Oscillatory Strain Research Articles

REDIM reduced chemistry for the simulation of counterflow diffusion flames with oscillating strain rates

The dynamic behaviour and structures of laminar counterflow diffusion methane flames under oscillatory strain rates are investigated based on both detailed and reduced chemistry. It is known both from experiment and numerical studies that flame can deviate from its quasi-steady manner for high frequencies, which makes the well-known steady laminar flamelet model questionable. In this work, the Reaction-diffusion manifolds (REDIM) concept for simplified chemistry is applied to study the laminar counterflow diffusion flames with oscillating strain rates. In the construction of REDIM, one needs little knowledge of the studied system, and the REDIM reduced chemistry can cover both stable and unstable (extinction) regimes of the studied system. It is shown that the REDIM can capture both the steady and unsteady behaviours of the flame structures even for high frequencies, where the standard laminar steady flamelet approach is not appropriate.

Non-linear rheological study of hydrogel sliding friction in water and concentrated hyaluronan solution

Studying sliding friction of hydrogels in liquid is important for understanding biological friction. This work applies the non-linear rheology approach to study the friction of elastic hydrogels against adhesive glass in water and in concentrated hyaluronan (HA) solution. Using a rheometer in parallel plate geometry, stress-strain Lissajous curves are obtained from the oscillatory strain sweep test. Non-linearity and energy dissipation are characterized the strain-hardening ratio S, and “energy dissipation occupancy” κ, respectively. For friction in water, a clear transition from a linear viscoelastic to non-linear viscoelastic response occurs at a critical strain amplitude. Whereas, in HA solution, significant friction reduction and non-linear viscoelastic response occurs, related to the rheological behaviors of HA film intercalated at the gel/glass interface.

Relation between structure and stability of toothpaste with two-step yielding

Rheological measurements are performed to examine the yielding behavior of different commercial and lab-made toothpaste. Several toothpaste are reported to yield via a two-step process which is noted in dynamic oscillatory strain sweeps. The two-step yielding is best seen as two plateaus for storage modulus in a typical plot of storage modulus as a function of applied strain amplitude. Such behavior in structured materials is usually attributed to rupture of the network at lower strains which is followed by the breakup of aggregates at higher strains. In the case of toothpaste, the network and aggregates are formed by particles, such as silica, mediated by polymers, such as xanthan gum and carboxymethyl cellulose. The toothpaste in which such two-step yielding is more pronounced are shown to be less stable, i.e., lose their ability to retain shape when deposited on a toothbrush.

Temperature dependency of magnetorheological fluids’ properties under varying strain amplitude and rate

The temperature dependencies of the rheological and viscoelastic properties of magnetorheological (MR) fluids were investigated experimentally using a rotary rheometer. The shear flow and oscillatory shear strain experiments were conducted over a wide temperature range (−5 to 50 °C) for different levels of magnetic flux density, and strain amplitude and rate. The temperature effect is also investigated considering three different MR fluids with varying solid particles concentration. The measured shear stress-strain data were used to evaluate the effects of temperature and magnetic field on the pre- and post-yield properties of the MR fluids. The acquired data under harmonic strain excitations swept in the 0.005–100% strain amplitude and different levels of steady temperatures in the −5 °C to 50 °C range were analyzed to identify storage and loss moduli as functions of the temperature, shear strain amplitude and frequency. The results suggested strong influence of temperature on the mechanical properties of the fluids in the absence of the magnetic field, especially at temperatures below 10 °C. The magnetic field, however, constituted the dominant effect. In the presence of a magnetic field, the temperature effect could be observed only at low strain levels. The temperature dependency of the mechanical properties also varied considerably with the iron particle fraction of the MR fluid. The critical strain amplitude also increased with increasing magnetic field density, while the linear storage modulus approached saturation with magnetic flux density above 0.2 T.

Abstract 1177: Mechanical strain induces phenotypic changes in breast cancer cells and promotes immunosuppression in the tumor microenvironment

Abstract Introduction: Cells within the breast tumor mass are met with a variety of biophysical or mechanical signals that is associated with elevated compression or solid stress within the tumor interior, tension at the tumor periphery, and altered interstitial fluid pressure. Understanding how the mechanical stress within the tumor microenvironment (TME) regulates cancer cell phenotype is of interest, yet the response of breast cancer (BCa) cells to these forces is largely unknown. Our study aims to identify the impact of mechanical stress on BCa cell phenotype by mimicking the tension at the tumor periphery. Materials and Methods: BCa cells (MCF-7 or 4T1.2) were cultured to confluence on collagen coated FlexCell culture plates. These plates were then subjected to 10% uniaxial cyclic/oscillatory strain at 0.3 Hz, or 10% constant strain, or no strain for 48 hours. Strained or control cells were isolated for analysis of proliferation (MTT assay), and migration (8.0 μm pore transwell). Exosomes from conditioned media were isolated via differential centrifugation and purified exosomes were characterized by ImageStream. 5x105 4T1.2 cells or PKH-labeled strained or control cells were injected into the mammary fat pad of BALB/c mice. Tumor volume was measured over 14 days. Tumor-infiltrating immune cells and the uptake of exosomes were analyzed by flow cytometry on day-14 post implantation. Results: We determined significant increases in proliferation and migration of 4T1.2 and MCF-7 cells in vitro following exposure to oscillatory forces. The populations of CD63+, CD63+CD24+ and CD63+PD-L1+ exosomes were increased when 4T1.2 cells were exposed to oscillatory strain compared to unstrained control cells. Further, we investigated how oscillatory forces affect tumor growth and tumor-immune cell interactions in vivo by using a syngeneic, orthotopic mouse model of BCa. Mice implanted with 4T1.2 cells that were pre-exposed to oscillatory forces showed a significant increase in primary tumor growth at 8 and 11 days post tumor challenge. The percentages of tumor-infiltrating monocytic myeloid-derived suppressor cells (M-MDSC) and recruited macrophages were increased in the TME of mice implanted with 4T1.2 cells that were pre-exposed to oscillatory forces, while the granulocytic MDSC subset was not significantly different between the two groups. A marginal decrease in the percentage of CD8+ T cells was noted in the TME of mice implanted with strained 4T1.2 when compared to controls, suggesting immune suppression in the TME. Furthermore, exosome uptakes by M-MDSC and recruited macrophages were increased in the TME of mice implanted with PKH-labeled 4T1.2 cells, exposed to oscillatory strain. Conclusion: Together, these data indicate that exposure to mechanical stress changes BCa cell phenotype to an invasive and protumorigenic phenotype that promotes immunosuppressive effects in the TME. Citation Format: Yong Wang, Paige E. Severino, Kayla Goliwas, Kenneth Hough, Derek Van Vessem, Hong Wang, Andra R. Frost, Selvarangan Ponnazhagen, Joel L. Berry, Jessy S. Deshane. Mechanical strain induces phenotypic changes in breast cancer cells and promotes immunosuppression in the tumor microenvironment [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2019; 2019 Mar 29-Apr 3; Atlanta, GA. Philadelphia (PA): AACR; Cancer Res 2019;79(13 Suppl):Abstract nr 1177.

Orthogonal superposition rheometry of model colloidal glasses with short-ranged attractions

Attractive colloidal glasses are unique as their dynamical arrest is a combination of entropic crowding effects and energetic bonds formation. When such systems are subjected to flow, their dynamics are activated in a way which differs from hard-sphere glasses that melt through a “convective cage release mechanism.” Here, we investigate the microscopic dynamics by measuring the relaxation spectrum during flow using orthogonal superposition rheometry. A small amplitude oscillatory strain is imposed perpendicularly to a steady shear flow, and superposition moduli are measured. Brownian dynamic simulations are utilized complementary to extract the moduli from mean-squared displacements using the generalized Stokes–Einstein relation. At low Péclet number, a crossover frequency between elastic and viscous moduli is detected, representing the relaxation time associated with shear-induced particles escape from their frustration (localization) under flow. For the repulsive glass, this is related to shear-induced cage renewal of particles. For attractive glasses, however, when particles escape their localized length (bonds), they move with no further hindrance with the escape time, which is independent of attraction strength and interestingly faster than that in the repulsive glass. This is attributed to particle localization at shorter length scales due to bonding. At high Péclet, a second low frequency crossover is observed and a low frequency elastic dominated response emerges. This elastic response may originate from slow relaxation of hydroclusters or be a consequence of more intricate nature of superposition moduli. At high frequencies, both orthogonal moduli increase relative to quiescent state due to shear-induced cage deformation, which slows down in-cage dynamics.

Waterless single screw extrusion of pasta-filata cheese: Process design based on thermo-rheological material properties

Process design of a waterless single screw extrusion of pasta-filata cheese was established based on the material properties during the major steps plasticization, conveying and texturization. Thermo-rheological properties of model cheese curds (pH 5.8 adjusted by citric acid) were determined by small amplitude oscillatory strain experiments (20 – 80 °C) to narrow a promising range of the process temperature ϑprocess. It was shown that ϑprocess should be set according to the following relation: ϑgel-sol (full plasticization) ≤ ϑproduct ≤ ϑtanδmax (peak flowability). Critical shear rates (γ˙crit) of plasticized model cheese were analyzed by a capillary rheometer and translated to the screw speeds (SS) by considering the default configuration of the waterless extruder. Upscaling of process conditions was evaluated with regards to product homogeneity and chemical composition, resulting in the most promising parameters, ϑprocess = 63 °C and SS = 10 rpm. Experiments using fermented and ripened cheese curd (pH 5.0) corroborated the proposed process design strategy.

Strength of Mechanical Memories is Maximal at the Yield Point of a Soft Glass.

We show experimentally that both single and multiple mechanical memories can be encoded in an amorphous bubble raft, a prototypical soft glass, subject to an oscillatory strain. In line with recent numerical results, we find that multiple memories can be formed sans external noise. By systematically investigating memory formation for a range of training strain amplitudes spanning yield, we find clear signatures of memory even beyond yielding. Most strikingly, the extent to which the system recollects memory is largest for training amplitudes near the yield strain and is a direct consequence of the spatial extent over which the system reorganizes during the encoding process. Our study further suggests that the evolution of force networks on training plays a decisive role in memory formation in jammed packings.

Rheological predictions of sensory attributes of lotions.

Complex behavior of 33 commercial lotions was investigated in order to identify correlations between laboratory instrumental measurements and sensory attributes of these products. Sensory attributes were evaluated by trained panelists. Six attributes were identified as potentially related to rheology, which belong to three main sensory categories: appearance, pickup, and rub out. Potential rheological predictors were extracted from the data of rotational rheometry. Yield stress and instantaneous viscosity maximum (IVM) were determined in stress ramp. Alternative definitions of yield stress based on step-shear and oscillatory strain sweeps were also considered along with linear viscoelastic moduli, G' and G″. Statistical analysis has shown all these definitions of yield stress and IVM are in fact closely correlated and that IVM is the best overall predictor of most attributes although G'/G″ ratio also is significant for rub out attributes. However, integrity of shape, the main appearance attribute, is even better predicted by an imitative slump-like test in which image analysis is used to quantify sample spreading on a flat surface.

Mechanopharmacology and Synergistic Relaxation of Airway Smooth Muscle.

Asthmatic airways are stiffer than normal. We have shown that the cytoskeletal passive stiffness of airway smooth muscle (ASM) can be regulated by intracellular signaling pathways, especially those associated with Rho kinase (ROCK). We have also shown that an oscillatory strain reduces the passive stiffness of ASM and its ability to generate force. Here, we investigated the combined effect of inhibiting the ASM contraction with β2 agonist and decreasing the ASM cytoskeletal stiffness with ROCK inhibitor and/or force oscillation (FO) on the relaxation of contracted ASM. We hypothesize that the ASM relaxation can be synergistically enhanced by the combination of these interventions, because drug-induced softening of the cytoskeleton enhances the FO-induced relaxation and vice versa. Sheep tracheal strips were isotonically contracted to acetylcholine (3 × 10−5 M). At the plateau of shortening, β2 agonist salbutamol (10−7 M), ROCK inhibitor H1152 (10−7 M), and FO (square wave, 1 Hz, amplitude 6% maximal active force) were applied either alone or in combination. After adjusting for nonspecific time-dependent variation, relengthening by individual interventions with low-dose salbutamol or H1152, or small amplitude FO was not significantly different from zero. However, significant relengthening was observed in all combination treatments. The relengthening was greater than the mathematical sum of relengthening caused by individual treatments thereby demonstrating synergistic relaxation. The ASM stiffness did not change with salbutamol or H1152 treatments, but was lower with FO in combination with H1152. The results suggest that the mechanopharmacological treatment can be an effective therapy for asthma.

Prestrain and cholinergic receptor-dependent differential recruitment of mechanosensitive energy loss and energy release elements in airway smooth muscle.

We tested the hypothesis that oscillatory airway smooth muscle (ASM) mechanics is governed by mechanosensitive energy loss and energy release elements that can be recruited by prestrain and cholinergic stimulation. We measured mechanical energy loss and mechanical energy release in unstimulated and carbachol-stimulated bovine ASM held at prestrains ranging from 0.3 to 1.0 Lo (reference length) and subjected to sinusoidal length oscillation at 1 hz with oscillatory strain amplitudes ranging from 0.1 to 1.5% Lo. We found that oscillatory ASM mechanics during sinusoidal length oscillation is governed predominantly by one class of nonlinear mechanosensitive energy loss element and one class of nonlinear mechanosensitive energy release element with differential mechanosensitivities to oscillatory strain amplitude. The greater mechanosensitivity of the energy loss element than energy release element may explain the bronchodilatory effect of deep inspiration. Prestrain, an important determinant of ASM responsiveness, differentially increased energy loss and energy release in unstimulated and carbachol-stimulated ASM. Cholinergic stimulation, an important cause of bronchoconstriction and airway inflammation, also differentially increased energy loss and energy release. When prestrain and cholinergic stimulation were combined, we found that prestrain and cholinergic stimulation synergistically increased energy loss and energy release by ASM. The relationship between recruitment of energy loss elements and recruitment of energy release elements was nonlinear, suggesting that energy loss and energy release elements are not coupled in ASM cells. These findings imply that large lung volume and cholinergic ASM activation would synergistically increase mechanical energy expenditure during inspiration and mechanical recoil of ASM during expiration. NEW & NOTEWORTHY We report for the first time that oscillatory airway smooth muscle mechanics is governed predominantly by one class of nonlinear mechanosensitive energy loss element and one class of nonlinear mechanosensitive energy release element with differential mechanosensitivities to oscillatory strain amplitude. Prestrain and cholinergic stimulation synergistically and differentially recruit energy loss and energy release elements. The greater mechanosensitivity of the energy loss element than the energy release element may explain the bronchodilatory effect of deep inspiration.

Rheology of silica dispersions stabilized by polymers

Silica dispersions form the backbone of many consumer products, such as toothpaste. They are typically used in combination with polymeric binders/thickeners which stabilize these dispersions. In this paper rheological properties and stability, defined in terms of viscosity loss in real-time aging, of silica dispersions in the presence of the two most commonly used polymers, Xanthan gum and carboxymethyl cellulose (CMC), are considered. These two polymers represent two different types of rheological effects. Xanthan gum imparts stable viscosity to dispersions of silica particles, whereas the dispersion of the same particles with CMC results in slow viscosity loss during aging. The difference between the two polymers is also characterized by oscillatory strain sweeps. Silica dispersions without polymers tend to yield via a two-step process with two distinct plateaus of the storage modulus, G’. While the origin of such behavior is not completely understood, one possible explanation attributes it to the two-tier structure of these dispersions which can be thought of as a network of interconnected aggregates. As strain amplitude increases, the network breaks first, followed by breakup of aggregates. With Xanthan gum added, the two yield points converge indicating integration of the particles into a uniform space-filling network. CMC, on the other hand, while thickening the dispersion, retains the two-step yielding, presumably due to failure to interconnect the particles. Such two-step yielding is indeed rather common for toothpastes.

Oscillatory Strain Promotes Vessel Stabilization and Alignment through Fibroblast YAP-Mediated Mechanosensitivity.

Endothelial cells form the interior layer of blood vessels and, as such, are constantly exposed to shear stress and mechanical strain. While the impact of shear stress on angiogenesis is widely studied, the role of mechanical strain is less understood. To this end, endothelial cells and fibroblasts are cocultured under oscillatory strain to create a vessel network. The two cell types show distinctly different sensitivities to the mechanical stimulation. The fibroblasts, sense the stress directly, and respond by increased alignment, proliferation, differentiation, and migration, facilitated by YAP translocation into the nucleus. In contrast, the endothelial cells form aligned vessels by tracking fibroblast alignment. YAP inhibition in constructs under mechanical strain results in vessel destruction whereas less damage is observed in the YAP‐inhibited static control. Moreover, the mechanical stimulation enhances vessel development and stabilization. Additionally, vessel orientation is preserved upon implantation into a mouse dorsal window chamber and promotes the invading host vessels to orient in the same manner. This study sheds light on the mechanisms by which mechanical strain affects the development of blood vessels within engineered tissues. This can be further utilized to engineer a more organized and stable vasculature suitable for transplantation of engineered grafts.

Interrelation between the Portevin Le-Chatelier effect and necking in AlMg alloys

Plastic flow instability caused by the Portevin Le-Chatelier (PLC) effect and its influence on the necking instability were studied in a binary and a precipitation-strengthened AlMg alloy using the digital image correlation (DIC) technique. Coarse-grained structure and two different fine-grained states distinctly distinguished by dislocation density were produced in both alloys using similar routes of thermomechanical processing. The patterns of stress serrations and strain localization observed at different strain rates include virtually all common types of behavior of the PLC effect. Besides, particular spatiotemporal patterns testifying to a concurrency between the propagation and localization of deformation bands are detected at low strain rates. Despite this diversity, the analysis of deformation curves with smoothened-out serrations bears evidence that the onset of necking always corresponds to the geometric Considère condition. Nevertheless, visualization of the evolution of the local strain-rate field using DIC indicates that the two mechanisms of plastic instability are closely interrelated and modify each other's behavior. The neck formation is associated with a progressive immobilization of the PLC bands, ending by the ultimate strain localization. The coexistence of two kinds of instability during necking gives rise to specific spatiotemporal patterns including oscillatory strain localization.

A vacuum-actuated microtissue stretcher for long-term exposure to oscillatory strain within a 3D matrix.

Although our understanding of cellular behavior in response to extracellular biological and mechanical stimuli has greatly advanced using conventional 2D cell culture methods, these techniques lack physiological relevance. To a cell, the extracellular environment of a 2D plastic petri dish is artificially flat, extremely rigid, static and void of matrix protein. In contrast, we developed the microtissue vacuum-actuated stretcher (MVAS) to probe cellular behavior within a 3D multicellular environment composed of innate matrix protein, and in response to continuous uniaxial stretch. An array format, compatibility with live imaging and high-throughput fabrication techniques make the MVAS highly suited for biomedical research and pharmaceutical discovery. We validated our approach by characterizing the bulk microtissue strain, the microtissue strain field and single cell strain, and by assessing F-actin expression in response to chronic cyclic strain of 10%. The MVAS was shown to be capable of delivering reproducible dynamic bulk strain amplitudes up to 13%. The strain at the single cell level was found to be 10.4% less than the microtissue axial strain due to cellular rotation. Chronic cyclic strain produced a 35% increase in F-actin expression consistent with cytoskeletal reinforcement previously observed in 2D cell culture. The MVAS may further our understanding of the reciprocity shared between cells and their environment, which is critical to meaningful biomedical research and successful therapeutic approaches.

Rheological and sensory properties of toothpastes

Complex rheological trends of several commercially available and lab-made prototype toothpastes are reported. The flow curves are generated using the rotational rheometers with a series of rheological procedures, comprising of stress ramps, creep-recovery, stepped-shear rates, and dynamic oscillatory strain sweeps performed on toothpastes. Intricacies due to the history and the effects of pre-conditioning of the samples are discussed. However, the main goal of this work was to identify the correlations between the rheological measurements and the consumer-perceived properties of toothpastes. Shape retention and stringiness are the main sensory properties of interest that were identified and evaluated by the panelists. A custom-built experimental setup is used to quantify shape retention of a toothpaste ribbon on a brush and on a flat surface in a test which resonates with the popular slump test. It is demonstrated that the degree of shape retention correlates with the yield stress and the instantaneous viscosity. A comparison of yield stresses obtained using different methods in relation to degree of shape retention is presented. An experimental setup designed to measure stringiness of toothpastes is delineated. The stringiness measured with this device correlates well with human perception and also with the slope of the flow curve, i.e., the higher the degree of shear thinning, the less stringy the pastes tend to be. For lab-made prototype toothpastes, basic structure-property relations are established in terms of correlations between the three formulation variables: thickening silica, Xanthan gum, and carboxymethyl cellulose (CMC).

Shear banding in large amplitude oscillatory shear (LAOStrain and LAOStress) of soft glassy materials

We study theoretically shear banding in soft glassy materials subject to large amplitude time-periodic shear flows, considering separately the protocols of large amplitude oscillatory shear strain, large amplitude square or triangular or sawtooth strain rate, and large amplitude oscillatory shear stress. In each case, we find shear banding to be an important part of the material's flow response for a broad range of values of the frequency $\omega$ and amplitude of the imposed oscillation. Crucially, and highly counterintuitively, in the glass phase this persists even to the lowest frequencies accessible numerically (that seems consistent with it persisting even when $\omega\to 0$), although the soft glassy rheology model we use has an underlying monotonic constitutive curve of shear stress as a function of shear rate, and is therefore unable to support shear banding as its steady state response at constant shear rate. We attribute this to the repeated competition, within each flow cycle, of glassy aging and flow rejuvenation. Besides reporting significant banding in the glass phase, where the flow curve has a yield stress, we also observe it at noise temperatures just above the glass point, where the flow curve is of power law fluid form. Thus, our results suggest a predisposition to shear banding in flows of even extremely slow time-variation, for both aging yield stress fluids, and for power law fluids with sluggish relaxation timescales. We show that shear banding can have a pronounced effect on the shape of the Lissajous-Bowditch curves that are commonly used to fingerprint complex fluids rheologically. We therefore counsel caution in seeking to compute such curves calculations that impose upfront a homogeneous shear flow, discarding the possibility of banding. We also analyze the stress response to the imposed strain waveforms in terms of a `sequence of physical processes'.

Identification of thermal shear bands in a low molecular weight polymer melt under oscillatory strain field

We present real-time micro-thermal measurements of the response of viscous fluids (low molecular weight unentangled and entangled polymer melts) submitted to an oscillatory mechanical shear strain (in conditions of conventional viscoelastic measurements). We show that thermal changes occur at the early steps of the applied deformation. A succession of thermodynamic states is identified showing the formation of non-uniform temperature shear bands along the strain direction. These thermal shear bands indicate the coexistence of cold and warm zones appearing in phase with the deformation. The synchronism of the temperature variation with the mechanical strain reveals a reversible process of elastic type indicating that viscous liquids might exhibit thermoelastic behaviors.

Study of selected thermoplastics using dynamic mechanical analysis

The aim of given paper is to study selected polymers using dynamic mechanical analysis method (DMA). DMA is one of the most useful techniques for the study of the viscoelastic behaviour of thermoplastic polymers. In relation to DMA, an oscillatory stress and strain is applied to the material at specific frequencies and temperatures and based on this mentioned fact hereinbefore, the resulting changes after the loading in the material are measured. This technique allows detecting the melting temperature and the glass transition temperature of the thermoplastic materials. Furthermore, some spectroscopy techniques, such as energy dispersive X-ray spectroscopy (EDX) and infrared spectroscopy (IR), were also used for the investigation of the thermoplastics. The thermoplastics used for examination, namely polyethylene, polystyrene, polypropylene and polyethylene terephthalate, were gained from the waste of the packaging.

Fractal approaches to characterize the structure of capillary suspensions using rheology and confocal microscopy.

The rheological properties of a particle suspension can be substantially altered by adding a small amount of a secondary fluid that is immiscible with the bulk phase. The drastic change in the strength of these capillary suspensions arises due to the capillary forces, induced by the added liquid, leading to a percolating particle network. Using rheological scaling models, fractal dimensions are deduced from the yield stress and from oscillatory strain amplitude sweep data as function of the solid volume fraction. Exponents obtained using aluminum-oxide-based capillary suspensions, with a preferentially wetting secondary fluid, indicate an increase in the particle gel's fractal dimension with increasing particle size. This may be explained by a corresponding relative reduction in the capillary force compared to other forces. Confocal images using a glass model system show the microstructure to consist of compact particle flocs interconnected by a sparse backbone. Thus, using the rheological models two different fractal dimensionalities are distinguished - a lower network backbone dimension (D = 1.86-2.05) and an intrafloc dimension (D = 2.57-2.74). The latter is higher due to the higher local solid volume fraction inside of the flocs compared to the sparse backbone. Both of these dimensions are compared with values obtained by analysis of spatial particle positions from 3D confocal microscopy images, where dimensions between 2.43 and 2.63 are computed, lying between the two dimension ranges obtained from rheology. The fractal dimensions determined via this method corroborate the increase in structural compactness with increasing particle size.