Time–connectivity superposition and the gel/glass duality of weak colloidal gels

Colloidal gels result from the aggregation of Brownian particles suspended in a solvent. Gelation is induced by attractive interactions between individual particles that drive the formation of clusters, which in turn aggregate to form a space-spanning structure. We study this process in aluminosilicate colloidal gels through time-resolved structural and mechanical spectroscopy. Using the time–connectivity superposition principle a series of rapidly acquired linear viscoelastic spectra, measured throughout the gelation process by applying an exponential chirp protocol, are rescaled onto a universal master curve that spans over eight orders of magnitude in reduced frequency. This analysis reveals that the underlying relaxation time spectrum of the colloidal gel is symmetric in time with power-law tails characterized by a single exponent that is set at the gel point. The microstructural mechanical network has a dual character; at short length scales and fast times it appears glassy, whereas at longer times and larger scales it is gel-like. These results can be captured by a simple three-parameter constitutive model and demonstrate that the microstructure of a mature colloidal gel bears the residual skeleton of the original sample-spanning network that is created at the gel point. Our conclusions are confirmed by applying the same technique to another well-known colloidal gel system composed of attractive silica nanoparticles. The results illustrate the power of the time–connectivity superposition principle for this class of soft glassy materials and provide a compact description for the dichotomous viscoelastic nature of weak colloidal gels.

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Recognition of Structures Leading to Transition in a Low Pressure Turbine Cascade: Effect of Reduced Frequency

Volume 2A: Turbomachinery ◽

10.1115/gt2019-91222 ◽

2019 ◽

Author(s):

D. Lengani ◽

D. Simoni ◽

M. Ubaldi ◽

P. Zunino ◽

F. Bertini

Keyword(s):

Boundary Layer ◽

Suction Side ◽

Low Pressure ◽

Turbine Cascade ◽

Turbulent Structures ◽

Time Resolved ◽

Low Pressure Turbine ◽

Reduced Frequency ◽

Displacement Thickness ◽

Wake Passing

Abstract The boundary layer developing over the suction side of a low pressure turbine cascade operating under unsteady inflow conditions has been experimentally investigated. Time-resolved Particle Image Velocimetry (PIV) measurements have been performed in two orthogonal planes, the blade to blade and a wall parallel plane embedded within the boundary layer, for two different wake reduced frequencies. Proper Orthogonal Decomposition (POD) has been used to analyze the data and to provide an interpretation of the most significant flow structures for each phase of the wake passing cycle. To this purpose, a POD based procedure that sorts the data synchronizing the measurements of the two planes has been developed. Phase averaged data are then obtained for both cases. Moreover, once properly sorted, POD has been applied to sub-ensembles of data at the same relative phase within the wake passing cycle. Detailed information on the most energetic turbulent structures at a particular phase are obtained with this procedure (called phased POD), overcoming the limit of classical phase average that just provides a statistical representation of the turbulence field. Furthermore, the synchronization of the measurements in the two planes allows the computation of the characteristic dimension of boundary layer structures that are responsible for transition. These structures are often identified as vortical filaments parallel to the wall, typically referred to as boundary layer streaks. The largest and most energetic structures are observed when the wake centerline passes over the rear part of the suction side, and they appear practically the same for both reduced frequencies. The passing wake forces transition leading to the breakdown of the boundary layer streaks. Otherwise, the largest differences between the low and high reduced frequency are observed in the calmed region. The post-processing of these two planes further allowed us to compute the spacing of the streaks and make it non-dimensional by the boundary layer displacement thickness observed for each phase. The non-dimensional value of the streaks spacing is about constant, irrespective of the reduced frequency.

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Spatiotemporal Control of Supramolecular Polymerization and Gelation of Metal-Organic Polyhedra

10.26434/chemrxiv.13414646.v1 ◽

2020 ◽

Author(s):

alexandre legrand ◽

Li-Hao Liu ◽

Philipp Royla ◽

Takuma Aoyama ◽

Gavin Craig ◽

...

Keyword(s):

Acid Concentration ◽

Self Assembly ◽

Colloidal Particles ◽

Soft Materials ◽

Supramolecular Materials ◽

Time Resolved ◽

Colloidal Gel ◽

Metal Organic ◽

Spatiotemporal Control ◽

Gel Network

In coordination-based supramolecular materials such as metallogels, simultaneous temporal and spatial control of their assembly remains challenging. Here, we demonstrate that the combination of light with acids as stimuli allows for the spatiotemporal control over the architectures, mechanical properties, and shape of porous soft materials based on metal-organic polyhedra (MOPs). First, we show that the formation of a colloidal gel network from a preformed kinetically trapped MOP solution can be triggered upon addition of trifluoroacetic acid (TFA), and that acid concentration determines the reaction kinetics. As determined by time-resolved dynamic light scattering, UV-vis absorption and <sup>1</sup>H NMR spectroscopies and rheology measurements, the consequences of the increase in acid concentration are (i) an increase in the cross-linking between MOPs; (ii) a growth in the size of the colloidal particles forming the gel network; (iii) an increase in the density of the colloidal network; and (iv) a decrease in the ductility and stiffness of the resulting gel. We then demonstrate that irradiation of a dispersed photoacid generator, pyranine, allows the spatiotemporal control of the gel formation by locally triggering the self-assembly process. Using this methodology, we show that the gel can be patterned into a desired shape. Such precise positioning of the assembled structures, combined with the stable and permanent porosity of MOPs, could allow their integration into devices for applications such as sensing, separation, catalysis, or drug release.

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Interpartical Attractions and the Mechanical Properties of Colloidal Gels

MRS Proceedings ◽

10.1557/proc-249-279 ◽

1991 ◽

Vol 249 ◽

Cited By ~ 5

Author(s):

C. J. Rueb ◽

C. F. Zukoski

Keyword(s):

Mechanical Properties ◽

Elastic Modulus ◽

Shear Rate ◽

Power Law ◽

Oscillation Frequency ◽

Critical Strain ◽

Low Frequency ◽

Gel Point ◽

Colloidal Gels ◽

Storage And Loss Moduli

ABSTRACTThe influence of the strength of interparticle attractions on the mechanical properties of colloidal gels is explored. As attractions increase, suspensions gel. At the gel point the zero shear rate viscosity diverges while the low frequency modulus becomes measurable. In addition at the gel point, storage and loss moduli were of the same order and displayed power law sealing on oscillation frequency. With much stronger attractions, the critical strain required to rupture the gel scales in a power law manner or elastic modulus. These observations are discussed in terns of recently developed models of gel fonnation and dynamics.

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Understanding of the Multiscale Self-Assembly of Metal-Organic Polyhedra Towards Functionally Graded Porous Gels

10.26434/chemrxiv.9746177.v1 ◽

2019 ◽

Author(s):

alexandre legrand ◽

Gavin A. Craig ◽

Mickaele Bonneau ◽

Saori Minami ◽

Kenji Urayama ◽

...

Keyword(s):

Self Assembly ◽

Energy Transport ◽

Soft Materials ◽

Functionally Graded ◽

Colloidal Gels ◽

Time Resolved ◽

Colloidal Aggregation ◽

Synthetic Materials ◽

Multiple Length Scales ◽

Metal Organic

Spatial heterogeneity and gradients within porous materials are key for controlling their mechanical properties and mass/energy transport, both in biological and synthetic materials. However, it is still challenging to induce such complexity in well-defined microporous materials such as crystalline metal-organic frameworks (MOFs). Here we show a method to generate a continuous gradient of porosity over multiple length scales by taking advantage of the amorphous nature of supramolecular polymers based on metal-organic polyhedra (MOPs). First, we use time-resolved dynamic light scattering (TRDLS) to elucidate the mechanism of hierarchical self-assembly of MOPs into colloidal gels and to understand the relationship between the MOP concentrations and the architecture of the resulting colloidal networks. These features directly impact on the viscoelastic response of the gels and their mechanical strength. We then show that gradients of stiffness and porosity can be created within the gel by applying centrifugal force at the point of colloidal aggregation. These results with the creation of asymmetric and graded pore configuration in soft materials could lead to the emergence of advanced properties that are coupled to asymmetric molecule/ion transport as seen in biological systems.<br>

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Recognition of Structures Leading to Transition in a Low-Pressure Turbine Cascade: Effect of Reduced Frequency

Journal of Turbomachinery ◽

10.1115/1.4046618 ◽

2020 ◽

Vol 142 (6) ◽

Author(s):

D. Lengani ◽

D. Simoni ◽

M. Ubaldi ◽

P. Zunino ◽

F. Bertini

Keyword(s):

Boundary Layer ◽

Suction Side ◽

Low Pressure ◽

Turbine Cascade ◽

Turbulent Structures ◽

Time Resolved ◽

Low Pressure Turbine ◽

Streaky Structures ◽

Reduced Frequency ◽

Displacement Thickness

Abstract The boundary layer developing over the suction side of a low-pressure turbine cascade operating under unsteady inflow conditions has been experimentally investigated. Time-resolved particle image velocimetry (PIV) measurements have been performed in two orthogonal planes, the blade-to-blade and a wall-parallel plane embedded within the boundary layer, for two different wake-reduced frequencies. Proper orthogonal decomposition (POD) has been used to analyze the data and to provide an interpretation of the most significant flow structures for each phase of the wake passing cycle. Detailed information on the most energetic turbulent structures at a particular phase is obtained with a newly developed procedure that overcomes the limit of classical phase average. The synchronization of the measurements in the two planes allows the computation of the characteristic dimension of boundary layer streaky structures that are responsible for transition. The largest and most energetic structures are observed when the wake centerline passes over the rear part of the suction side, and they appear practically the same for both reduced frequencies. The passing wake forces transition leading to the breakdown of the boundary layer streaks. Otherwise, the largest differences between the low and high reduced frequency are observed in the calmed region. The postprocessing of these two planes allowed computing the spacing of the streaky structures and making it nondimensional by the boundary layer displacement thickness observed for each phase. The nondimensional value of the streaks spacing is about constant, irrespective of the reduced frequency.

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Multibranch and Period Tripling Flutter

5th International Symposium on Fluid Structure International, Aeroeslasticity, and Flow Induced Vibration and Noise ◽

10.1115/imece2002-33050 ◽

2002 ◽

Cited By ~ 1

Author(s):

O. O. Bendiksen

Keyword(s):

Superposition Principle ◽

High Mass ◽

Nonlinear Phenomena ◽

Aeroelastic Response ◽

Reduced Frequency ◽

Flutter Analysis ◽

Mass Ratios ◽

Transonic Flutter ◽

Low Mass ◽

The Right

This paper discusses two nonlinear phenomena of relevance in transonic flutter analysis and testing: (1) The possible appearance of more than one flutter mode (branch) in the aeroelastic response, for certain transonic Mach numbers at high mass ratios; and, (2) the possibility of bifurcations to subharmonic flutter at low mass ratios. In the first instance, the superposition principle breaks down and flutter may not necessarily occur when the first aeroelastic eigenvalue crosses into the right half-plane. In the second instance, the nonlinearities open up a new route to flutter, whereby the reduced frequency of the critical aeroelastic mode is lowered into the unstable range through a period-tripling bifurcation. Neither behavior can be understood within the framework of classical linear aeroelasticity.

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Mechanical Properties of Colloidal Gels

MRS Proceedings ◽

10.1557/proc-155-83 ◽

1989 ◽

Vol 155 ◽

Cited By ~ 14

Author(s):

W.-H. Shih ◽

J. Liu ◽

W. Y. Shih ◽

S. I. Kim ◽

M. Sarikaya ◽

...

Keyword(s):

Power Law ◽

Particle Concentration ◽

Colloidal Particles ◽

Colloidal Suspension ◽

The Other ◽

Colloidal Gels ◽

Yield Strain ◽

Colloidal Gel ◽

Type Of Behavior ◽

Gel Network

A colloidal suspension can be either dispersed or flocculated depending on the interaction between the colloidal particles. If the interaction is repulsive, particles can relax to the minimum of the potential due to their neighboring particles, and the system can reach an equilibrium dispersed state. In the case of attractive interaction, particles form aggregates that settle to the bottom of the container. As the concentration of particles is increased, the overcrowding of the aggregates produces a continuous network throughout the suspension before they settle and a colloidal gel is formed. A major difference between a colloidal gel and a colloidal suspension is that the gel can sustain finite stress and is therefore viscoelastic. Previously we studied the storage modulus and the yield strain of boehmite gels and found that they are related to the particle concentration in a power-law fashion [1]. Similar scaling behavior of the shear modulus was found for other colloidal particulate networks by Buscall et al. [2]. We developed a scaling theory [1] which successfully explains the experimental results on boehmite gels. The theory further predicts that there can be two types of power-law behavior depending on the relative elastic strength of the clusters to that of the links between clusters within the gel network. Furthermore, there can be a crossover from one type of behavior to the other as the particle concentration is varied.

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Structure Evolution of Epoxidized Natural Rubber (ENR) in the Melt State by Time-Resolved Mechanical Spectroscopy

Materials ◽

10.3390/ma13040946 ◽

2020 ◽

Vol 13 (4) ◽

pp. 946

Author(s):

Rossella Arrigo ◽

Leno Mascia ◽

Jane Clarke ◽

Giulio Malucelli

Keyword(s):

Natural Rubber ◽

Rheological Behavior ◽

Structural Changes ◽

Viscoelastic Behavior ◽

Relaxation Modulus ◽

Epoxidized Natural Rubber ◽

Structure Evolution ◽

Gradual Transition ◽

Mechanical Spectroscopy ◽

Time Resolved

In this work, time-resolved mechanical spectroscopy (TRMS) was used to accurately characterize the rheological behavior of an epoxidized natural rubber (ENR) containing 25 mol% of epoxy groups. Conventional rheological tests are not suitable to characterize with accuracy the frequency-dependent linear viscoelastic behavior of materials, such as ENR, in a transient configurational state. For this reason, TRMS was used to determine the true rheological behavior of ENR, as well as to gain some insights into the changes of its macromolecular architecture under the dynamic conditions experienced during the measurements. The constructed master curves for the moduli revealed a gradual transition of the ENR rheological state from liquid-like to solid-like through the formation of an “elastic gel” throughout the bulk of the polymer. Furthermore, the evolution of the stress relaxation modulus revealed a slow relaxation mechanism, resulting from thermally activated reactions in the molten state attributed to the formation of crosslinks. Finally, the crosslink density evolution was estimated from the TRMS data and compared with results derived from equilibrium solvent-swelling measurements. These demonstrated the accuracy of the TRMS data in the prediction of the structural changes that can take place in polymers during processing.

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Embedding orthogonal memories in a colloidal gel through oscillatory shear

Soft Matter ◽

10.1039/c9sm02222h ◽

2020 ◽

Vol 16 (15) ◽

pp. 3746-3752

Author(s):

Eric M. Schwen ◽

Meera Ramaswamy ◽

Chieh-Min Cheng ◽

Linda Jan ◽

Itai Cohen

Keyword(s):

Network Structure ◽

Flow Direction ◽

Oscillatory Shear ◽

Attractive Interaction ◽

Colloidal Gels ◽

Colloidal Gel

We investigate shear training memories in colloidal gels, which include an attractive interaction and network structure, and discover that such systems can support memories both along and orthogonal to the training flow direction.

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