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Local mobility and microstructure in periodically sheared soft particle glasses and their connection to macroscopic rheology
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10.1122/1.4802631
/content/sor/journal/jor2/57/3/10.1122/1.4802631
http://aip.metastore.ingenta.com/content/sor/journal/jor2/57/3/10.1122/1.4802631

Figures

Image of FIG. 1.
FIG. 1.

(a) Periodic simulation box. (b) Imposed oscillatory shear rate. (c) Schematic diagram showing pairwise interactions between particles where and are directions parallel and perpendicular to the particle–particle facet, respectively; and are the velocity of particles and , respectively; is the center-to center distance between and ; is the parallel component of the relative velocity between and . [(c) Has been reproduced from .]

Image of FIG. 2.
FIG. 2.

Theoretical flow curve (——) given by Eq. (4) and experimental flow curve (●) in the same set of coordinates for the microgel suspension at  = 2 wt. % with  = 18 kPa (  = 35 Pa,  = 0.067,  = 510 Pa, and  =  mPa s). The inset shows the variations of / versus computed from simulations from which the effective volume fraction of the experimental suspension is determined.

Image of FIG. 3.
FIG. 3.

Mean square displacements of particles in the , , and directions versus oscillation number for different strain amplitudes: (a)  /   = 3.0, 1.5, 0.3 (top to bottom); (b) /  = 30, 15, 3.0 (top to bottom). The frequency is .

Image of FIG. 4.
FIG. 4.

Mean square displacements of particles in the , , and directions at small and large strain amplitudes versus oscillation number for different frequencies. (a) Small strain amplitude ( /  = 0.09) at frequencies of (top to bottom). (b) Large strain amplitude ( /  = 30) at frequencies (top to bottom).

Image of FIG. 5.
FIG. 5.

Shear-induced diffusion coefficients computed from the mean square displacements of particles. (a) Variations with the strain amplitude of the diffusion coefficients (, , ) computed from (◇), (△), and (▽), at nondimensional frequency ; the data for  /   < 1 have been estimated from the last computed oscillation where the mean square displacements approach their plateau values. (b) Variations with frequency of the nondimensional averaged diffusion coefficient,  = (  +   +  )/3 at /  = 30 (◼) and /  = 3.0 (●). (c) Variations of the averaged diffusion coefficients / for /  > 1 with the nondimensional shear-rate amplitude [squares represent averaged data from (a); same symbols as in (b)].

Image of FIG. 6.
FIG. 6.

Microstructure of soft particle glass at rest; the volume fraction is  = 0.80. (a) Static radial distribution function; (b) Pair distribution function shown in the plane. (c) Pair distribution function shown in the azimuthal plane with the most probable center-to-center distance indicated by a white dashed-dotted line and a black arrow.

Image of FIG. 7.
FIG. 7.

Microstructure of soft particle glass ( = 0.80) subjected to small amplitude oscillations (  = 0.09; /  = 2 × 10). (a) Variations of the strain (- - -) and stress () waveforms over one cycle and positions of the five characteristic points where () is presented. (b) Pair distribution functions in the azimuthal plane; the most probable center-to-center separation at rest is indicated in the maximum and zero stress states by a white dashed-dotted line and a black arrow. (c) () spherical harmonics.

Image of FIG. 8.
FIG. 8.

Microstructure of soft particle glass ( = 0.80) subjected to medium amplitude oscillations (  = 3.0; /  = 2 × 10). (a) Variations of the strain (- - -) and stress (—) waveforms over one cycle and positions of the six characteristic points where () is presented. (b) Pair distribution functions in the azimuthal plane; the most probable center-to-center separation at rest indicated in the zero stress states by a white dashed-dotted line and a black arrow. (c) () spherical harmonics.

Image of FIG. 9.
FIG. 9.

Microstructure of soft particle glass ( = 0.80) subjected to large amplitude oscillations (  = 30; /  = 2 × 10). (a) Variations of the strain (- - -) and stress (—) waveforms over one cycle and positions of the six characteristic points where () is presented. (b) Pair distribution functions in the azimuthal plane; the most probable center-to-center separation at rest is indicated in the zero stress states by a white dashed-dotted line and a black arrow; (c) () spherical harmonics.

Image of FIG. 10.
FIG. 10.

Storage modulus (◻ and —) and loss modulus (◇ and −−) versus reduced frequency from simulations (symbols) and experiments (lines) in the low strain amplitude or linear regime at  = 0.09. A reference slope of 0.5 is shown.

Image of FIG. 11.
FIG. 11.

Storage modulus (◻ and —), loss modulus (◇ and ----), and stress amplitude (● and ……) as functions of strain amplitude / , from simulations (symbols) and experiments (lines) at a frequency of ∗ = 2 × 10 rad/s. Dotted lines represent power law variations with exponents and , respectively, as discussed in the text.

Image of FIG. 12.
FIG. 12.

Bowditch–Lissajous plots from simulations and experiments at different strain amplitudes. Left to right: linear viscoelastic regime [ /  = 0.09; panels (a) and (d)]; medium amplitude regime [inner to outer: /  = 0.09, 1.5, 3.0; panels (b) and (e)]; large amplitude regime [inner to outer: /  = 3.0, 15, 30, 60; panels (c) and (f)]. The symbols in panels (a)–(c) represent the shear stress values which are predicted from the () spherical harmonics as discussed in the text.

Image of FIG. 13.
FIG. 13.

Cage modulus versus strain amplitude at /  = 2 × 10 from simulations (○) and experiments (●). For comparison, the values of the low frequency storage modulus at low strain amplitude are also plotted (◻: simulations; —: experiments).

Image of FIG. 14.
FIG. 14.

Flowing portions of the BL plots for different strain amplitudes and frequencies (symbols) collapsed and superimposed to the flow curve from steady shear (lines). For the sake of comparison between experiments and simulations, the data are represented in the set of reduced coordinates exemplified in Eq. (4) . Simulations (a) and experiments (b).

Tables

Generic image for table
TABLE I.

Material properties of the experimental and simulated suspensions with  = 2 wt. % and  = 0.80, respectively. The storage modulus and yield stress of the experimental microgel suspensions are  = 510 Pa and  = 35 Pa.

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/content/sor/journal/jor2/57/3/10.1122/1.4802631
2013-04-29
2014-04-20
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Local mobility and microstructure in periodically sheared soft particle glasses and their connection to macroscopic rheology
http://aip.metastore.ingenta.com/content/sor/journal/jor2/57/3/10.1122/1.4802631
10.1122/1.4802631
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