Discontinuous thinning in active microrheology of soft complex matter

R. Wulfert, U. Seifert, and T. Speck

Phys. Rev. E 94, 062610 – Published 27 December 2016

Abstract

Employing theory and numerical simulations, we demonstrate discontinuous force thinning due to the driven motion of an external probe in a host medium. We consider two cases: an ideal structureless medium (modeling ultrasoft materials such as polymer melts) and a dilute bath of interacting repulsive particles. When the driving of the probe exceeds a critical force, the microviscosity of the medium drops abruptly by about an order of magnitude. This phenomenon occurs for strong attractive interactions between a large probe and a sufficiently dense host medium.

Received 17 February 2016
Revised 28 September 2016

DOI:https://doi.org/10.1103/PhysRevE.94.062610

Physics Subject Headings (PhySH)

Rheology

Complex fluids

Brownian dynamics

Polymers & Soft MatterStatistical Physics & Thermodynamics

Authors & Affiliations

R. Wulfert¹, U. Seifert¹, and T. Speck²

¹II. Institut für Theoretische Physik, Universität Stuttgart, Pfaffenwaldring 57, 70550 Stuttgart, Germany
²Institut für Physik, Johannes Gutenberg-Universität Mainz, Staudingerweg 7-9, 55128 Mainz, Germany

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Vol. 94, Iss. 6 — December 2016

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Images

Figure 1
(a–d) Microstructural deformation around the attractive probe for increasing mean velocities $\bar{v}$ in terms of the conditional probability $g (r; \bar{v})$ in the $x - y$ plane. Probe and bath particles interact via a Lennard-Jones potential with $ɛ = 5$ and $σ = 1$ . (e) Velocity-force relations $μ_{0} f (\bar{v})$ for ascending values of $μ_{0} ρ$ (bottom to top) at a relative bath particle size $b = 1 / 19$ . Above $μ_{0} ρ ≃ 0.036$ , the flow curves become nonmonotonous and dynamically unstable regions emerge across intermediate $\bar{v}$ . Dashed lines and shaded areas represent a tentative equal-area Maxwell construction to restore invertibility.
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Figure 2
(a) Relative microviscosity $η_{mrh} / η = μ_{0} f / \bar{v}$ as a function of driving force $f$ for two different parameters $μ_{0} ρ$ . Solid lines represent numerical solutions of the pair-Smoluchowski Eq. (5). Data points from Brownian dynamics simulations with fixed $b = 1 / 19$ fall onto the numerical solution with statistical errors smaller than the symbol size. In the unstable case with $μ_{0} ρ = 0.098$ , simulations reveal a sharp discontinuous transition between two separate frictional regimes. The transition force depends on the rate and direction along which $f$ is varied (see arrows), leading to hysteretic behavior. (b, c) Individual probe trajectories $x_{0} (t)$ for initial forces (b) below and (c) above the discontinuity. In order to escape the metastable initial state, a rare fluctuation has to carry the system close enough toward its stable steady state, followed by a marked and abrupt shift in the probe velocity.
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Figure 3
Relative microviscosity $η_{mrh} / η = μ_{0} f / \bar{v}$ as a function of force $f$ at fixed $ε_{b} = 1.0$ and number density $ρ = 6 ϕ / (π b^{3}) = 0.92$ for increasing bath particle size in terms of the WCA-potential range $σ_{b}$ : (a) $σ_{b} = 0.05$ , (b) $σ_{b} = 0.10$ , and (c) $σ_{b} = 0.20$ . Bath particles have a relative hydrodynamic diameter $b = 0.1$ corresponding to a probe mobility of $μ_{0} = 0.091$ . The flow curve according to the ideal-bath model (dashed lines) serves as a reference for the noninteracting ( $σ_{b} = 0$ ) case.
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Figure 4
Mapping of dynamically stable and unstable regimes in terms of volume-fraction $ϕ$ and relative bath diameter $b$ . Along $ϕ / (b^{2} + b^{3}) = c = const$ (thin lines), the microrheological flow curves are invariant. The thick line (red line) demarcates the two regimes, here for a Lennard-Jones potential with $σ = 1$ and $ɛ = 5$ . The shaded area corresponds to the region that is unstable and dilute ( $ϕ ≪ 1$ ), where the pair approximation becomes valid even for a hard-sphere bath. Letters (a)–(c) indicate the state points shown in Figs. 3–3 at constant density $ρ = 0.92$ , with $b$ equal to the effective hard-sphere diameter $b_{BH}$ of the bath particles and $ϕ$ calculated accordingly.
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Figure 5
(a–f) Microstructural deformation around the moving probe in terms of the conditional probability $g (r; \bar{v})$ in the $x - y$ plane parameterized by the mean probe velocity $\bar{v}$ . Probe and bath particles interact via the AO depletion-attraction potential $u_{AO} (r)$ with a polymer reservoir packing-fraction $η_{p}^{r} = 0.5$ and polymer-colloid size ratio $q = 0.10$ .
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Figure 6
(a) Master-curves $ζ (\bar{v})$ for the AO-model with polymer packing-fraction $η_{p}^{r} = 0.5$ and varying polymer-colloid size ratios $q$ (dashed lines) complemented by the hard-sphere case (solid line) corresponding to $η_{p}^{r} = 0$ . (b) Velocity-force relations $μ_{0} f (\bar{v})$ based on the master-curve $ζ (\bar{v})$ (solid lines) at $η_{p}^{r} = 0.5, q = 0.10$ for ascending values of $μ_{0} ρ$ (bottom to top). Dashed lines represent Maxwell constructions across unstable ranges. (c) Relative microviscosity $η_{mrh} / η = μ_{0} f / \bar{v}$ as a function of force $f$ for the same values of $μ_{0} ρ$ used in (b). Dashed lines indicate discontinuous transition according to Maxwell construction.
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