Scientific machine learning for modeling and simulating complex fluids.

The formulation of rheological constitutive equations-models that relate internal stresses and deformations in complex fluids-is a critical step in the engineering of systems involving soft materials. While data-driven models provide accessible alternatives to expensive first-principles models and less accurate empirical models in many engineering disciplines, the development of similar models for complex fluids has lagged. The diversity of techniques for characterizing non-Newtonian fluid dynamics creates a challenge for classical machine learning approaches, which require uniformly structured training data. Consequently, early machine-learning based constitutive equations have not been portable between different deformation protocols or mechanical observables. Here, we present a data-driven framework that resolves such issues, allowing rheologists to construct learnable models that incorporate essential physical information, while remaining agnostic to details regarding particular experimental protocols or flow kinematics. These scientific machine learning models incorporate a universal approximator within a materially objective tensorial constitutive framework. By construction, these models respect physical constraints, such as frame-invariance and tensor symmetry, required by continuum mechanics. We demonstrate that this framework facilitates the rapid discovery of accurate constitutive equations from limited data and that the learned models may be used to describe more kinematically complex flows. This inherent flexibility admits the application of these "digital fluid twins" to a range of material systems and engineering problems. We illustrate this flexibility by deploying a trained model within a multidimensional computational fluid dynamics simulation-a task that is not achievable using any previously developed data-driven rheological equation of state.

Quantifying the hydrodynamic contribution to electrical transport in non-Brownian suspensions.

Electrical transport in semiconducting and metallic particle suspensions is an enabling feature of emerging grid-scale battery technologies. Although the physics of the transport process plays a key role in these technologies, no universal framework has yet emerged. Here, we examine the important contribution of shear flow to the electrical transport of non-Brownian suspensions. We find that these suspensions exhibit a strong dependence of the transport rate on the particle volume fraction and applied shear rate, which enables the conductivity to be dynamically changed by over 107 decades based on the applied shear rate. We combine experiments and simulations to conclude that the transport process relies on a combination of charge and particle diffusion with a rate that can be predicted using a quantitative physical model that incorporates the self-diffusion of the particles.

Elastoviscoplasticity, hyperaging, and time-age-time-temperature superposition in aqueous dispersions of bentonite clay.

Clay slurries are both ubiquitous and essential in the oil exploration industry, and are most commonly employed as drilling fluids. Due to its natural abundance, bentonite clay is often the de facto choice for these materials. Understanding and predicting the mechanical response of these fluids is critical for safe and efficient drilling operations. However, rheological modeling of bentonite clay suspensions is complicated by the fact that thermally-driven microscopic arrangements of particle aggregates lead to a continual evolution of the viscoelastic properties and the yield stress of the suspension with time. Ergodic relations fundamental to linear viscoelastic theory, such as the Boltzmann superposition principle, do not hold in this scenario of 'rheological aging'. We present an approach for modeling the linear viscoelastic response of aging bentonite suspensions across a range of temperatures that is based on the transformation from laboratory time to an effective 'material time' domain in which time-translation invariance holds, and the typical relations of non-aging linear viscoelastic theory apply. In particular, we model the constitutive relationship between stress and strain-rate in the bentonite suspensions as fractional Maxwell gels with constant relaxation dynamics in the material time domain, in parallel with a non-aging Newtonian viscous contribution to the total stress. This approach is supported by experimental measurements of the stress relaxation and rapid time-resolved measurements of the linear viscoelastic properties performed using optimized exponential chirps. This data is then reduced to master curves in the material domain using time-age-time superposition to obtain best fits of the model parameters over a range of operating temperatures.

Thermally fluctuating, semiflexible sheets in simple shear flow.

We perform Brownian dynamics simulations of semiflexible colloidal sheets with hydrodynamic interactions and thermal fluctuations in shear flow. As a function of the ratio of bending rigidity to shear energy (a dimensionless quantity we denote S) and the ratio of bending rigidity to thermal energy, we observe a dynamical transition from stochastic flipping to crumpling and continuous tumbling. This dynamical transition is broadened by thermal fluctuations, and the value of S at which it occurs is consistent with the onset of chaotic dynamics found for athermal sheets. The effects of different dynamical conformations on rheological properties such as viscosity and normal stress differences are also quantified. Namely, the viscosity in a dilute dispersion of sheets is found to decrease with increasing shear rate (shear-thinning) up until the dynamical crumpling transition, at which point it increases again (shear-thickening), and non-zero first normal stress differences are found that exhibit a local maximum with respect to temperature at large S (small shear rate). These results shed light on the dynamical behavior of fluctuating 2D materials dispersed in fluids and should greatly inform the design of associated solution processing methods.

Robust estimation of charge carrier diffusivity using transient photoluminescence microscopy.

Transient microscopy has emerged as a powerful tool for imaging the diffusion of excitons and free charge carriers in optoelectronic materials. In many excitonic materials, extraction of diffusion coefficients can be simplified because of the linear relationship between signal intensity and local excited state population. However, in materials where transport is dominated by free charge carriers, extracting diffusivities accurately from multidimensional data is complicated by the nonlinear dependence of the measured signal on the local charge carrier density. To obtain accurate estimates of charge carrier diffusivity from transient microscopy data, statistically robust fitting algorithms coupled to efficient 3D numerical solvers that faithfully relate local carrier dynamics to raw experimental measurables are sometimes needed. Here, we provide a detailed numerical framework for modeling the spatiotemporal dynamics of free charge carriers in bulk semiconductors with significant solving speed reduction and for simulating the corresponding transient photoluminescence microscopy data. To demonstrate the utility of this approach, we apply a fitting algorithm using a Markov chain Monte Carlo sampler to experimental data on bulk CdS and methylammonium lead bromide (MAPbBr3) crystals. Parameter analyses reveal that transient photoluminescence microscopy can be used to obtain robust estimates of charge carrier diffusivities in optoelectronic materials of interest, but that other experimental approaches should be used for obtaining carrier recombination constants. Additionally, simplifications can be made to the fitting model depending on the experimental conditions and material systems studied. Our open-source simulation code and fitting algorithm are made freely available to the scientific community.

A theory of mechanical stress-induced H2O2 signaling waveforms in Planta.

Recent progress in nanotechnology-enabled sensors that can be placed inside of living plants has shown that it is possible to relay and record real-time chemical signaling stimulated by various abiotic and biotic stresses. The mathematical form of the resulting local reactive oxygen species (ROS) wave released upon mechanical perturbation of plant leaves appears to be conserved across a large number of species, and produces a distinct waveform from other stresses including light, heat and pathogen-associated molecular pattern (PAMP)-induced stresses. Herein, we develop a quantitative theory of the local ROS signaling waveform resulting from mechanical stress in planta. We show that nonlinear, autocatalytic production and Fickian diffusion of H2O2 followed by first order decay well describes the spatial and temporal properties of the waveform. The reaction-diffusion system is analyzed in terms of a new approximate solution that we introduce for such problems based on a single term logistic function ansatz. The theory is able to describe experimental ROS waveforms and degradation dynamics such that species-dependent dimensionless wave velocities are revealed, corresponding to subtle changes in higher moments of the waveform through an apparently conserved signaling mechanism overall. This theory has utility in potentially decoding other stress signaling waveforms for light, heat and PAMP-induced stresses that are similarly under investigation. The approximate solution may also find use in applied agricultural sensing, facilitating the connection between measured waveform and plant physiology.

Hydrodynamics control shear-induced pattern formation in attractive suspensions.

Dilute suspensions of repulsive particles exhibit a Newtonian response to flow that can be accurately predicted by the particle volume fraction and the viscosity of the suspending fluid. However, such a description fails when the particles are weakly attractive. In a simple shear flow, suspensions of attractive particles exhibit complex, anisotropic microstructures and flow instabilities that are poorly understood and plague industrial processes. One such phenomenon, the formation of log-rolling flocs, which is ubiquitously observed in suspensions of attractive particles that are sheared while confined between parallel plates, is an exemplar of this phenomenology. Combining experiments and discrete element simulations, we demonstrate that this shear-induced structuring is driven by hydrodynamic coupling between the flocs and the confining boundaries. Clusters of particles trigger the formation of viscous eddies that are spaced periodically and whose centers act as stable regions where particles aggregate to form flocs spanning the vorticity direction. Simulation results for the wavelength of the periodic pattern of stripes formed by the logs and for the log diameter are in quantitative agreement with experimental observations on both colloidal and noncolloidal suspensions. Numerical and experimental results are successfully combined by means of rescaling in terms of a Mason number that describes the strength of the shear flow relative to the rupture force between contacting particles in the flocs. The introduction of this dimensionless group leads to a universal stability diagram for the log-rolling structures and allows for application of shear-induced structuring as a tool for assembling and patterning suspensions of attractive particles.

Buckling, crumpling, and tumbling of semiflexible sheets in simple shear flow.

As 2D materials such as graphene, transition metal dichalcogenides, and 2D polymers become more prevalent, solution processing and colloidal-state properties are being exploited to create advanced and functional materials. However, our understanding of the fundamental behavior of 2D sheets and membranes in fluid flow is still lacking. In this work, we perform numerical simulations of athermal semiflexible sheets with hydrodynamic interactions in shear flow. For sheets initially oriented near the flow-vorticity plane, we find buckling instabilities of different mode numbers that vary with bending stiffness and can be understood with a quasi-static model of elasticity. For different initial orientations, chaotic tumbling trajectories are observed. Notably, we find that sheets fold or crumple before tumbling but do not stretch again upon applying greater shear.

Shear driven vorticity aligned flocs in a suspension of attractive rigid rods.

A combination of rheology, optical microscopy and computer simulations was used to investigate the microstructural changes of a semi-dilute suspension of attractive rigid rods in an imposed shear flow. The aim is to understand the relation of the microstructure with the viscoelastic response, and the yielding and flow behaviour in different shear regimes of gels built from rodlike colloids. A semi-dilute suspension of micron sized, rodlike silica particles suspended in 11 M CsCl salt solution was used as a model system for attractive rods' gel. Upon application of steady shear the gel microstructure rearranges in different states and exhibits flow instabilities depending on shear rate, attraction strength, volume fraction and geometrical confinement. At low rod volume fractions, the suspension forms large, vorticity aligned, particle rich flocs that roll in the flow-vorticity plane, an effect that is due to an interplay between hydrodynamic interactions and geometrical confinement as suggested by computer simulations. Experimental data allow the creation of a state diagram, as a function of volume fraction and shear rates, identifying regimes of stable (or unstable) floc formation and of homogeneous gel or broken clusters. The transition is related to dimensionless Mason number, defined as the ratio of shear forces to interparticle attractive force.

Underscreening and hidden ion structures in large scale simulations of concentrated electrolytes.

The electrostatic screening length predicted by Debye-Hückel theory decreases with increasing ionic strength, but recent experiments have found that the screening length can instead increase in concentrated electrolytes. This phenomenon, referred to as underscreening, is believed to result from ion-ion correlations and short-range forces such as excluded volume interactions among ions. We use Brownian Dynamics to simulate a version of the Restrictive Primitive Model for electrolytes over a wide range of ion concentrations, ionic strengths, and ion excluded volume radii for binary electrolytes. We measure the decay of the charge-charge correlation among ions in the bulk and compare it against scaling trends found experimentally and determined in certain weak coupling theories of ion-ion correlation. Moreover, we find that additional large scale ion structures emerge at high concentrations. In this regime, the frequency of oscillations computed from the charge-charge correlation function is not dominated by electrostatic interactions but rather by excluded volume interactions and with oscillation periods on the order of the ion diameter. We also find the nearest neighbor correlation of ions sharing the same charge transitions from negative at small concentrations to positive at high concentrations, representing the formation of small, like-charge ion clusters. We conclude that the increase in local charge density due to the formation of these clusters and the topological constraints of macroscopic charged surfaces can help explain the degree of underscreening observed experimentally.

The Importance of Unbound Ligand in Nanocrystal Superlattice Formation.

Significant experimental and theoretical work has been devoted to understanding why colloidal nanocrystals (NCs) self-assemble into such a diverse array of structures. Previous research has focused on factors such as nanocrystal charging, the ratio of ligand length to core radius, core faceting, and ligand coverage among many controllable parameters. Here, we demonstrate that the presence of unbound/free ligand in colloidal suspension plays a pivotal role in determining NC superlattice (SL) structure and orientation. We investigated the structure of PbS NC SLs with grazing-incidence small-angle X-ray scattering (GISAXS) while using nuclear magnetic resonance (NMR) to quantify the bound and unbound ligand populations. Through a series of controlled additions of unbound oleic acid to solutions of identically sized oleate-capped NCs with different bound ligand coverages, we mapped the continuous evolution of the final SL structure from body-centered cubic (BCC) to face-centered cubic (FCC) through a series of body-centered tetragonal (BCT) intermediate phases. Strikingly, this phase transformation pathway is identical to the uniaxial contraction observed when evaporating solvent, suggesting that unbound ligand and solvent occupy a similar space within the SL unit cell. Molecular dynamics simulations of single NCs confirm that unbound ligand readily swells the bound ligand shell over all exposed NC facets-even without explicit rebinding to the NC surface-and we establish limitations on the range of tunability via this approach based on Flory-Rehner gel-swelling theory. Furthermore, we explain the effect of high free ligand fraction on the early time dynamics of spin coating concentrated colloidal dispersions, which can disrupt the formation of long-range SL order. The controlled addition of unbound ligand represents a novel mechanism for directing superlattice structure and highlights the experimental importance of fully characterizing bound and unbound ligand populations.

Spontaneous Electrokinetic Magnus Effect.

Colloids dispersed in electrolytes and exposed to an electric field produce a locally polarized cloud of ions around them. Above a critical electric field strength, an instability occurs causing these ion clouds to break symmetry leading to spontaneous rotation of particles about an axis orthogonal to the applied field, a phenomenon named Quincke rotation. In this Letter, we characterize a new mode of electrokinetic transport. If the colloids have a net charge, Quincke rotation couples with electrophoretic motion and propels particles in a direction orthogonal to both the applied field and the axis of rotation. This motion is a spontaneous, electrokinetic analogue to the well-known Magnus effect. Typically, motion orthogonal to a field requires anisotropy in particle shape, dielectric properties, or boundary geometry. Here, the electrokinetic Magnus (EKM) effect occurs for spheres with isotropic properties in an unbounded environment, with the Quincke rotation instability providing the broken symmetry needed to drive orthogonal motion. We study the EKM effect using explicit ion, Brownian dynamics simulations and develop a simple, continuum, analytic electrokinetic theory, which are in agreement. We also explain how nonlinearities in the theoretical description of the ions affect Quincke rotation and the EKM effect.

Effect of Protein Surface Charge Distribution on Protein-Polyelectrolyte Complexation.

Charge anisotropy or the presence of charge patches at protein surfaces has long been thought to shift the coacervation curves of proteins and has been used to explain the ability of some proteins to coacervate on the "wrong side" of their isoelectric point. This work makes use of a panel of engineered superfolder green fluorescent protein mutants with varying surface charge distributions but equivalent net charge and a suite of strong and weak polyelectrolytes to explore this concept. A patchiness parameter, which assessed the charge correlation between points on the surface of the protein, was used to quantify the patchiness of the designed mutants. Complexation between the polyelectrolytes and proteins showed that the mutant with the largest patchiness parameter was the most likely to form complexes, while the smallest was the least likely to do so. The patchiness parameter was found to correlate well with the phase behavior of the protein-polymer mixtures, where both macrophase separation and the formation of soluble aggregates were promoted by increasing the patchiness depending on the polyelectrolyte with which the protein was mixed. Increasing total charge and increasing strength of the polyelectrolyte promote interactions for oppositely charged polyelectrolytes, while charge regulation is also key to interactions for similarly charged polyelectrolytes, which must interact selectively with oppositely charged patches.

Verifying Death Reports in the Platelet Inhibition and Patient Outcomes (PLATO) Trial.

BACKGROUND: Excess vascular deaths in the PLATO trial comparing ticagrelor to clopidogrel have been repeatedly challenged by the Food and Drug Administration (FDA) reviewers and academia. Based on the Freedom of Information Act, BuzzFeed won a court order and shared with us the complete list of reported deaths for the ticagrelor FDA New Drug Application (NDA) 22-433. This dataset was matched against local patient-level records from PLATO sites monitored by the sponsor. STUDY QUESTION: Whether FDA death data in the PLATO trial matched the local site records. STUDY DESIGN: The NDA spreadsheet contains 938 precisely detailed PLATO deaths. We obtained and validated local evidence for 52 deaths among 861 PLATO patients from 14 enrolling sites in 8 countries and matched those with the official NDA dataset submitted to the FDA. MEASURES AND OUTCOMES: Existence, precise time, and primary cause of deaths in PLATO. RESULTS: Discrepant to the NDA document, sites confirmed 2 extra unreported deaths (Poland and Korea) and failed to confirm 4 deaths (Malaysia). Of the remaining 46 deaths, dates were reported correctly for 42 patients, earlier (2 clopidogrel), or later (2 ticagrelor) than the actual occurrence of death. In 12 clopidogrel patients, cause of death was changed to "vascular," whereas 6 NDA ticagrelor "nonvascular" or "unknown" deaths were site-reported as of "vascular" origin. Sudden death was incorrectly reported in 4 clopidogrel patients, but omitted in 4 ticagrelor patients directly affecting the primary efficacy PLATO endpoint. CONCLUSIONS: Many deaths were inaccurately reported in PLATO favoring ticagrelor. The full extent of mortality misreporting is currently unclear, while especially worrisome is a mismatch in identifying primary death cause. Because all PLATO events are kept in the cloud electronic Medidata Rave capture system, securing the database content, examining the dataset changes or/and repeated entries, identifying potential interference origin, and assessing full magnitude of the problem are warranted.

Collective mode Brownian dynamics: A method for fast relaxation of statistical ensembles.

Sampling equilibrium configurations of correlated systems of particles with long relaxation times (e.g., polymeric solutions) using conventional molecular dynamics and Monte Carlo methods can be challenging. This is especially true for systems with complicated, extended bond network topologies and other interactions that make the use and design of specialized relaxation protocols infeasible. We introduce a method based on Brownian dynamics simulations that can reduce the computational time it takes to reach equilibrium and draw decorrelated samples. Importantly, the method is completely agnostic to the particle configuration and the specifics of interparticle forces. In particular, we develop a mobility matrix that excites non-local, collective motion of N particles and can be computed efficiently in O(N) time. Particle motion in this scheme is computed by integrating the overdamped Langevin equation with an Euler-Maruyama scheme, in which Brownian displacements are drawn efficiently using a low-rank representation of the mobility matrix in position and wave space. We demonstrate the efficacy of the method with various examples from the realm of soft condensed matter and release a massively parallel implementation of the code as a plugin for the open-source package HOOMD-blue [J. A. Anderson et al., J. Comput. Phys. 227, 5342 (2008) and J. Glaser et al., Comput. Phys. Commun. 192, 97 (2015)] which runs on graphics processing units.

Brain Amygdala Volume Increases in Veterans and Active-Duty Military Personnel With Combat-Related Posttraumatic Stress Disorder and Mild Traumatic Brain Injury.

OBJECTIVE: To identify amygdalar volumetric differences associated with posttraumatic stress disorder (PTSD) in individuals with comorbid mild traumatic brain injury (mTBI) compared with those with mTBI-only and to examine the effects of intracranial volume (ICV) on amygdala volumetric measures. SETTING: Marine Corps Base and VA Healthcare System. PARTICIPANTS: A cohort of veterans and active-duty military personnel with combat-related mTBI (N = 89). DESIGN: Twenty-nine participants were identified with comorbid PTSD and mTBI. The remaining 60 formed the mTBI-only control group. Structural images of brains were obtained with a 1.5-T MRI scanner using a T1-weighted 3D-IR-FSPGR pulse sequence. Automatic segmentation was performed in Freesurfer. MAIN MEASURES: Amygdala volumes with/without normalizations to ICV. RESULTS: The comorbid mTBI/PTSD group had significantly larger amygdala volumes, when normalized to ICV, compared with the mTBI-only group. The right and left amygdala volumes after normalization to ICV were 0.122% ± 0.012% and 0.118% ± 0.011%, respectively, in the comorbid group compared with 0.115% ± 0.012% and 0.112% ± 0.009%, respectively, in the mTBI-only group (corrected P < .05). CONCLUSIONS: The ICV normalization analysis performed here may resolve previous literature discrepancies. This is an intriguing structural finding, given the role of the amygdala in the challenging neuroemotive symptoms witnessed in casualties of combat-related mTBI and PTSD.

A Rare Case of Lichen Planus-Like Atopic Dermatitis Involving the Hands.

Lichen planus-like atopic dermatitis clinically mimics lichen planus and can pose a diagnostic challenge. We report a case of a 55-year-old African American woman who developed intensely pruritic papules and plaques on bilateral hands. Histological examination demonstrated acute spongiotic dermatitis with lymphocyte exocytosis into the epidermis. Taken together, a diagnosis of lichen planus-like atopic dermatitis was made. This case serves to highlight that lichen planus-like atopic dermatitis can develop on hands and that it presents as spongiotic dermatitis with lymphocyte exocytosis into the epidermis. Correlating the clinical presentation with histopathological findings will assist in establishing the diagnosis and guiding appropriate management.

Colloidal Gelation through Thermally Triggered Surfactant Displacement.

Colloidal systems that undergo gelation attract much attention in both fundamental studies and practical applications. Rational tuning of interparticle interactions allows researchers to precisely engineer colloidal material properties and microstructures. Here, contrary to the traditional approaches where modulating attractive interactions is the major focus, we present a platform wherein colloidal gelation is controlled by tuning repulsive interactions. By including amphiphilic oligomers in colloidal suspensions, the ionic surfactants on the colloids are replaced by the nonionic oligomer surfactants at elevated temperatures, leading to a decrease in electrostatic repulsion. The mechanism is examined by carefully characterizing the colloids, and subsequently allowing the construction of interparticle potentials to capture the material behaviors. With the thermally triggered surfactant displacement, the dispersion assembles into a macroporous viscoelastic network and the gelling mechanism is robust over a wide range of compositions, colloid sizes, and component chemistries. This stimulus-responsive gelation platform is general and offers new strategies to engineer complex viscoelastic soft materials.

Short and Soft: Multidomain Organization, Tunable Dynamics, and Jamming in Suspensions of Grafted Colloidal Cylinders with a Small Aspect Ratio.

The yet virtually unexplored class of soft colloidal rods with a small aspect ratio is investigated and shown to exhibit a very rich phase and dynamic behavior, spanning from liquid to nearly melt state. Instead of the nematic order, these short and soft nanocylinders alter their organization with increasing concentration from isotropic liquid with random orientation to small domains with preferred local orientation and eventually a multidomain arrangement with a local orientational order. The latter gives rise to a kinetically suppressed state akin to structural glass with detectable terminal relaxation, which, on further increasing concentration, reveals features of hexagonally packed order as in ordered block copolymers. The respective dynamic response comprises four regimes, all above the overlapping concentration of 0.02 g/mL:(I) from 0.03 to 0.1 g/mol, the system undergoes a liquid-to-solidlike transition with a structural relaxation time that grows by 4 orders of magnitude. (II) From 0.1 to 0.2 g/mL, a dramatic slowing-down is observed and is accompanied by an evolution from isotropic to a multidomain structure. (III) Between 0.2 and 0.6 g/mol, the suspensions exhibit signatures of shell interpenetration and jamming, with the colloidal plateau modulus depending linearly on concentration. (IV) At 0.74 g/mL, in the densely jammed state, the viscoelastic signature of hexagonally packed cylinders from microphase-separated block copolymers is detected. These properties set short and soft nanocylinders apart from long colloidal rods (with a large aspect ratio) and provide insights for fundamentally understanding the physics in this intermediate soft colloidal regime and for tailoring the flow properties of nonspherical soft colloids.

Surface heterogeneity affects percolation and gelation of colloids: dynamic simulations with random patchy spheres.

Surface heterogeneity of colloidal particles has a significant impact on their structure in solution and their rheological properties. During particle synthesis, heterogeneous chemical functionalization, processes of self-assembly, or phase separation, can all lead to heterogeneous colloidal surfaces which impart anisotropic interactions to suspended particles. Additionally, an important class of colloids, biological macromolecules, exhibit similar localized, short-ranged, anisotropic interactions, which have a significant impact on their solution properties. Therefore, understanding the assembly and rheology of such colloids can provide insight into a wide variety of relevant physical systems. In this computational study, we investigate dispersions of particles having surface patches with randomized functionality as a model for heterogeneous colloids. We use Brownian dynamics simulations with hydrodynamic interactions to explore the differences between these random patchy particles and homogeneous (or isotropic) particles. The common basis used for comparing dispersions of particles with different surface functionality is equality of the second virial coefficient, so that dispersions of particles with different patterns of surface heterogeneity are similar thermodynamically at low particle concentrations. We show that at modest particle concentrations, significant deviations from the isotropic model are evident in the dispersion micro-structure, giving drastically different percolation transition points depending on the degree of surface heterogeneity. However, these deviations can be rationalized and a universal percolation criteria derived in terms of the osmotic pressure of the dispersion. Heterogeneous interactions also impose extra constraints on the relative translation and rotation between neighboring particles, which increase the viscosity and elastic modulus of aggregated dispersions and gels built from heterogeneous colloids and shifts the gel point measurably.