The steady flow of three viscoelastic fluids (Oldroyd-B, FENE-P, and Owens model for blood) in a two-dimensional channel, partly bound by a deformable, finite thickness neo-Hookean solid, is computed. The limiting Weissenberg number beyond which computations fail to converge is found to increase with increasing dimensionless solid elasticity parameter Γ, following the trend Owens > FENE- P > Oldroyd-B. The highly shear thinning nature of Owens model leads to the elastic solid always collapsing into the channel, for the wide range of values of Γ considered here. In the case of the FENE-P and Oldroyd-B models, however, the fluid-solid interface can be either within the channel, or bulge outwards, depending on the value of Γ. This behaviour differs considerably from predictions of earlier models that treat the deformable solid as a zero-thickness membrane, in which case the membrane always lies within the channel. The capacity of the solid wall to support both pressure and shear stress, in contrast to the zero-thickness membrane that only responds to pressure, is responsible for the observed difference. Compar- ison of the stress and velocity fields in the channel for the three viscoelastic fluids, with the predictions for a Newtonian fluid, reveals that shear thinning rather than elasticity is the key source of the observed differences in behaviour.
The electroosmotic flow of non-Newtonian fluids in deformable microchannels is fundamentally important in the understanding of the hydrodynamics in physiological flows. The performance of these microchannels is governed by the load bearing capacity indicating the maximum amount of load that the device can withstand. While significant research efforts are aimed towards the coupling of electrokinetics with substrate deformability, the corresponding enhancement in the performances still remains elusive. Towards this, employing an intricate coupling between substrate compliance, hydrodynamic, and …
We investigate the effects of helical swimmer shape (i.e., helical pitch angle and tail thickness) on swimming dynamics in a constant viscosity viscoelastic (Boger) fluid via a combination of particle tracking velocimetry, particle image velocimetry and 3D simulations of the FENE-P model. The 3D printed helical swimmer is actuated in a magnetic field using a custom-built rotating Helmholtz coil. Our results indicate that increasing the swimmer tail thickness and pitch angle enhances the normalized swimming speed (i.e., ratio of swimming speed in the Boger fluid to that of the Newtonian fluid).…
A microfluidic device is constructed from PDMS with a single channel having a short section that is a thin flexible membrane, in order to investigate the complex fluid-structure interaction that arises between a flowing fluid and a deformable wall. Experimental measurements of membrane deformation and pressure drop are compared with predictions of two-dimensional and three-dimensional computational models which numerically solve the equations governing the elasticity of the membrane coupled with the equations of motion for the fluid. It is shown that the two-dimensional model, which assumes a …
We report an investigation of the equilibrium and dynamic properties of polyelectrolyte solutions confined between platinum surfaces with a dynamic Surface Force Apparatus. The polyelectrolyte adsorbs on the surfaces in a dense compact layer bearing a surface charge in good agreement with the theoretical predictions. The flow of the solution on this charged adsorbed layer is probed over four decades of spatial scales and one decade of frequency by dynamic measurements. At distances larger than the hundredth of nanometers, the flow of the viscoelastic solution is well described by a partial sli…
The motion of a rotating helical body in a viscoelastic fluid is considered. In the case of force-free swimming, the introduction of viscoelasticity can either enhance or retard the swimming speed and locomotive efficiency, depending on the body geometry, fluid properties, and the body rotation rate. Numerical solutions of the Oldroyd-B equations show how previous theoretical predictions break down with increasing helical radius or with decreasing filament thickness. Helices of large pitch angle show an increase in swimming speed to a local maximum at a Deborah number of order unity. The numer…
We use the impact of drops on a small solid target as a tool to investigate the behavior of viscoelastic fluids under extreme deformation rates. We study two classes of transient networks: semidilute solutions of supramolecular polymers and suspensions of spherical oil droplets reversibly linked by polymers. The two types of samples display very similar linear viscoelastic properties, which can be described with a Maxwell fluid model, but contrasting nonlinear properties due to different network structure. Upon impact, weakly viscoelastic samples exhibit a behavior qualitatively similar to tha…
We study pattern formation during tensile deformation of confined viscoelastic layers. The use of a model system (PDMS with different degrees of crosslinking) allows us to go continuously from a viscous liquid to an elastic solid. We observe two distinct regimes of fingering instabilities: a regime called "elastic" with interfacial crack propagation where the fingering wavelength only scales with the film thickness, and a bulk regime called "viscoelastic" where the fingering instability shows a Saffman-Taylor-like behavior. We find good quantitative agreement with theory in both cases and pres…
We have derived the general solution of a wave equation describing the dynamics of two-layere viscoelastic polymer materials of arbitrary thickness deposited on solid (quartz) surfaces in a fluid environment. Within the Voight model of viscoelastic element, we calculate the acoustic response of the system to an applied shear stress, i.e. we find the shift of the quartz generator resonance frequency and of the dissipation factor, and show that it strongly depends on the viscous loading of the adsorbed layers and on the shear storage and loss moduli of the overlayers. These results can readily b…
We study the frictional behavior of both elastic and viscoelastic thin coatings bonded to a seemingly rigid substrate and sliding against a rough profile in the presence of Coulomb friction at the interface. The aim is to explore the effect of the coupling between the normal and tangential displacement fields arising from the finiteness of the material thickness and to quantify the contribution this can have on energy losses. We found that, due to normal-tangential coupling, asymmetric contacts and consequently additional friction are observed even for purely elastic layers, indeed associated …
Characterizing the softness of deformable materials having partial elastic and partial viscous behaviour via soft lubrication experiments has emerged as a versatile and robust methodology in recent times. However, a straightforward extension of the classical elastohydrodynamic lubrication theory that is commonly employed for characterizing elastic materials turns out to be rather inadequate in explaining the response of such viscoelastic materials subjected to dynamic loading conditions, despite adhering to a mathematically acceptable framework via the complex Young's modulus as a material pro…
Thin elastic sheets supported on compliant media form wrinkles under lateral compression. Since the lateral pressure is coupled to the sheet's deformation, varying it periodically in time creates a parametric excitation. We study the resulting parametric resonance of wrinkling modes in sheets supported on semi-infinite elastic or viscoelastic media, at pressures smaller than the critical pressure of static wrinkling. We find distinctive behaviors as a function of excitation amplitude and frequency, including (a) a different dependence of the dynamic wrinkle wavelength on sheet thickness compar…
When a soft elastic cylinder is bent beyond a critical radius of curvature, a sharp fold in the form of a kink appears at its inner side while the outer side remains smooth. The critical radius increases linearly with the diameter of the cylinder while remaining independent of its elastic modulus, although, its maximum deflection at the location of the kink depends on both the diameter and the modulus of the cylinders. Experiments are done also with annular cylinders of varying wall thickness which exhibits both the kinking and the ovalization of the cross-section. The kinking phenomenon appea…
Recent experiments have shown that liquid drops on highly deformable substrates exhibit mutual interactions. This is similar to the Cheerios effect, the capillary interaction of solid particles at a liquid interface, but now the roles of solid and liquid are reversed. Here we present a dynamical theory for this inverted Cheerios effect, taking into account elasticity, capillarity and the viscoelastic rheology of the substrate. We compute the velocity at which droplets attract, or repel, as a function of their separation. The theory is compared to a simplified model in which the viscoelastic di…
Using a dynamic Surface Force Apparatus, we demonstrate that the notion of slip length used to describe the boundary flow of simple liquids, is not appropriate for viscoelastic liquids. Rather, the appropriate description lies in the original Navier's partial slip boundary condition, formulated in terms of an interfacial friction coefficient. We establish an exact analytical expression to extract the interfacial friction coefficient from oscillatory drainage forces between a sphere and a plane, suitable for dynamic SFA or Atomic Force Microscopy non-contact measurements. We use this model to i…
In order to investigate the rheological properties of viscoelastic fluids by mesoscopic hydrodynamics methods, we develop a multi-particle collision dynamics (MPC) model for a fluid of harmonic dumbbells. The algorithm consists of alternating streaming and collision steps. The advantage of the harmonic interactions is that the integration of the equations of motion in the streaming step can be performed analytically. Therefore, the algorithm is computationally as efficient as the original MPC algorithm for Newtonian fluids. The collision step is the same as in the original MPC method. All part…
Understanding and harnessing the coupling between lubrication pressure and elasticity provides materials design strategies for applications such as adhesives, coatings, microsensors, and biomaterials. Elastic deformation of compliant solids caused by viscous forces can also occur during dynamic force measurements in instruments such as the surface forces apparatus (SFA) or the atomic force microscope (AFM). We briefly review hydrodynamic interactions in the presence of soft, deformable interfaces in the lubrication limit. More specifically, we consider the scenario of two surfaces approaching …
We characterize the spatiotemporal deformation of an elastic film during the radial drainage of fluid from a narrowing gap. Elastic deformation of the film takes the form of a dimple and prevents full contact to be reached. With thinner elastic film the stress becomes increasingly supported by the underlying rigid substrate and the dimple formation is suppressed, which allows the surfaces to reach full contact. We highlight the lag due to viscoelasticity on the surface profiles, and that for a given fluid film thickness deformation leads to stronger hydrodynamic forces than for rigid surfaces.
Kinneyia are a class of microbially mediated sedimentary fossils. Characterised by clearly defined ripple structures, Kinneyia are generally found in areas that were formally littoral habitats and covered by microbial mats. To date there has been no conclusive explanation of the processes involved in the formation of these fossils. Microbial mats behave like viscoelastic fluids. We propose that the key mechanism involved in the formation of Kinneyia is a Kelvin-Helmholtz type instability induced in a viscoelastic film under flowing water. A ripple corrugation is spontaneously induced in the fi…
The adhesion of a stiff film onto a curved substrate often generates elastic stresses in the film that eventually give rise to its delamination. Here we predict that delamination of very thin films can be dramatically suppressed through tiny, smooth deformations of the substrate, dubbed here "wrinklogami", that barely affect the macroscale topography. This "pro-lamination" effect reflects a surprising capability of smooth wrinkles to suppress compression in elastic films even when spherical or other doubly-curved topography is imposed, in a similar fashion to origami folds that enable construc…
The effects of elasticity on filament thinning and breakup are investigated in microchannel cross flow. When a viscous solution is stretched by an external immiscible fluid, a low 100 ppm polymer concentration strongly affects the breakup process, compared to the Newtonian case. Qualitatively, polymeric filaments show much slower evolution, and their morphology features multiple connected drops. Measurements of filament thickness show two main temporal regimes: flow- and capillary-driven. At early times both polymeric and Newtonian fluids are flow-driven, and filament thinning is exponential. …
In this paper, we investigate the periodic peeling behavior of opposing symmetric peeling fronts involving an elastic tape peeled off from a deformable substrate of finite thickness, backed onto a rigid foundation. We treat the problem by means of an energetic formulation, and we found that, depending on the values of the initial detached length $l$, substrate thickness $h$, and peeling periodicity $λ$, the translational invariance of the peeling process is lost and restored, as the elastic interaction between the peeling fronts is limited by the substrate thickness. Indeed, given $h$ and $λ$,…
