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 present a reduced parameter describing the transition between the two regimes and allowing to predict the observed patterns over the whole range of viscoelastic properties.
We investigate the lateral dynamics in a purely viscous lipid membrane surrounded by viscoelastic media such as polymeric solutions. We first obtain the generalized frequency-dependent mobility tensor and focus on the case when the solvent is sandwiched by hard walls. Due to the viscoelasticity of the solvent, the mean square displacement of a disk embedded in the membrane exhibits an anomalous diffusion. An useful relation which connects the mean square displacement and the solvent modulus is provided. We also calculate the cross-correlation of the particle displacements which can be applied …
The viscoelastic dynamics of nano-confined water is studied by means of atomic force microscopy (AFM). We observe a nonlinear viscoelastic behavior remarkably similar to that widely observed in metastable complex fluids. We show that the origin of the measured nonlinear viscoelasticity in nano-confined water is a strain rate dependent relaxation time and slow dynamics. By measuring the viscoelastic modulus at different frequencies and strains, we find that the intrinsic relaxation time of nano-confined water is in the range 0.1-0.0001 s, orders of magnitude longer than that of bulk water, and …
Motivated from the classical expressions of the mean squared displacement and the velocity autocorrelation function of Brownian particles suspended either in a Newtonian viscous fluid or trapped in a harmonic potential, we show that for all time-scales the mean squared displacement of Brownian microspheres with mass $m$ and radius $R$ suspended in any linear, isotropic viscoelastic material is identical to the creep compliance of a linear mechanical network that is a parallel connection of the linear viscoelastic material with an inerter with distributed inertance, $m_R=\frac{m}{\text{6}πR}$. …
This second part of paper develops a theory of linear viscoelastic nematodynamics applicable to LCP. The viscous and elastic nematic components in theory are described by using the LEP approach for viscous nematics and de Gennes free energy for weakly elastic nematic elastomers. The case of applied external magnetic field exemplifies the occurrence of non-symmetric stresses. In spite of multi- (10) parametric character of the theory, the use of nematic operators presents it in an elegant form. When the magnetic field is absent, the theory is simplified for symmetric case with 6 parameters, and…
We experimentally study the dynamics of active particles (APs) in a viscoelastic fluid under various geometrical constraints such as flat walls, spherical obstacles and cylindrical cavities. We observe that the main effect of the confined viscoelastic fluid is to induce an effective repulsion on the APs when moving close to a rigid surface, which depends on the incident angle, the surface curvature and the particle activity. Additionally, the geometrical confinement imposes an asymmetry to their movement, which leads to strong hydrodynamic torques, thus resulting in detention times on the wall…
New exact solutions are exhibited within the framework of finite viscoelasticity. More precisely, the solutions correspond to finite-amplitude, transverse, linearly-polarized, inhomogeneous motions superposed upon a finite homogeneous static deformation. The viscoelastic body is composed of a Mooney-Rivlin viscoelastic solid, whose constitutive equation consists in the sum of an elastic part (Mooney-Rivlin hyperelastic model) and a viscous part (Newtonian viscous fluid model). The analysis shows that the results are similar to those obtained for the purely elastic case; inter alia, the normals…
The deformation and break-up of Newtonian/viscoelastic droplets are studied in confined shear flow. Our numerical approach is based on a combination of Lattice-Boltzmann models (LBM) and finite difference schemes, the former used to model two immiscible fluids with variable viscous ratio, and the latter used to model the polymer dynamics. The kinetics of the polymers is introduced using constitutive equations for viscoelastic fluids with finitely extensible non-linear elastic dumbbells with Peterlin's closure (FENE-P). We quantify the droplet response by changing the polymer relaxation time $τ…
The unique ability of a red blood cell to flow through extremely small microcapillaries depends on the viscoelastic properties of its membrane. Here, we study in vitro the response time upon flow startup exhibited by red blood cells confined into microchannels. We show that the characteristic transient time depends on the imposed flow strength, and that such a dependence gives access to both the effective viscosity and the elastic modulus controlling the temporal response of red cells. A simple theoretical analysis of our experimental data, validated by numerical simulations, further allows us…
We provide a detailed study of the interplay between the different interactions which appear in the Brownian motion of a micronsized sphere immersed in a viscoelastic fluid measured with optical trapping interferometry. To explore a wide range of viscous, elastic and optical forces, we analyze two different viscoelastic solutions at various concentrations, which provide a dynamic polymeric structure surrounding the Brownian sphere. Our experiments show that, depending of the fluid, optical forces, even if small, slightly modify the complex modulus at low frequencies. Based on our findings, we …
Rheological responses are the most relevant features to describe soft matter. So far, such constitutive relations are still not well understood in terms of small scale properties, although this knowledge would help the design of synthetic and bio-materials. Here, we investigate, computational and analytically, how mesoscopic-scale interactions influence the macroscopic behavior of viscoelastic materials. We design a coarse-grained approach where the local elastic and viscous contributions can be controlled. Applying molecular dynamics simulations, we mimic real indentation assays. When elastic…
We study theoretically the velocity cross-correlations of a viscous fluid confined in a slit between two viscoelastic media. We analyze the effect of these correlations on the motions of particles suspended in the fluid. The compliance of the confining boundaries gives rise to a long-ranged pair correlation, decaying only as $1/r$ with the interparticle distance $r$. We show how this long-ranged effect may be used to extract the viscoelastic properties of the confining media without embedding tracer particles in them. We discuss the remarkable robustness of such a potential technique with resp…
The mesoscale rheology of a lamellar phase of a block copolymer is modeled as a structured fluid of uniaxial symmetry. The model predicts a viscoelastic response that depends on the angle between the the local lamellar planes and velocity gradients. We focus on the stability under oscillatory shear of a two layer configuration comprising a parallel and a perpendicularly oriented domain, so that the two layers have a different viscoelastic modulus $G^{*}(ω)$. A long wave, low Reynolds number expansion is introduced to analytically obtain the region of stability. When the response of the two lay…
The paper develops a continuum theory of weak viscoelastic nematodynamics of Maxwell type. It may describe the molecular elasticity effects in mono-domain flows of liquid crystalline polymers as well as the viscoelastic effects in suspensions of uniaxially symmetric particles in polymer fluids. Along with viscoelastic and nematic kinematics, the theory employs a general form of weakly elastic thermodynamic potential and the Leslie-Ericksen-Parodi type constitutive equations for viscous nematic liquids, while ignoring inertia effects and the Frank (orientation) elasticity in liquid crystal poly…
The sliding of non-Newtonian drops down planar surfaces results in a complex, entangled balance between interfacial forces and non linear viscous dissipation, which has been scarcely inspected. In particular, a detailed understanding of the role played by the polymer flexibility and the resulting elasticity of the polymer solution is still lacking. To this aim, we have considered polyacrylamide (PAA) solutions of different molecular weights, suspended either in water or glycerol/water mixtures. In contrast to drops with stiff polymers, drops with flexible polymers exhibit a remarkable elongati…
We determine both the in-plane and out-of-plane dynamics of viscoelastic membranes separating two viscous fluids in order to understand microrheological studies of such membranes. We demonstrate the general viscoelastic signatures in the dynamics of shear, bending, and compression modes. We also find a screening of the otherwise two-dimensional character of the response to point forces due to the presence of solvent. Finally, we show that there is a linear, hydrodynamic coupling between the in-plane compression modes of the membrane and the out-of-plane bending modes in the case where the memb…
Many swimming microorganisms, such as bacteria and sperm, use flexible flagella to move through viscoelastic media in their natural environments. In this paper we address the effects a viscoelastic fluid has on the motion and beating patterns of elastic filaments. We treat both a passive filament which is actuated at one end, and an active filament with bending forces arising from internal motors distributed along its length. We describe how viscoelasticity modifies the hydrodynamic forces exerted on the filaments, and how these modified forces affect the beating patterns. We show how high vis…
Spectra of thermal fluctuations of a wide range of interfaces, from liquid/air, viscoelastic material/air, liquid/liquid, to liquid/viscoelastic material interfaces, were measured over 100 Hz to 10 MHz frequency range. The obtained spectra were compared with the fluctuation theory of interfaces, and found to be mostly in quite good agreement, when the theory was generalized to apply to thermal fluctuations of liquid/viscoelastic material interfaces. The spectra were measured using a system that combines light reflection, statistical noise reduction through averaged correlations, and confocal m…
Stressed soft materials commonly present viscoelastic signatures in the form of power-law or exponential decay. Understanding the origins of such rheologic behaviors is crucial to find proper technological applications. Using an elastic network model of macromolecules immersed in a viscous fluid, we numerically reproduce those characteristic viscoelastic relaxations and show how the microscopic interactions determine the rheologic response. We find that exponential relaxations are indeed the most common behavior. However, power laws may arise when drag forces between the macromolecules and the…
We propose numerical simulations of viscoelastic fluids based on a hybrid algorithm combining Lattice-Boltzmann models (LBM) and Finite Differences (FD) schemes, the former used to model the macroscopic hydrodynamic equations, and the latter used to model the polymer dynamics. The kinetics of the polymers is introduced using constitutive equations for viscoelastic fluids with finitely extensible non-linear elastic dumbbells with Peterlin's closure (FENE-P). The numerical model is first benchmarked by characterizing the rheological behaviour of dilute homogeneous solutions in various configurat…
We investigate the dynamics of freely expanding liquid sheets prepared with fluids with different rheological properties, (i) viscous fluids with a zero-shear viscosity $η_0$ in the range $(1-1000) \, \mathrm{mPa.s}$ and (ii) viscoelastic Maxwell fluids whose elastic modulus, $G_0$, characteristic relaxation time, $τ$, and zero-shear viscosity, $η_0=G_0 τ$, can be tuned over several orders of magnitude. The sheets are produced by impacting a drop of fluid on a small cylindrical solid target. For viscoelastic fluids, we show that, when $τ$ is shorter than the typical lifetime of the sheet ($\si…
We introduce a comprehensive scheme to physically quantify both viscous and elastic rheological nonlinearities simultaneously, using an imposed large amplitude oscillatory shear (LAOS) strain. The new framework naturally lends a physical interpretation to commonly reported Fourier coefficients of the nonlinear stress response. Additionally, we address the ambiguities inherent in the standard definitions of viscoelastic moduli when extended into the nonlinear regime, and define new measures which reveal behavior that is obscured by conventional techniques.
The effects of elasticity on the break-up of liquid threads in microfluidic cross-junctions is investigated using numerical simulations based on the "lattice Boltzmann models" (LBM). Working at small Capillary numbers, we investigate the effects of non-Newtonian phases in the transition from droplet formation at the cross-junction (DCJ) and droplet formation downstream of the cross-junction (DC) (Liu & Zhang, ${\it Phys. Fluids.}$ ${\bf 23}$, 082101 (2011)). Viscoelasticity is found to influence the break-up point of the threads, which moves closer to the cross-junction and stabilizes. This is…
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…
In order to address basic questions of importance to microrheology, we study the dynamics of a rigid sphere embedded in a model viscoelastic medium consisting of an elastic network permeated by a viscous fluid. We calculate the complete response of a single bead in this medium to an external force and compare the result to the commonly-accepted, generalized Stokes-Einstein relation (GSER). We find that our response function is well approximated by the GSER only within a particular frequency range determined by the material parameters of both the bead and the network. We then discuss the releva…
We investigate freely expanding viscoelastic sheets. The sheets are produced by the impact of drops on a quartz plate covered with a thin layer of liquid nitrogen that suppresses shear viscous dissipation as a result of the cold Leidenfrost effect. The time evolution of the sheet is simultaneously recorded from top and side views using high-speed cameras. The investigated viscoelastic fluids are Maxwell fluids, which are characterized by low elastic moduli, and relaxation times that vary over almost two orders of magnitude, thus giving access to a large spectrum of viscoelastic and elastocapil…
A broad survey of viscoelastic data demonstrates that van der Waals, hydrogen-bonded, and ionic liquids, as well as polymeric, inorganic, and metallic melts share a structural relaxation pattern virtually insensitive to their morphological details. This mechanical simplicity is connected with that characterizing the fast reorientation dynamics prevailing in liquids devoid of a distinguishable secondary loss peak. By these means one is able to uncover a generic spectral pattern which rationalizes the recently reported "universality" of relaxation strength vs. stretching of the dielectric respon…
Intricate fluid displacement patterns, arising from the unstable growth of interfacial perturbations, can be driven by fluid viscoelasticity and surface tension. A soft glassy suspension ages, $i.e.$ its mechanical moduli evolve with time, due to the spontaneous formation of suspension microstructures. The shear and time-dependent rheology of an aging suspension can be exploited to generate a wide variety of interfacial patterns during its displacement by a Newtonian fluid. Using video imaging, we report a rich array of interfacial pattern morphologies: dense viscous, dendritic, viscoelastic f…
A necessary condition for the validity of the linear viscoelastic model for a (passive) polymeric cylinder with an ultrasonic hysteresis-type absorption submerged in a non-viscous fluid requires that the absorption efficiency is positive (Qabs > 0) satisfying the law of the conservation of energy. This condition imposes restrictions on the values attributed to the normalized absorption coefficients for the compressional and shear-wave wavenumbers for each partial-wave mode n. The forbidden values produce negative axial radiation force, absorption and extinction efficiencies, as well as an enha…
Viscoelastic liquids are characterized by a finite static viscosity and a zero yield stress, whereas soft solids have an infinite viscosity and a non-zero yield stress. The rheological nature of viscoelastic materials has long been a challenge, and it is still a matter of debate. Here, we provide for the first time the constitutive equations of linear viscoelasticity for magnetic wires in yield stress materials, together with experimental measurements using Magnetic Rotational Spectroscopy (MRS). With MRS, the wires are submitted to a rotational magnetic field as a function of frequency and th…
We determine the linear viscoelastic response of jammed packings of athermal repulsive viscous spheres, a model for emulsions, wet foams, and soft colloidal suspensions. We numerically measure the complex shear modulus, a fundamental characterization of the response, and demonstrate that low frequency response displays dynamic critical scaling near unjamming. Viscoelastic shear response is governed by the relaxational eigenmodes of a packing. We use scaling arguments to explain the distribution of eigenrates, which develops a divergence at unjamming. We then derive the critical exponents chara…
Spherical cellular aggregates are in vitro systems to study the physical and biophysical properties of tissues. We present a novel approach to characterize the mechanical properties of cellular aggregates using micropipette aspiration technique. We observe an aspiration in two distinct regimes, a fast elastic deformation followed by a viscous flow. We develop a model based on this viscoelastic behavior to deduce the surface tension, viscosity, and elastic modulus. A major result is the increase of the surface tension with the applied force, interpreted as an effect of cellular mechanosensing.
We investigate the break-up of Newtonian/viscoelastic droplets in a viscoelastic/Newtonian matrix under the hydrodynamic conditions of a confined shear flow. Our numerical approach is based on a combination of Lattice-Boltzmann models (LBM) and Finite Difference (FD) schemes. LBM are used to model two immiscible fluids with variable viscosity ratio (i.e. the ratio of the droplet to matrix viscosity); FD schemes are used to model viscoelasticity, and the kinetics of the polymers is introduced using constitutive equations for viscoelastic fluids with finitely extensible non-linear elastic dumbbe…
The eukaryotic cell nucleus harbors the DNA genome that is organized in a dynamic chromatin network and embedded in a viscous crowded fluid. This environment directly affects enzymatic reactions and target search processes that access the DNA sequence information. However, its physical properties as a reaction medium are poorly understood. Here, we exploit mobility measurements of differently sized inert green fluorescent tracer proteins to characterize the viscoelastic properties of the nuclear interior of a living human cell. We find that it resembles a viscous fluid on small and large scale…
We study the spreading dynamics of a sphere-shaped elastic non-Newtonian liquid drop on a spherical substrate in the capillary driven regime. We use the simplified Phan Thien Tanner model to represent the rheology of the elastic non-Newtonian drop. We consider the drop to be a crater on a flat substrate to calculate the viscous dissipation near the contact line. Following the approach compatible with the capillary-viscous force balance, we establish the evolution equation for describing the temporal evolution of the contact line during spreading. We show that the contact line velocity obtained…
We experimentally investigate the bursting dynamics of confined liquid film suspended in air and find a viscous dynamics distinctly different from the non-confined counterpart, due to lack of circular symmetry in the shape of expanding hole: the novel confined-viscous bursting proceeds at a constant speed and a rim formed at the bursting tip does not grow. We find a confined-viscous to confined-inertial crossover, as well as a nonconfined-inertial to confined-inertial crossover, at which bursting speed does not change although the circular symmetry in the hole shape breaks dynamically.
We perform traction experiments on simple liquids highly confined between parallel plates. At small separation rates, we observe a simple response corresponding to a convergent Poiseuille flow. Dramatic changes in the force response occur at high separation rates, with the appearance of a force plateau followed by an abrupt drop. By direct observation in the course of the experiment, we show that cavitation accounts for these features which are reminiscent of the utmost complex behavior of adhesive films under traction. Surprisingly enough, this is observed here in purely viscous fluids.
We explore the dynamics of a flexible fiber transported by a viscous flow in a Hele-Shaw cell of height comparable to the fiber height. We show that long fibers aligned with the flow experience a buckling instability. Competition between viscous and elastic forces leads to the deformation of the fiber into a wavy shape convolved by a Bell-shaped envelope. We characterize the wavelength and phase velocity of the deformation as well as the growth and spreading of the envelope. Our study of the spatio-temporal evolution of the deformation reveals a linear and absolute instability arising from a l…
We present a simple and \emph{non-invasive} experimental procedure to measure the linear viscoelastic properties of cells by passive video particle tracking microrheology. In order to do this, a generalised Langevin equation is adopted to relate the time-dependent thermal fluctuations of a bead, chemically bound to the cell's \emph{exterior}, to the frequency-dependent viscoelastic moduli of the cell. It is shown that these moduli are related to the cell's cytoskeletal structure, which in this work is changed by varying the solution osmolarity from iso- to hypo-osmotic conditions. At high freq…
Dynamics of particle lane formation in confined viscoelastic fluids under shear
JGC Corporation（JGC公司）；Tokyo University of Science（东京科学大学）；Meiji Institute for Advanced Study of Mathematical Science (MIMS), Meiji University（明治大学高等数学科学研究院（MIMS）, 明治大学）；Water Frontier Science & Technology Research Center, and Division of Colloid Interface, Research Institute for Science & Technology, Tokyo University of Science（东京科学大学理工学院胶体界面学部与水前沿科学技术研究中心）；Faculty of Engineering and Physical Sciences, University of Surrey（萨里大学工程与物理科学学院）
Finite difference method in prolate spheroidal coordinates for freely suspended spheroidal particles in linear flows of viscous and viscoelastic fluids
We report measurements of viscoelastic properties of thin polymer films of 10-100 nm at the MHz range. These thin films are confined between a quartz crystal resonator and a millimetric bead layer, producing an increase of both resonance frequency and dissipation of the quartz resonator. The shear modulus and dynamic viscosity of thin films extracted from these measurements are consistent with the bulk values of the polymer. This modified quartz resonator provides an easily realizable and effective tool for probing the rheological properties of thin films at ambient environment.
We show that a viscoelastic thin sheet driven out of equilibrium by active structural remodelling develops a rich variety of shapes as a result of a competition between viscous relaxation and activity. In the regime where active processes are faster than viscoelastic relaxation, wrinkles that are formed due to remodelling are unable to relax to a configuration that minimises the elastic energy and the sheet is inherently out of equilibrium. We argue that this non-equilibrium regime is of particular interest in biology as it allows the system to access morphologies that are unavailable if restr…
Using a two-fluid model for viscoelastic polymer solutions, we study analytically fluid transport driven by a transverse, small amplitude traveling wave propagation. The pumping flow far from the waving boundary is shown to be strongly wave number and viscosity dependent, in contrast to a viscous Newtonian fluid. We find the two qualitatively different regimes: In one regime relevant to small wave numbers, the fluidic transport is almost the same as the Newtonian case, and uniform viscoelastic constitutive equations provide a good approximation. In the other regime, the pumping is substantiall…
Recently, many interesting features of the hydrodynamically coupled motions of the Brownian particles in a viscous fluid have been reported which are impossible for the uncoupled motions of the similar particles. However, it is expected that those physics in a viscoelastic fluid is much more interesting due to the presence of the additional frequency dependent elasticity of the medium. Thus, a theory describing the equilibrium dynamics of two hydrodynamically coupled Brownian harmonic oscillators in a viscoelastic Maxwell fluid has been derived which appears with new and impressive aspects. In…
