Applicability of the Generalized Stokes-Einstein Equation of Mode-Coupling Theory to Near-Critical Polyelectrolyte Complex Solutions.

We examine whether the mode-coupling theory of Kawasaki and Ferrell (KF) [Kawasaki, K. Kinetic Equations and Time Correlation Functions of Critical Fluctuations. Ann. Phys. 1970, 61 (1), 1-56; Ferrell, R. A. Decoupled-Mode Dynamical Scaling Theory of the Binary-Liquid Phase Transition. Phys. Rev. Lett. 1970, 24 (21), 1169-1172] can describe dynamic light scattering (DLS) measurements of the dynamic structure factor of near-critical polyelectrolyte complex (PC) solutions that have been previously shown to exhibit a theoretically unanticipated lower critical solution temperature type phase behavior, i.e., phase separation upon heating, and a conventional pattern of static critical properties (low angle scattering intensity and static correlation, ξs) as a function of reduced temperature. Good qualitative accord is observed between our DLS measurements and the KF theory. In particular, we observe that the collective diffusion coefficient Dc of the PC solutions obeys the generalized Stokes-Einstein equation (GSE), Dc = kBT/6πηξs, where ξs is specified from our previous measurements and where η is measured by capillary rheometry under the same thermodynamic conditions as in our previous study of these solutions, allowing for a no-free-parameter test of the GSE. We also find that even the wavevector (q)-dependent collective diffusion coefficient Dc(q), measured by varying the scattering angle in the DLS measurements over a large range, is also well-described by the mean-field version of the KF theory. We find it remarkable that the KF theory provides such a robust description of collective diffusion in these complex charged polyelectrolyte blends under near-critical conditions given that charge fluctuations and association of the polymers might be expected to lead to physical complications that would invalidate the standard model of uncharged fluid mixtures.

A small-volume microcapillary rheometer.

We demonstrate a capillary device used to measure the shear rate-dependent viscosity of microliter scale volumes. Liquid samples are driven pneumatically through a microcapillary and partially fill a larger glass capillary. The glass capillary is mounted on an optical linear sensor to track the air-liquid meniscus in real time and trigger the reversal of flow direction by switching a pneumatic valve. Each transit provides a volumetric flow rate measurement, which is used with the pressure drop to determine viscosity as a function of shear rate. A given sample of at least 50 µL can be measured over at least 2 to 3 decades in shear rate, in the range of 10 to 105 s-1, and be essentially fully recovered. Validation by comparison to reference measurements is performed using samples of Newtonian and non-Newtonian fluid, with viscosity ranging from 1 to 100 mPa s. The range of operation and uncertainty arising from instrumentation, meniscus effects, and inertial effects are discussed. The performance of this rheometer is advantageous, especially for use and reuse of small volumes.

Blood vessel-on-a-chip examines the biomechanics of microvasculature.

We use a three-dimensional (3D) microvascular platform to measure the elasticity and membrane permeability of the endothelial cell layer. The microfluidic platform is connected with a pneumatic pressure controller to apply hydrostatic pressure. The deformation is measured by tracking the mean vessel diameter under varying pressures up to 300 Pa. We obtain a value for the Young's modulus of the cell layer in low strain where a linear elastic response is observed and use a hyperelastic model that describes the strain hardening observed at larger strains (pressure). A fluorescent dye is used to track the flow through the cell layer to determine the membrane flow resistance as a function of applied pressure. Finally, we track the 3D positions of cell nuclei while the vessel is pressurized to observe local deformation and correlate inter-cell deformation with the local structure of the cell layer. This approach is able to probe the mechanical properties of blood vessels in vitro and provides a methodology for investigating microvascular related diseases.

Entrance effects and high shear rate rheology of shear banding wormlike micelle fluids in a microcapillary flow.

The viscosity of a shear-banding wormlike micelle solution at high shear rates is investigated using capillary rheology and particle streak velocimetry. Measurements of the flow profile and pressure gradient show an extended entrance region, which exceeds a length to diameter ratio of 100, to reach a fully developed flow. We characterized this entrance region for capillaries with different cross-sections and use the results to select a downstream portion of the capillary where viscosity measurements can be made on fully developed flow. Measurements from this portion of the channel show a shear-thinning power-law behavior for all channel geometries from shear rates of 1000 s -1 to 120000 s -1. Varying the surfactant concentration shows two distinct power-law behaviors that depend on both shear rate and concentration and are an indication of change in micelle length.

Capillary RheoSANS: measuring the rheology and nanostructure of complex fluids at high shear rates.

Complex fluids containing micelles, proteins, polymers and inorganic nanoparticles are often processed and used in high shear environments that can lead to structural changes at the nanoscale. Here, capillary rheometry is combined with small-angle neutron scattering (SANS) to simultaneously measure the viscosity and nanostructure of model complex fluids at industrially-relevant high shear rates. Capillary RheoSANS (CRSANS) uses pressure-driven flow through a long, flexible, silica capillary to generate wall shear rates up to 106 s-1 and measure pressure drops up to 500 bar. Sample volumes as small as 2 mL are required, which allow for measurement of supply-limited biological and deuterated materials. The device design, rheology and scattering methodologies, and broad sample capabilities are demonstrated by measuring a variety of model systems including silica nanoparticles, NIST monoclonal antibodies, and surfactant worm-like micelles. For a shear-thinning suspension of worm-like micelles, CRSANS measurements are in good agreement with traditional RheoSANS measurements. Collectively, these techniques provide insight into relationships between nanostructure and steady-shear viscosity over eight orders of magnitude in shear rate. Overall, CRSANS expands the capabilities of traditional RheoSANS instruments toward higher shear rates, enabling in situ structural measurements of soft materials at shear rates relevant to extrusion, coating, lubrication, and spraying applications.

Three-dimensional structures and symmetry breaking in viscoelastic cross-channel flow.

Using holographic particle tracking, we report the three-dimensional flow structure organizing the viscoelastic instability in cross-channel flow. Beyond a critical Wi, the advective core flow undergoes an out-of-plane instability marked by the emergence of tertiary flow, resembling that of the toroidal vortices in Taylor-Couette geometry. The out-of-plane flow component distorts the separatrix between the impinging inflow streams, triggering symmetry breaking normal to the extension plane. As extensional rate increases, progressively higher order modes of the separatrix are observed, akin to Euler buckling of a rigid column. The disturbances propagate upstream via stress fluctuations despite viscous dissipation. These complex flow structures may be generic to elastic turbulence in mixed flows.

The Impact of the Metal Interface on the Stability and Quality of a Therapeutic Fusion Protein.

Subvisible particle formation, which occurs after the sterile filtration step of the fill/finish process, is a challenge that may occur during the development of biotherapeutics with complex molecular structures. Here, we show that a stainless steel pump head from a rotary piston pump produces more protein aggregates, past the limit of the acceptable quality range for subvisible particle counts, in comparison to a ceramic pump head. The quartz crystal microbalance was used to quantify the primary layer, proteins irreversibly adsorbed at the solid-liquid interface, and the secondary diffuse gel-like layer interacting on top of the primary layer. The results showed that the mass of protein irreversibly adsorbed onto stainless steel sensors is greater than on an aluminum oxide surface (ceramic pump mimic). This suggests that the amount of adsorbed protein plays a role in surface-induced protein aggregation at the solid-liquid interface.

Flow Resistance and Structures in Viscoelastic Channel Flows at Low Re.

The flow of viscoelastic fluids in channels and pipes remains poorly understood, particularly at low Reynolds numbers. Here, we investigate the flow of polymeric solutions in straight channels using pressure measurements and particle tracking. The flow friction factor f_{η} versus flow rate exhibits two regimes: a transitional regime marked by rapid increase in drag, and a turbulentlike regime characterized by a sudden decrease in drag and a weak dependence on flow rate. Lagrangian trajectories show finite transverse modulations not seen in Newtonian fluids. These curvature perturbations far downstream can generate sufficient hoop stresses to sustain the flow instabilities in the parallel shear flow.

Upstream vortex and elastic wave in the viscoelastic flow around a confined cylinder.

The viscoelastic flow past a cylinder is a classic benchmark problem that is not completely understood. Using novel 3D holographic particle velocimetry, we report three main discoveries of the elastic instability upstream of a single cylinder in viscoelastic channel flow. First, we observe that upstream vortices initiate at the corner between the cylinder and the wall and grow with increasing flow rate. Second, beyond a critical Weissenberg, the flow upstream becomes unsteady and switches between two bistable configurations, leading to symmetry breaking in the cylinder axis direction that is highly three-dimensional in nature. Lastly, we find that the disturbance of the elastic instability propagates relatively far upstream via an elastic wave, and is weakly correlated with that in the cylinder wake. The wave speed and the extent of the instability increase with Weissenberg number, indicating an absolute instability in viscoelastic fluids.

Flow fluctuations in wormlike micelle fluids.

We investigate the unstable flow of wormlike micelle solutions in pressure driven capillary flow, with a focus on the effect of entrance geometry on the fluid fluctuations. The flow is measured at different points in the capillary using particle image velocimetry while simultaneously measuring the pressure drop across the entire capillary. The fluctuations are characterized by rapid flow rate jumps that correspond with a decrease in the pressure drop followed by a longer recovery period. Velocimetry measurements in the entrance region show a transition to unstable flow above a critical flow rate, where large flow circulations are observed in the tapered geometry and localized jets are observed in an abrupt contraction. The transition to this unstable flow is shown to occur at a similar dimensionless extension rate normalized by the micelle relaxation time. A rapid breakdown in micelle alignment is observed in polarized light microscopy at the onset of the flow rate jump, indicating the importance of rapid micelle structural changes on the fluctuations. We characterize the system by analyzing the power spectral densities and develop a dynamical systems model to describe the relationship between pressure and flow rate. These developments provide understanding to control flow fluctuations and motivation for more detailed study of the coupling of fluid microstructure transitions and flow fluctuations.

Protein Adsorption and Layer Formation at the Stainless Steel-Solution Interface Mediates Shear-Induced Particle Formation for an IgG1 Monoclonal Antibody.

Passage of specific protein solutions through certain pumps, tubing, and/or filling nozzles can result in the production of unwanted subvisible protein particles (SVPs). In this work, surface-mediated SVP formation was investigated. Specifically, the effects of different solid interface materials, interfacial shear rates, and protein concentrations on SVP formation were measured for the National Institute of Standards and Technology monoclonal antibody (NISTmAb), a reference IgG1 monoclonal antibody (mAb). A stainless steel rotary piston pump was used to identify formulation and process parameters that affect aggregation, and a flow cell (alumina or stainless steel interface) was used to further investigate the effect of different interface materials and/or interfacial shear rates. SVP particles produced were monitored using flow microscopy or flow cytometry. Neutron reflectometry and a quartz crystal microbalance with dissipation monitoring were used to characterize adsorption and properties of NISTmAb at the stainless steel interface. Pump/shear cell experiments showed that the NISTmAb concentration and interface material had a significant effect on SVP formation, while the effects of interfacial shear rate and passage number were less important. At the higher NISTmAb concentrations, the adsorbed protein became structurally altered at the stainless steel interface. The primary adsorbed layer remained largely undisturbed during flow, suggesting that SVP formation at high NISTmAb concentration was caused by the disruption of patches and/or secondary interactions.

Jetting of a shear banding fluid in rectangular ducts.

Non-Newtonian fluids are susceptible to flow instabilities such as shear banding, in which the fluid may exhibit a markedly discontinuous viscosity at a critical stress. Here we report the characteristics and causes of a jetting flow instability of shear banding wormlike micelle solutions in microfluidic channels with rectangular cross sections over an intermediate volumetric flow regime. Particle-tracking methods are used to measure the three-dimensional flow field in channels of differing aspect ratios, sizes, and wall materials. When jetting occurs, it is self-contained within a portion of the channel where the flow velocity is greater than the surroundings. We observe that the instability forms in channels with aspect ratio greater than 5, and that the location of the high-velocity jet appears to be sensitive to stress localizations. Jetting is not observed in a lower concentration solution without shear banding. Simulations using the Johnson-Segalman viscoelastic model show a qualitatively similar behavior to the experimental observations and indicate that compressive normal stresses in the cross-stream directions support the development of the jetting flow. Our results show that nonuniform flow of shear thinning fluids can develop across the wide dimension in rectangular microfluidic channels, with implications for microfluidic rheometry.

Complex Arrangement of Orthogonal Nanoscale Columns via a Supramolecular Orientational Memory Effect.

Memory effects, including shape, chirality, and liquid-crystallinity, have enabled macroscopic materials with novel functions. However, the generation of complex supramolecular nanosystems via memory effects has not yet been investigated. Here, we report a cyclotriveratrylene-crown (CTV) compound that self-assembles into supramolecular columns and spheres forming, respectively, hexagonal and cubic mesophases. Upon transition from one phase to the other, an epitaxial relationship holds, via an unprecedented supramolecular orientational memory effect. Specifically, the molecular orientation and columnar character of supramolecular packing is preserved in the cubic phase, providing an otherwise inaccessible structure comprising orthogonally oriented domains of supramolecular columns. The continuous columnar character of tetrahedrally distorted supramolecular spheres self-organized from the CTV derivative in the faces of the Pm3̅n lattice is the basis of this supramolecular orientational memory, which holds throughout cycling in temperature between the two phases. This concept is expected to be general for other combinations of periodic and quasiperiodic arrays generated from supramolecular spheres upon transition to supramolecular columns.

Reversible Adsorption Kinetics of Near Surface Dimer Colloids.

We investigate the effect of shape on reversible adsorption kinetics using colloidal polystyrene dimers near a solid glass surface as a model system. The interaction between colloid and wall is tuned using electrostatic, depletion, and gravity forces to produce a double-well potential. The dwell time in each of the potential wells is measured from long duration particle trajectories. The height of each monomer relative to the glass surface is measured to a resolution of <20 nm by in-line holographic microscopy. The measured transition probability distributions are used in kinetic equations to describe the flux of particles to and from the surface. The dimers are compared to independent isolated monomers to determine the effects of shape on adsorption equilibria and kinetics. To elucidate these differences, we consider both mass and surface coverage and two definitions of surface coverage. The results show that dimers with single coverage produce slower adsorption, lower surface coverage, and higher mass coverage in comparison to those of monomers, while dimers with double coverage adsorb faster and result in higher surface coverage.

Rheology of clustering protein solutions.

High viscosity is a major challenge with protein therapeutics at extremely high concentrations. To overcome this obstacle, it is essential to understand the relationship between the concentration of a protein solution and its viscosity as a function of shear rate and temperature. Here, lysozyme is a model charged globular protein having both short-ranged attraction (SA) and long-ranged repulsion (LR) that promote the formation of dynamic clusters at high concentrations. We report viscosity measurements from a micro-capillary rheometer (using only several microliters of solution) over a wide range of lysozyme solution concentrations, shear rates, and temperatures. Solution structural relaxation dynamics are also probed by dynamic light scattering (DLS). As a result of lysozyme's SALR interactions, the viscosity increased dramatically across all shear rates with increasing concentration and decreasing temperature. While most of the solutions exhibited Newtonian behavior, shear thinning was exhibited at the highest concentration (480 g/l) and lowest temperatures at shear rates above approximately 10(4 )s(-1). The onset shear rate for thinning and a structural relaxation rate estimated from a slow-mode measured by DLS are compared. These measurements provide insights into the properties of protein solutions and their microscopic structural origins.

Depletion-driven crystallization of cubic colloids sedimented on a surface.

Cubic colloids, sedimented on a surface and immersed in a solution of depletant molecules, were modeled with a family of shapes which smoothly varies from squares to circles. Using Wang-Landau simulations with expanded ensembles, we observe the formation of rhombic lattices, square lattices, hexagonal lattices, and a fluid phase. This systematic investigation includes locating transitions between all combinations of the three lattice structures upon changing the shape and transitions between the fluid and crystal upon changing the depletant concentration. The rhombic lattice deforms smoothly between square-like and hexagonal-like angles, depending on both the shape and the depletant concentration. Our results on the effect of the depletant concentration, depletant size, and colloid shape to influence the stability of the fluid and the lattice structures may help guide experimental studies with recently synthesized cubic colloids.

Rheological Signature of Frictional Interactions in Shear Thickening Suspensions.

Colloidal shear thickening presents a significant challenge because the macroscopic rheology becomes increasingly controlled by the microscopic details of short ranged particle interactions in the shear thickening regime. Our measurements here of the first normal stress difference over a wide range of particle volume fractions elucidate the relative contributions from hydrodynamic lubrication and frictional contact forces, which have been debated. At moderate volume fractions we find N_{1}<0, consistent with hydrodynamic models; however, at higher volume fractions and shear stresses these models break down and we instead observe dilation (N_{1}>0), indicating frictional contact networks. Remarkably, there is no signature of this transition in the viscosity; instead, this change in the sign of N_{1} occurs while the shear thickening remains continuous. These results suggest a scenario where shear thickening is driven primarily by the formation of frictional contacts, with hydrodynamic forces playing a supporting role at lower concentrations. Motivated by this picture, we introduce a simple model that combines these frictional and hydrodynamic contributions and accurately fits the measured viscosity over a wide range of particle volume fractions and shear stress.

Short-Time Glassy Dynamics in Viscous Protein Solutions with Competing Interactions.

The glass transition of colloidal dispersions interacting with both a short-ranged attraction and long-ranged repulsion is studied using highly purified lysozyme solutions. Newtonian liquid behavior is observed at all conditions while measurements of the dynamics in the short-time limit show features typical of glassy colloidal systems at high protein concentrations. This interesting behavior is due to the competition of the attraction and repulsion that produces a heterogeneous microstructure only at intermediate range length scales. The results demonstrate that theories for the macroscopic properties of systems with competing interactions need to include intermediate range order.

Rheology and dynamics of colloidal superballs.

Recent advances in colloidal synthesis make it possible to generate a wide array of precisely controlled, non-spherical particles. This provides a unique opportunity to probe the role that particle shape plays in the dynamics of colloidal suspensions, particularly at higher volume fractions, where particle interactions are important. We examine the role of particle shape by characterizing both the bulk rheology and micro-scale diffusion in a suspension of pseudo-cubic silica superballs. Working with these well-characterized shaped colloids, we can disentangle shape effects in the hydrodynamics of isolated particles from shape-mediated particle interactions. We find that the hydrodynamic properties of isolated superballs are marginally different from comparably sized hard spheres. However, shape-mediated interactions modify the suspension microstructure, leading to significant differences in the self-diffusion of the superballs. While this excluded volume interaction can be captured with a rescaling of the superball volume fraction, we observe qualitative differences in the shear thickening behavior of moderately concentrated superball suspensions that defy simple rescaling onto hard sphere results. This study helps to define the unknowns associated with the effects of shape on the rheology and dynamics of colloidal solutions.

Critical examination of the colloidal particle model of globular proteins.

Recent studies of globular protein solutions have uniformly adopted a colloidal view of proteins as particles, a perspective that neglects the polymeric primary structure of these biological macromolecules, their intrinsic flexibility, and their ability to sample a large configurational space. While the colloidal perspective often serves as a useful idealization in many cases, the macromolecular identity of proteins must reveal itself under thermodynamic conditions in which the native state is no longer stable, such as denaturing solvents and high protein concentrations where macromolecules tend to have screened excluded volume, charge, and hydrodynamic interactions. Under extreme pH conditions, charge repulsion interactions within the protein chain can overcome the attractive hydrogen-bonding interactions, holding it in its native globular state. Conformational changes can therefore be expected to have great significance on the shear viscosity and other rheological properties of protein solutions. These changes are not envisioned in conventional colloidal protein models and we have initiated an investigation of the scattering and rheological properties of model proteins. We initiate this effort by considering bovine serum albumin because it is a globular protein whose solution properties have also been extensively investigated as a function of pH, temperature, ionic strength, and concentration. As we anticipated, near-ultraviolet circular dichroism measurements and intrinsic viscosity measurements clearly indicate that the bovine serum albumin tertiary structure changes as protein concentration and pH are varied. Our findings point to limited validity of the colloidal protein model and to the need for further consideration and quantification of the effects of conformational changes on protein solution viscosity, protein association, and the phase behavior. Small-angle Neutron Scattering measurements have allowed us to assess how these conformational changes influence protein size, shape, and interprotein interaction strength.