We employ a matrix-based solver for the linear rheology of fluid-immersed disordered spring networks to reveal four distinct dynamic response regimes. One regime - completely absent in the known vacuum response - exhibits coupled fluid flow and network deformation, with both components responding non-affinely. This regime contains an additional plateau (peak) in the frequency-dependent storage (loss) modulus - features which vanish without full hydrodynamic interactions. The mechanical response of immersed networks such as biopolymers and hydrogels is thus richer than previously established, and offers additional modalities for design and control through fluid interactions.
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 …
Disordered fibre networks are ubiquitous in nature and have a wide range of industrial applications as novel biomaterials. Predicting their viscoelastic response is straightforward for affine deformations that are uniform over all length scales, but when affinity fails, as has been observed experimentally, modelling becomes challenging. Here we introduce a numerical methodology to predict the steady-state viscoelastic spectra and degree of affinity for disordered fibre networks driven at arbitrary frequencies. Applying this method to a peptide gel model reveals a monotonic increase of the shea…
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 consider an immersed elastic body that is actively driven through a structured fluid by a motor or an external force. The behavior of such a system generally cannot be solved analytically, necessitating the use of numerical methods. However, current numerical methods omit important details of the microscopic structure and dynamics of the fluid, which can modulate the magnitudes and directions of viscoelastic restoring forces. To address this issue, we develop a simulation platform for modeling viscoelastic media with tensorial elasticity. We build on the lattice Boltzmann algorithm and inco…
In this paper I present a simple and self-consistent framework based on microrheology that allows one to obtain the mechanical response of viscoelastic fluids and gels from the motion of probe particles immersed on it. By considering a non-markovian Langevin equation, I obtain general expressions for the mean-squared displacement and the time-dependent diffusion coefficient that are directly related to the memory kernels and the response function, and which allow one to obtain estimates for the complex shear modulus and the complex viscosity of the material. The usefulness of such approach is …
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 study the Brownian motion of microbeads immersed in water and in a viscoelastic wormlike micelles solution by optical trapping interferometry and diffusing wave spectroscopy. Through the mean-square displacement obtained from both techniques, we deduce the mechanical properties of the fluids at high frequencies by explicitly accounting for inertia effects of the particle and the surrounding fluid at short time scales. For wormlike micelle solutions, we recover the 3/4 scaling exponent for the loss modulus over two decades in frequency as predicted by the theory for semiflexible polymers.
When a polymer solution undergoes viscoelastic phase separation, the polymer-rich phase forms a network-like structure even if it is a minor phase. This unique feature is induced by polymer dynamics, which are constrained by the temporal entanglement of polymer chains. The fundamental mechanisms of viscoelastic phase separation have already been elucidated by theory and experiments over the past few decades; however, it is not yet well understood how viscoelastic phase separation occurs in multicomponent polymer solutions. Here, we construct a new viscoelastic phase separation model for ternar…
We theoretically investigate the looping dynamics of a linear polymer immersed in a viscoelastic fluid. The dynamics of the chain is governed by a Rouse model with a fractional memory kernel recently proposed by Weber et al. (S. C. Weber, J. A. Theriot, and A. J. Spakowitz, Phys. Rev. E 82, 011913 (2010)). Using the Wilemski-Fixman (G. Wilemski and M. Fixman, J. Chem. Phys. 60, 866 (1974)) formalism we calculate the looping time for a chain in a viscoelastic fluid where the mean square displacement of the center of mass of the chain scales as t^(1/2). We observe that the looping time is faster…
This paper presents a numerical method for the simulation of fluid-structure interaction specifically tailored to interactions between Newtonian fluids and a large number of slender viscoelastic Cosserat rods. Because of their high flexibility and low weight the rods considered here exhibit large deflections, even under moderate fluid loads. Their motion, in turn, modifies the flow so that fluid and structures are strongly coupled to each other which is numerically very challenging. The paper proposes a new coupling approach based on an immersed boundary method which improves upon existing met…
Motivated from the central role of the mean-square displacement and its second time-derivative -- that is the velocity autocorrelation function $\left\langle v(0)v(t)\right\rangle=\frac{1}{2} \frac{\mathrm{d}^{2} \left\langle Δr^{2} (t)\right\rangle}{\mathrm{d}t^{2}} $ in the description of Brownian motion, we revisit the physical meaning of the first time-derivative of the mean-square displacement of Brownian particles. By employing a rheological analogue for Brownian motion, we show that the time-derivative of the mean-square displacement $\frac{\mathrm{d}\left\langle Δr^{2} (t) \right\rangl…
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…
The presence of bacterial biofilms in clinical and industrial settings is a major issue worldwide. A biofilm is a viscoelastic matrix, composed of bacteria producing a network of Extracellular Polymeric Substances (EPS) to which bacteria crosslink. Modelling of complex biofilms is relevant to provide accurate descriptions and predictions that include parameters as hydrodynamics, dynamics of the bacterial population and solute mass transport. However, up-to-date numerical modelling, even at a coarse-grained level, is not satisfactorily. In this work, we present a numerical coarse-grain model of…
We investigate the viscoelastic properties of entangled networks of semiflexible polymers. At intermediate time scales the elastic response of these networks to shear deformation is described by the plateau modulus $G$. Different scaling laws with polymer concentration $c$ have been proposed based on the assumption that the deformation field is affine on all length scales. We develop a numerical approach that allows to calculate the modulus via free energy changes for both affine and non-affine deformations. The non-affine deformation field is obtained by a free energy minimization. Our findin…
Active fluids comprise a variety of systems composed of elements immersed in a fluid environment which can convert some form of energy into directed motion; as such they are intrinsically out-of-equilibrium in the absence of any external forcing. A fundamental problem in the physics of active matter concerns the understanding of how the characteristics of the autonomous propulsion and agent-agent interactions determine the collective dynamics of the system. We study numerically suspensions of self-propelled diffusiophoretic colloids, in (quasi)-2d configurations, accounting for both dynamicall…
Fundamental understanding of the effect of microscopic parameters on the dynamics of probe particles in different complex environments has wide implications. Examples include diffusion of proteins in the biological hydrogels, porous media, polymer matrix, etc. Here, we use extensive molecular dynamics simulations to investigate the dynamics of the probe particle in a polymer network on a diamond lattice which provides substantial crowding to mimic the cellular environment. Our simulations show that the dynamics of the probe increasingly becomes restricted, non-Gaussian and subdiffusive on incr…
