, by analytically solving the Stokes equations in a wedge geometry of arbitrary contact angle. The flow field is described by similarity solutions, with exponents that match the singular boundary condition due to evaporation. We demonstrate that there are three contributions to the flow in a wedge: the evaporative flux, the downward motion of the liquid–air interface and the eigenmode solution which fulfils the homogeneous boundary conditions. Below a critical contact angle of , the evaporative flux solution will dominate, while above this angle the eigenmode solution dominates. We demonstrate that for small contact angles, the velocity field is very accurately described by the lubrication approximation. For larger contact angles, the flow separates into regions where the flow is reversing towards the drop centre.

The force network ensemble for granular packings

For packings of hard but not perfectly rigid particles, the length scales that govern the packing geometry and the contact forces are well separated. This separation of length scales is explored in the force network ensemble, where one studies the space of allowed force configurations for a given, frozen contact geometry. Here we review results of this approach, which yields nontrivial predictions for the effect of packing dimension and anisotropy on the contact force distribution P(f), the response to overall shear and point forcing, all of which can be studied in great numerical detail. Moreover, there are emerging analytical approaches that very effectively capture, for example, the form of force distributions.

Elasto-capillarity at the nanoscale: on the coupling between elasticity and surface energy in soft solids

The capillary forces exerted by liquid drops and bubbles on a soft solid are directly measured using molecular dynamics simulations. The force on the solid by the liquid near the contact line is neither oriented along the liquid vapor interface nor perpendicular to the solid surface, as usually assumed, but points towards the liquid. It is shown that the elastic deformations induced by this force can only be explained if, in contrast to an incompressible liquid, the surface stress is different from the surface energy. Using thermodynamic variations we show that the surface stress and the surface energy can both be determined accurately by measuring the deformation of a slender body plunged in a liquid. The results obtained from molecular dynamics fully confirm those recently obtained experimentally [Marchand et al., Phys. Rev. Lett., (2012), 108, 094301] for an elastomeric wire.

Rush-hour in evaporating coffee drops

The pioneering work of Deegan et al. [Nature 389, (1997)] showed how a drying sessile droplet suspension of particles presents a maximum evaporating flux at its contact line which drags liquid and particles creating the well known coffee stain ring. In this Fluid Dynamics Video, measurements using micro Particle Image Velocimetry and Particle Tracking clearly show an avalanche of particles being dragged in the last moments, for vanishing contact angles and droplet height. This explains the different characteristic packing of the particles in the layers of the ring: the outer one resembles a crystalline array, while the inner one looks more like a jammed granular fluid. Using the basic hydrodynamic model used by Deegan et al. [Phys. Rev. E 62, (2000)] it will be shown how the liquid radial velocity diverges as the droplet life comes to an end, yielding a good comparison with the experimental data. 1 Technical Details of the submitted video A single experiment is shown in the included video (low quality, higher quality): an evaporating droplet of about 3μl containing fluorescent polystyrene ∗a.g.marin@utwente.nl ar X iv :1 01 0. 31 68 v1 [ ph ys ic s. fl udy n] 1 5 O ct 2 01 0 particles of 1μm in a concentration of 0.2%w/w (∼ 7x10part/cm) evaporates at 23°C and controlled humidity of 30% on a thin glass slide. Visualization is performed from side view and bottom view simultaneously. For the side view, a x10 long distance microscope and a high definition digital video camera is employed. The images are then processed with a self-made MATLAB algorithm to obtain contact angle, volume and radius of the droplet in time. Bottom view is performed with an inverted microscope, using x40 magnification and a intensified PCO sensicam camera and focusing at the first observable layer of particles close to the glass slide. A self-made MATLAB μPIV algorithm is then used to process the images and extract the velocity field in time. For more information about this work, we would like to invite you to assist to the presentation from Hanneke Gelderblom at the 63rd Annual American Physics Society Meeting (Division of Fluid Dynamics) in Long Beach, CA (Abstract CS.00004, Nov 21st, 2010).The pioneering work of Deegan et al. [Nature 389, (1997)] showed how a drying sessile droplet suspension of particles presents a maximum evaporating flux at its contact line which drags liquid and particles creating the well known coffee stain ring. In this Fluid Dynamics Video, measurements using micro Particle Image Velocimetry and Particle Tracking clearly show an avalanche of particles being dragged in the last moments, for vanishing contact angles and droplet height. This explains the different characteristic packing of the particles in the layers of the ring: the outer one resembles a crystalline array, while the inner one looks more like a jammed granular fluid. Using the basic hydrodynamic model used by Deegan et al. [Phys. Rev. E 62, (2000)] it will be shown how the liquid radial velocity diverges as the droplet life comes to an end, yielding a good comparison with the experimental data.

Similarity theory of lubricated Hertzian contacts

We consider a heavily loaded, lubricated contact between two elastic bodies at relative speed U, such that there is substantial elastic deformation. As a result of the interplay between hydrodynamics and non-local elasticity, a fluid film develops between the two solids, whose thickness scales as U 3/5. The film profile h is selected by a universal similarity solution along the upstream inlet. Another similarity solution is valid at the outlet, which exhibits a local minimum in the film thickness. The two solutions are connected by a hyperbolic problem underneath the contact. Our asymptotic results for a soft sphere pressed against a hard wall are shown to agree with both experiment and numerical simulations.

Lubrication of soft viscoelastic solids

Lubrication flows appear in many applications in engineering, biophysics, and in nature. Separation of surfaces and minimisation of friction and wear is achieved when the lubrication fluid builds up a lift force. In this paper we analyse soft lubricated contacts by treating the solid walls as viscoelastic: soft materials are typically not purely elastic, but dissipate energy under dynamical loading conditions. We present a method for viscoelastic lubrication and focus on three canonical examples, namely Kelvin-Voigt-, Standard Linear-, and Power Law-rheology. It is shown how the solid viscoelasticity affects the lubrication process when the timescale of loading becomes comparable to the rheological timescale. We derive asymptotic relations between lift force and sliding velocity, which give scaling laws that inherit a signature of the rheology. In all cases the lift is found to decrease with respect to purely elastic systems.