The viscoelastic behavior of polymer solutions is commonly measured using oscillating shear rheometry, however, the accuracy of such methods is limited by the oscillating frequency of the equipment and since the relaxation time of the dilute polymer solutions is short, this requires measurement at very high frequencies. Microrheology has been proposed to overcome this technical challenge. Yet the equipment for resolving the statistics of particle displacements in microrheology is expensive. In this work, we measured the viscoelastic behavior of Methocel solutions at various concentrations using a conventional epi-fluorescence microscope coupled to a high-speed intensified camera. Statistical Particle Tracking is used in analyzing the mean-squared displacement of the dispersive particles. Relaxation times ranging from 0.76 - 9.00 ms and viscoelastic moduli, G' between 11.34 and 3.39 are reported for Methocel solutions of concentrations between 0.063 - 0.5%
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…
We study theoretically the surface response of a semi-infinite viscoelastic polymer network using the two-fluid model. We focus on the overdamped limit and on the effect of the network's intrinsic length scales. We calculate the decay rate of slow surface fluctuations, and the surface displacement in response to a localized force. Deviations from the large-scale continuum response are found at length scales much larger than the network's mesh size. We discuss implications for surface scattering and microrheology. We provide closed-form expressions that can be used for surface microrheology -- …
We investigate previously unclarified effects of fluid elasticity on shear-thickening in dilute suspensions in an Oldroyd-B viscoelastic fluid using a novel direct numerical simulation based on the smoothed profile method. Fluid elasticity is determined by the Weissenberg number Wi and by viscosity ratio $1-β=η_p/(η_s+η_p)$ which measures the coupling between the polymer stress and flow: $η_p$ and $η_s$ are the polymer and solvent viscosity, respectively.As $1-β$ increases, while the stresslet does not change significantly compared to that in the $β\to 1$ limit, the growth rate of the normaliz…
We present an efficient computational methodology to obtain the viscoelastic response of dilute solutions of semiflexible filaments. By considering an approach based on the fluctuation-dissipation theorem, we were able to evaluate the dynamical properties of probe particles immersed in solutions of semiflexible filaments from relaxation simulations with a relatively low computational cost and higher precision in comparison to those based on stochastic dynamics. We used a microrheological approach to obtain the complex shear modulus and the complex viscosity of the solution through its complian…
Active particle tracking microrheometers have the potential to perform accurate broad-band measurements of viscoelasticity within microscopic systems. Generally, their largest possible precision is limited by Brownian motion and low frequency changes to the system. The signal to noise ratio is usually improved by increasing the size of the driven motion compared to the Brownian as well as averaging over repeated measurements. New theory is presented here which gives the complex shear modulus when the motion of a spherical particle is driven by non-linear forces. In some scenarios error can be …
The unsteady, lineal translation of a solid spherical particle through viscoelastic fluids described by the Johnson-Segalman and Giesekus models is studied analytically. Solutions for the pressure and velocity fields as well as the force on the particle are expanded as a power series in the Weissenberg number. The momentum balance and constitutive equation are solved asymptotically for a steadily translating particle up to second order in the particle velocity, and rescaling of the pressure and velocity in the frequency domain is used to relate the solutions for steady lineal translation to th…
In microrheology, the local rheological properties such as viscoelasticity of a complex fluid are inferred from the free or forced motion of embedded colloidal probe particles. Theoretical machinery developed for forced-probe microrheology of colloidal suspensions focused on either constant-force (CF) or constant-velocity (CV) probes while in experiments neither the force nor the kinematics of the probe is fixed. More importantly, the constraint of CF or CV introduces a difficulty in the meaningful quantification of the fluctuations of the probe due to a thermodynamic uncertainty relation. It …
Particle-tracking microrheology of dilute active (self-propelled) colloidal suspensions is studied by considering the external force required to maintain the steady motion of an immersed constant-velocity colloidal probe. If the probe speed is zero, the suspension microstructure is isotropic but exhibits a boundary accumulation of active bath particles at contact due to their self-propulsion. As the probe moves through the suspension, the microstructure is distorted from the nonequilibrium isotropic state, which allows us to define a microviscosity for the suspension using the Stokes drag law.…
Transformer-Based Inverse Microrheology for Experimental Mechanics at Ultra-High Strain Rates
Materials Science Graduate Program, Texas Materials Institute, The University of Texas at Austin（材料科学研究生项目，德克萨斯材料研究所，德克萨斯大学奥斯汀分校）；Department of Mechanical Engineering, Michigan State University（机械工程系，密歇根州立大学）；Department of Aerospace Engineering and Engineering Mechanics, The University of Texas at Austin（航空航天工程与工程力学系，德克萨斯大学奥斯汀分校）；The Oden Institute of Computational Science and Engineering, University of Texas at Austin（奥登计算科学与工程研究所，德克萨斯大学奥斯汀分校）；Department of Mechanical Engineering, University of Wisconsin-Madison（机械工程系，威斯康星大学麦迪逊分校）
We discuss experimental investigations on steady streaming flows of dilute and semi-dilute polymer solutions in microfluidic devices. The effect of non-Newtonian behavior on steady streaming for different model fluids is determined by characterizing the evolution of the inner streaming layer as a function of oscillation frequency using particle tracking velocimetry. We find that steady streaming velocity profiles in constant-viscosity elastic liquids are qualitatively similar to those in Newtonian liquids. Steady streaming velocity profiles in elastic liquids with strong shear thinning, howeve…
Particles migrate in the transverse direction of the flow due to the existence of normal stress anisotropy in weakly viscoelastic liquids. We test the ability of theoretical predictions to predict the transverse velocity migration of particles in a confined Poiseuille flow according to the viscoelastic constitutive parameters of dilute polymers solutions. Firstly, we carefully characterize the viscoelastic properties of two families of dilute polymer solutions at various concentrations using shear rheometry and capillary breakup experiments. Secondly, we develop a specific 3D particle tracking…
To elucidate the key factor for the quantitative prediction of the shear-thickening in suspensions in viscoelastic fluids, direct numerical simulations of many-particle suspensions in a multi-mode Oldroyd-B fluid are performed using the smoothed profile method. Suspension flow under simple shear flow is solved under periodic boundary conditions by using Lees--Edwards boundary conditions for particle dynamics and a time-dependent oblique coordinate system that evolves with mean shear flow for fluid dynamics. Semi-dilute many-particle suspensions up to a particle volume fraction of 0.1 are inves…
We report the temporal and spatio-temporal stability analyses of anti-symmetric, free shear, viscoelastic flows obeying the Oldroyd-B constitutive equation in the limit of low to moderate Reynolds number and Weissenberg number. The resulting fourth order Orr-Sommerfeld equation is reduced to a set of six auxiliary equations which are numerically integrated starting from the rescaled far-field conditions, i.~e., via the Compound Matrix Method. Numerical results indicate that with increasing Weissenberg number: (a) the peak of the maximal growth rate (i. e., the maximum value of the imaginary co…
We show that viscoelastic plane Poiseuille flow becomes linearly unstable in the absence of inertia, in the limit of high elasticities, for ultra-dilute polymer solutions. While inertialess elastic instabilities have been predicted for curvilinear shear flows, this is the first ever report of a purely elastic linear instability in a rectilinear shear flow. The novel instability continues upto a Reynolds number ($Re$) of $O(1000)$, corresponding to the recently identified elasto-inertial turbulent state believed to underlie the maximum-drag-reduced regime. Thus, for highly elastic ultra-dilute …
Dilute polymer solutions are known to exhibit purely elastic instabilities even when the fluid inertia is negligible. Here we report the quantitative evidence of two consecutive oscillatory elastic instabilities in an elongation flow of a dilute polymer solution as realized in a T-junction geometry with a long recirculating cavity. The main result reported here is the observation and characterization of the first transition as a forward Hopf bifurcation resulted in a uniformly oscillating state due to breaking of time translational invariance. This unexpected finding is in contrast with previo…
Newtonian pipe flow is known to be linearly stable at all Reynolds numbers. We report, for the first time, a linear instability of pressure driven pipe flow of a viscoelastic fluid, obeying the Oldroyd-B constitutive equation commonly used to model dilute polymer solutions. The instability is shown to exist at Reynolds numbers significantly lower than those at which transition to turbulence is typically observed for Newtonian pipe flow. Our results qualitatively explain experimental observations of transition to turbulence in pipe flow of dilute polymer solutions at flow rates where Newtonian …
The formation of drops of a complex fluid, for instance including dissolved polymers and/or solid particles, has practical implications in several industrial and biophysical processes. In this Letter, we experimentally investigate the generation of drops of a viscoelastic suspension, made of non-Brownian spherical particles dispersed in a dilute polymer solution. Using high-speed imaging, we characterize the different stages of the detachment. Our experiments show that the particles primarily affect the initial Newtonian necking by increasing the fluid viscosity. In the viscoelastic regime, pa…
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…
A modal stability analysis shows that plane Poiseuille flow of an Oldroyd-B fluid becomes unstable to a `center mode' with phase speed close to the maximum base-flow velocity, $U_{max}$. The governing dimensionless groups are the Reynolds number $Re = ρU_{max} H/η$, the elasticity number $E = λη/(H^2ρ)$, and the ratio of solvent to solution viscosity $η_s/η$; here, $λ$ is the polymer relaxation time, $H$ is the channel half-width, and $ρ$ is the fluid density. For experimentally relevant values (e.g., $E \sim 0.1$ and $β\sim 0.9$), the predicted critical Reynolds number, $Re_c$, for the center…
Compound particles are a class of composite systems in which solid particles encapsulated in a fluid droplet are suspended in another fluid. They are encountered in various natural and biological processes, for e.g., nucleated cells, hydrogels, microcapsules etc. In this work, we analyze the flow in and around a concentric compound particle and investigate the deformation and reorientation dynamics of the confining drop and its stability against breakup in imposed linear flows. We obtain analytical expressions for the flow fields upto O(Ca) (capillary number) and the deformed shape of the conf…
When a dilute polymer solution experiences capillary thinning, it forms an almost uniformly cylindrical thread, which we study experimentally. In the last stages of thinning, when polymers have become fully stretched, the filament becomes prone to instabilities, of which we describe two: A novel "breathing" instability, originating from the edge of the filament, and a sinusoidal instability in the interior, which ultimately gives rise to a "blistering" pattern of beads on the filament. We describe the linear instability with a spatial resolution of 80 nm in the disturbance amplitude. For suffi…
We study experimentally the interfacial instability between a layer of dilute polymer solution and water flowing in a thin capillary. The use of microfluidic devices allows us to observe and quantify in great detail the features of the flow. At low velocities, the flow takes the form of a straight jet, while at high velocities, steady or advected wavy jets are produced. We demonstrate that the transition between these flow regimes is purely elastic -- it is caused by viscoelasticity of the polymer solution only. The linear stability analysis of the flow in the short-wave approximation captures…
The elasto-inertial effects on particle focusing in a square-tube flow were investigated experimentally and numerically. Microscale experiments using spherical particles in dilute polymer solutions demonstrated that the particles are focused on the midline and/or the diagonal in a downstream cross-section, depending on the polymer concentration. Numerical computations based on the FENE-P model for the viscoelastic flow reproduced these focusing patterns. It was revealed that the transitions among the patterns are accounted for by the elastic forces due to the first normal stress difference and…
We address the phenomenon of drag reduction by dilute polymeric additive to turbulent flows, using Direct Numerical Simulations (DNS) of the FENE-P model of viscoelastic flows. It had been amply demonstrated that these model equations reproduce the phenomenon, but the results of DNS were not analyzed so far with the goal of interpreting the phenomenon. In order to construct a useful framework for the understanding of drag reduction we initiate in this paper an investigation of the most important modes that are sustained in the viscoelastic and Newtonian turbulent flows respectively. The modes …
