Nuri Aksel

Vortices in film flow over strongly undulated bottom profiles at low Reynolds numbers

We present an experimental study of gravity driven films flowing down sinusoidal bottom profiles of high waviness. We find vortices in the valleys of the undulated bottom profile. They are observed at low Reynolds numbers down to the order of 10−5. The vortices are visualized employing a particle image velocimeter with fluorescent tracers. It turns out that the vortices are generated beyond a critical film thickness. Their size tends to a finite value for thick films. The critical film thickness depends on the waviness of the bottom undulation, the inclination angle, and on the surface tension but not on the Reynolds number. Increasing the waviness, a second vortex can be generated.

Instability of a liquid film flowing down an inclined wavy plane

A linear stability analysis of a Newtonian liquid film flowing down an inclined wavy plane is carried out. It is studied how wavy bottom variations, which are long compared to the film thickness, modify the stability of the steady film flow with respect to that down a flat inclined plane. By allowing for rather moderate bottom variations, it shows the impact of geometric nonlinearities on the instability. In this case, the spatial growth of disturbances becomes dependent on the phase along the bottom wave. Averaging over the bottom variations, it is found that on a large scale the critical Reynolds number for the onset of surface waves is higher than that for a flat bottom. As in the case of a flat bottom, the instability occurs at long wavelength. Locally, however, at the steep slopes the critical Reynolds number is lower than for a flat incline. In a certain range of waves numbers and Reynolds numbers, shorter waves may be excited at the steep slopes and damped at the flat ones.

Influence of inertia on eddies created in films creeping over strongly undulated substrates

We present an experimental study of gravity driven films flowing down a sinusoidal bottom profile of high amplitude. Eddies that are created in the valleys of the undulated bottom profile under creeping flow conditions are modified as inertia becomes significant. We find that the eddies become tilted and their size increases depending on the Froude number. Surface waves, which are generated from natural noise beyond a certain Froude number, induce an oscillation and a breakup of the separatrix by the turnstile-lobe mechanism. This leads to a material exchange between the eddy and the overlying film. We show how the surface waves are coupled to the eddies and discuss the time scales associated with the material exchange of suspended particles.

Investigation of the solid–liquid transition of highly concentrated suspensions in oscillatory amplitude sweeps

Suspensions of quasimonodisperse polymethylmethacrylate spheres with mean diameters of 4.7 and 3.1 μm, dispersed in a low-molecular-weight polydimethylsiloxane, were characterized using oscillatory shear amplitude sweeps. Thereby, the solid volume concentration was varied. The influence of the sample preparation, the mode of the experiment (controlled shear rate, controlled shear stress), and the parameters of the amplitude sweep such as logarithmic ramp time, measurement time, and frequency were investigated. The logarithmic ramp and the measurement time were found to be the substantial factors which especially influence the experimental results at low shear stress amplitudes. The frequency has an effect only at higher shear stress amplitudes where the material behaves linearly again. All suspensions showed a Hookean solid behavior at low shear stress amplitudes and a Newtonian fluid behavior at high shear stress amplitudes. In the transition range between the Hookean and the Newtonian behavior the analy...

Elastic constants and their admissible values for incompressible and slightly compressible anisotropic materials

SummaryConstitutive relations for incompressible (slightly compressible) anisotropic materials cannot (could hardly) be obtained through the inversion of the generalized Hookes law since the corresponding compliance tensor becomes singular (ill-conditioned) in this case. This is due to the fact that the incompressibility (slight compressibility) condition imposes some additional constraints on the elastic constants. The problem requires a special procedure discussed in the present paper. The idea of this procedure is based on the spectral decomposition of the compliance tensor but leads to a closed formula for the elasticity tensor without explicit using the eigenvalue problem solution. The condition of nonnegative (positive) definiteness of the material tensors restricts the elastic constants to belong to an admissible value domain. For orthotropic and transversely isotropic incompressible as well as isotropically compressible materials the corresponding domains are illustrated graphically.

Competing geometric and inertial effects on local flow structure in thick gravity-driven fluid films

The formation and presence of eddies within thick gravity-driven free-surface film flow over a corrugated substrate are considered, with the governing equations solved semianalytically using a complex variable method for Stokes flow and numerically via a full finite element formulation for the more general problem when inertia is significant. The effect of varying geometry (involving changes in the film thickness or the amplitude and wavelength of the substrate) and inertia is explored separately. For Stokes-like flow and varying geometry, excellent agreement is found between prediction and existing flow visualizations and measured eddy center locations associated with the switch from attached to locally detached flow. It is argued that an appropriate measure of the influence of inertia at the substrate is in terms of a local Reynolds number based on the characteristic corrugation length scale. Since, for small local Reynolds numbers, the local flow structure there becomes effectively decoupled from the i...

Shear rheology of a cell monolayer

We report a systematic investigation of the mechanical properties of fibroblast cells using a novel cell monolayer rheology (CMR) technique. The new technique provides quantitative rheological parameters averaged over ~106 cells making the experiments highly reproducible. Using this method, we are able to explore a broad range of cell responses not accessible using other present day techniques. We perform harmonic oscillation experiments and step shear or step stress experiments to reveal different viscoelastic regimes. The evolution of the live cells under externally imposed cyclic loading and unloading is also studied. Remarkably, the initially nonlinear response becomes linear at long timescales as well as at large amplitudes. Within the explored rates, nonlinear behaviour is only revealed by the effect of a nonzero average stress on the response to small, fast deformations. When the cell cytoskeletal crosslinks are made permanent using a fixing agent, the large amplitude linear response disappears and the cells exhibit a stress stiffening response instead. This result shows that the dynamic nature of the cross-links and/or filaments is responsible for the linear stress-strain response seen under large deformations. We rule out the involvement of myosin motors in this using the inhibitor drug blebbistatin. These experiments provide a broad framework for understanding the mechanical responses of the cortical actin cytoskeleton of fibroblasts to different imposed mechanical stimuli.

Bottom reconstruction in thin-film flow over topography: Steady solution and linear stability

We consider viscous gravity-driven films flowing over undulated substrates. Instead of the widely studied direct problem of finding the free surface for a given bottom topography, we focus on the inverse problem: Given a specific free surface shape, we seek the corresponding bottom topography which causes this free surface profile. As an asymptotic approach for thin films and moderate Reynolds numbers, we apply the weighted-residual integral boundary-layer method which enables us to derive a set of two evolution equations for the film thickness and the flow rate. We prescribe the free surface as a monofrequent periodic function and discuss the influence of inertia, film thickness, and surface tension on the shape of the corresponding substrate. For small free surface undulations, we can solve the bottom contour analytically and study its parametric dependence. The analytical results are then validated with numerical simulations. Furthermore, we consider the stability of the corresponding direct problem, w...

Hydraulic jumps and standing waves in gravity-driven flows of viscous liquids in wavy open channels

We experimentally study the flow of a viscous liquid down an inclined channel with a sinusoidal bottom profile of moderate waviness. Depending on the film thickness, we find different flow regimes that are usually not observed in the same system. Besides characterizing these regimes, we study the transition from one regime to the other. At low inclination angles, basins form due to nonmonotonously falling bottom slopes. At the inflow of the basins, we observe the formation of stationary hydraulic jumps as shock fronts and surface rollers. We report on a bistable region in which both phenomena can occur. At the low end of the bistable region, an instationary regime of a shock with a fingering lateral modulation is found. The bistability of shocks and surface rollers is traced back to that of the shock front and the fingering. At higher volume flux or inclination angles, standing waves are created in resonance with the bottom contour. At the rising edge of the resonance curves, we observe humps that seem to...

Adsorption behavior of nonionic surfactants studied by drop volume technique

This study shows that the drop volume technique can be used to determine the adsorption behavior and interfacial adsorption kinetics of surfactants at fluid interfaces. Using this tensiometric method, one can determine not only the interfacial tension of the pure phases, but also the critical concentration for the formation of micelles (CMC) in a surfactant system, the quasi-static (equilibrium) interfacial tension, the diffusion coefficient as a function of surfactant concentration, and the maximum adsorption density at the interface. The determination of the dynamic interfacial tension allows to indirectly characterize the kinetics of surfactant adsorption. The time dependence of the interfacial coverage resulting from this adsorption process is well described by two approximation solutions (for short and long adsorption times), with the result that the diffusion coefficients calculated as a function of surfactant concentration using these two methods show good agreement. The droplet formation and dripping process of a surfactant solution in a capillary was found to be quite different depending on whether the process occurred in gaseous or fluid surroundings. In particular, the formation of satellite droplets was different for the two different media, in terms of both the volume and shape of the satellite droplets.