Lagrangian stretching reveals stress topology in viscoelastic flows.

Viscoelastic flows are pervasive in a host of natural and industrial processes, where the emergence of nonlinear and time-dependent dynamics regulates flow resistance, energy consumption, and particulate dispersal. Polymeric stress induced by the advection and stretching of suspended polymers feeds back on the underlying fluid flow, which ultimately dictates the dynamics, instability, and transport properties of viscoelastic fluids. However, direct experimental quantification of the stress field is challenging, and a fundamental understanding of how Lagrangian flow structure regulates the distribution of polymeric stress is lacking. In this work, we show that the topology of the polymeric stress field precisely mirrors the Lagrangian stretching field, where the latter depends solely on flow kinematics. We develop a general analytical expression that directly relates the polymeric stress and stretching in weakly viscoelastic fluids for both nonlinear and unsteady flows, which is also extended to special cases characterized by strong kinematics. Furthermore, numerical simulations reveal a clear correlation between the stress and stretching field topologies for unstable viscoelastic flows across a broad range of geometries. Ultimately, our results establish a connection between the Eulerian stress field and the Lagrangian structure of viscoelastic flows. This work provides a simple framework to determine the topology of polymeric stress directly from readily measurable flow field data and lays the foundation for directly linking the polymeric stress to flow transport properties.

Rose Bengal Labeled Bovine Serum Albumin for Protein Transport Imaging in Subcutaneous Tissues Using Computed Tomography and Fluorescence Microscopy.

Subcutaneous (SC) injection of protein-based therapeutics is a convenient and clinically established drug delivery method. However, progress is needed to increase the bioavailability. Transport of low molecular weight (Mw) biotherapeutics such as insulin and small molecule contrast agents such as lipiodol has been studied using X-ray computed tomography (CT). This analysis, however, does not translate to the investigation of higher Mw therapeutics, such as monoclonal antibodies (mAbs), due to differences in molecular and formulation properties. In this study, an iodinated fluorescein analog rose bengal (RB) was used as a radiopaque and fluorescent label to track the distribution of bovine serum albumin (BSA) compared against unconjugated RB and sodium iodide (NaI) via CT and confocal microscopy following injection into ex vivo porcine SC tissue. Importantly, the high concentration BSA-RB exhibited viscosities more like that of viscous biologics than the small molecule contrast agents, suggesting that the labeled protein may serve as a more suitable formulation for the investigation of injection plumes. Three-dimensional (3D) renderings of the injection plumes showed that the BSA-RB distribution was markedly different from unconjugated RB and NaI, indicating the need for direct visualization of large protein therapeutics using conjugated tags rather than using small molecule tracers. Whereas this proof-of-concept study shows the novel use of RB as a label for tracking BSA distribution, our experimental approach may be applied to high Mw biologics, including mAbs. These studies could provide crucial information about diffusion in SC tissue and the influence of injection parameters on distribution, transport, and downstream bioavailability.

Concentration-Dependent Diffusion of Monoclonal Antibodies: Underlying Mechanisms of Anomalous Diffusion.

The development, storage, transport, and subcutaneous delivery of highly concentrated monoclonal antibody formulations pose significant challenges due to the high solution viscosity and low diffusion of the antibody molecules in crowded environments. These issues often stem from the self-associating behavior of the antibody molecules, potentially leading to aggregation. In this work, we used a dissipative particle dynamics-based coarse-grained model to investigate the diffusion behavior of IgG1 antibody molecules in aqueous solutions with 15 and 32 mM NaCl and antibody concentrations ranging from 10 to 400 mg/mL. We determined the coarse-grained interaction parameters by matching the calculated structure factor with the computational and experimental data from the literature. Our results indicate Fickian diffusion for antibody concentrations of 10 and 25 mg/mL and anomalous diffusion for concentrations exceeding 50 mg/mL. The anomalous diffusion was observed for ∼0.33 to 0.4 µs, followed by Fickian diffusion for all antibody concentrations. We observed a strong linear correlation between the diffusion behavior of the antibody molecules (diffusion coefficient D and anomalous diffusion exponent α) and the amount of aggregates present in the solution and between the amount of aggregates and the Coulomb interaction energy. The investigation of underlying mechanisms for anomalous diffusion revealed that in crowded environments at high antibody concentrations, the attractive interaction between electrostatically complementary regions of the antibody molecules could further bring the neighboring molecules closer to one another, ultimately resulting in aggregate formation. Further, the Coulomb attraction can continue to draw more molecules together, forming larger aggregates.

Rheology of bi-disperse dense fiber suspensions.

While significant progress has been made in the modeling and simulation of uniform fiber suspensions, no existing model has been validated for industrially-relevant concentrated suspensions containing fibers of multiple aspect ratios. In the present work, we investigate bi-disperse suspensions with two fiber populations in varying aspect ratios in a steady shear flow using direct numerical simulations. Moreover, we measure the suspension viscosity by creating a controlled length bidispersity for nylon fibers suspended in a Newtonian fluid. The results showed good agreement between the experimentally measured and numerically predicted viscosity for bi-disperse suspensions. The ratio between the aspect ratio of large to small fibers (size ratio) and the volume fraction of large fibers (composition) in bi-disperse systems strongly affected the rheological behavior of the suspension. The increment of relative viscosity associated with size ratio and composition can be explained by the decrease in the maximum flowable limit or jamming volume fraction. Moreover, the relative viscosity of bi-disperse suspensions collapses, when plotted against the reduced volume fraction, demonstrating the controlling influence of the jamming fraction in bi-disperse fiber suspensions.

Stress and stretching regulate dispersion in viscoelastic porous media flows.

In this work, we study the role of viscoelastic instability in the mechanical dispersion of fluid flow through porous media at high Péclet numbers. Using microfluidic experiments and numerical simulations, we show that viscoelastic instability in flow through a hexagonally ordered (staggered) medium strongly enhances dispersion transverse to the mean flow direction with increasing Weissenberg number (Wi). In contrast, preferential flow paths can quench the elastic instability in disordered media, which has two important consequences for transport: first, the lack of chaotic velocity fluctuations reduces transverse dispersion relative to unstable flows. Second, the amplification of flow along preferential paths with increasing Wi causes strongly-correlated stream-wise flow that enhances longitudinal dispersion. Finally, we illustrate how the observed dispersion phenomena can be understood through the lens of Lagrangian stretching manifolds, which act as advective transport barriers and coincide with high stress regions in these viscoelastic porous media flows.

Rheology of 3D printable ceramic suspensions: effects of non-adsorbing polymer on discontinuous shear thickening.

Concentrated suspensions of particles at volume fractions (ϕ) ≥ 0.5 often exhibit complex rheological behavior, transitioning from shear thinning to shear thickening as the shear stress or shear rate is increased. These suspensions can be extruded to form 3D structures, with non-adsorbing polymers often added as rheology modifiers to improve printability. Understanding how non-adsorbing polymers affect the suspension rheology, particularly the onset of shear thickening, is critical to the design of particle inks that will extrude uniformly. In this work, we examine the rheology of concentrated aqueous suspensions of colloidal alumina particles and the effects of adding non-adsorbing polyvinylpyrrolidone (PVP). First, we show that suspensions with ϕalumina = 0.560-0.575 exhibited discontinuous shear thickening (DST), where the viscosity increased by up to two orders of magnitude above an onset stress (τmin). Increasing ϕalumina from 0.550 to 0.575 increased the viscosity and yield stress in the shear thinning regime and decreased τmin. Next, PVP was added at concentrations within the dilute and semi-dilute non-entangled regimes of polymer conformation (ϕPVP = 0.005-0.050) to suspensions with constant ϕalumina = 0.550. DST was observed in all cases and increasing ϕPVP increased the viscosity and yield stress. Interestingly, increasing ϕPVP also increased τmin. We posit that the free PVP chains act as lubricants between alumina particles, increasing the stress needed to induce thickening. Finally, we demonstrate through direct comparisons of suspensions with and without PVP how non-adsorbing polymer addition can extend the extrusion processing window due to the increase in τmin.

Transport and lymphatic uptake of monoclonal antibodies after subcutaneous injection.

The subcutaneous injection has emerged to become a feasible self-administration practice for biotherapeutics due to the patient comfort and cost-effectiveness. However, the available knowledge about transport and absorption of these agents after subcutaneous injection is limited. Here, a mathematical framework to study the subcutaneous drug delivery of mAbs from injection to lymphatic uptake is presented. A three-dimensional poroelastic model is exploited to find the biomechanical response of the tissue by taking into account tissue deformation during the injection. The results show that including tissue deformability noticeably changes tissue poromechanical response due to the significant dependence of interstitial pressure on the tissue deformation. Moreover, the importance of the amount of lymph fluid at the injection site and the injection rate on the drug uptake to lymphatic capillaries is highlighted. Finally, variability of lymphatic uptake due to uncertainty in parameters including tissue poromechanical and lymphatic absorption parameters is evaluated. It is found that interstitial pressure due to injection is the major contributing factor in short-term lymphatic absorption, while the amount of lymph fluid at the site of injection determines the long-term absorption of the drug. Finally, it is shown that the lymphatic uptake results are consistent with experimental data available in the literature.

Assessment of Cavitation Intensity in Accelerating Syringes of Spring-Driven Autoinjectors.

PURPOSE: Cavitation is an undesired phenomenon that may occur in certain types of autoinjectors (AIs). Cavitation happens because of rapid changes of pressure in a liquid, leading to the formation of small vapor-filled cavities, which upon collapsing, can generate an intense shock wave that may damage the device container and the protein drug molecules. Cavitation occurs in the AI because of the syringe-drug relative displacement as a result of the syringe's sudden acceleration during needle insertion and the ensuing pressure drop at the bottom of the container. Therefore, it's crucial to analyze the potential effect of cavitation on AI. The goal of the current study is to investigate the effects of syringe and AI design parameters such as air gap size, syringe filling volume, fluid viscosity, and drive spring force (syringe acceleration) on the risk and severity of cavitation. METHODS: A model autoinjector platform is built to record the syringe and cavitation dynamics which we use to estimate the cavitation intensity in terms of extension rate and to study the effects of design parameters on the severity of cavitation. RESULTS: Our results show the generation of an intense shock wave and a high extension rate upon cavitation collapse. The induced extension rate increases with syringe acceleration and filling volume and decreases with viscosity and air gap size. CONCLUSION: The most severe cavitation occurred in an AI device with the larger drive spring force and the syringe of a smaller air gap size filled with a less viscous fluid and a larger filling volume.

New Model to Predict the Concentration-Dependent Viscosity of Monoclonal Antibody Solutions.

Concentrated monoclonal antibody solutions exhibit high solution viscosity, which is experimentally measured to be ∼1-2 orders of magnitude higher than the viscosity of water. However, physical processes responsible for the high antibody viscosity are not fully understood. We show that fluid occlusion due to the trapped solvent molecules within the boundaries formed by the aggregated antibodies is responsible for the elevated solution viscosity. We develop a theory to predict the viscosity of monoclonal antibodies based on the geometry of the antibody molecule and the aggregate morphology. We validate our theory with experiments and highlight useful insights obtained from the viscosity equation which could help in controlling the drug viscosity at the molecular design stage itself.

Monoclonal Antibody Aggregation near Silicone Oil-Water Interfaces.

In this work, we study the hydrodynamic behavior of monoclonal antibodies in the presence of silicone oil-water interfaces. We model the antibody molecules using a coarse-grained 24-bead model, where two beads are used to represent each antibody domain. We consider the spatial variation of the antibody polarity in our model as each bead represents a set of hydrophilic or hydrophobic amino acids. We use the dissipative particle dynamics scheme to represent the coarse-grained force field which governs the motion of the beads. In addition, interprotein interactions are modeled using an electrostatic force field. The model parameters are determined by comparing the structure factor against experimental structure factor data ranging from a low concentration regime (10 mg/mL) to a high concentration regime (150 mg/mL). Next, we conduct simulations for a suspension of antibody molecules in the presence of silicone oil-water interfaces. Protein loss from the bulk solution is noticed as the molecules adsorb at the interface. We observe dynamic cluster formation in the solution bulk and at the interface, as the antibody molecules self-associate along their trajectories. We quantify the aggregation using a density clustering algorithm and investigate the effect of the antibody concentration on the diffusivity of the antibody solution, aggregation propensity, and protein loss from the bulk. Our study shows that numerical simulations can be an important tool for understanding the molecular mechanisms driving protein aggregation near hydrophobic interfaces.

The Interface Motion and Hydrodynamic Shear of the Liquid Slosh in Syringes.

PURPOSE: Interface motion and hydrodynamic shear of the liquid slosh during the insertion of syringes upon autoinjector activation may damage the protein drug molecules. Experimentally validated computational fluid dynamics simulations are used in this study to investigate the interfacial motion and hydrodynamic shear due to acceleration and deceleration of syringes. The goal is to explore the role of fluid viscosity, air gap size, syringe acceleration, syringe tilt angle, liquid-wall contact angle, surface tension and fill volume on the interface dynamics caused by autoinjector activation. METHODS: A simplified autoinjector platform submerged in water is built to record the syringe and liquid motion without obstruction of view. The syringe kinematics is imported to the simulations based on OpenFOAM InterIsoFoam solver, which is used to study the effects of various physical parameters. RESULTS: The simulations agree with experiments on the air-liquid interface profile and interface area. The interfacial area and the volume of fluid subject to high strain rate decrease with the solution viscosity, increase with the air gap height, syringe velocity, tilt angle and syringe wall hydrophobicity, and hardly change with the surface tension and liquid column height. The hydrodynamic shear mainly occurs near the syringe wall and entrained bubbles. CONCLUSION: For a given dose of drug solution, the syringe with smaller radius and larger length will generate less liquid slosh. Reducing the air volume and syringe wall hydrophobicity are also helpful to reduce interface area and effective shear. The interface motion is reduced when the syringe axis is aligned with the gravitational direction.

Biofilms at interfaces: microbial distribution in floating films.

Cellular motility is a key function guiding microbial adhesion to interfaces, which is the first step in the formation of biofilms. The close association of biofilms and bioremediation has prompted extensive research aimed at comprehending the physics of microbial locomotion near interfaces. We study the dynamics and statistics of microorganisms in a 'floating biofilm', i.e., a confinement with an air-liquid interface on one side and a liquid-liquid interface on the other. We use a very general mathematical model, based on a multipole representation and probabilistic simulations, to ascertain the spatial distribution of microorganisms in films of different viscosities. Our results reveal that microorganisms can be distributed symmetrically or asymmetrically across the height of the film, depending on their morphology and the ratio of the film's viscosity to that of the fluid substrate. Long-flagellated, elongated bacteria exhibit stable swimming parallel to the liquid-liquid interface when the bacterial film is less viscous than the underlying fluid. Bacteria with shorter flagella on the other hand, swim away from the liquid-liquid interface and accumulate at the free surface. We also analyze microorganism dynamics in a flowing film and show how a microorganism's ability to resist 'flow-induced-erosion' from interfaces is affected by its elongation and mode of propulsion. Our study generalizes past efforts on understanding microorganism dynamics under confinement by interfaces and provides key insights on biofilm initiation at liquid-liquid interfaces.

Towards an analytical description of active microswimmers in clean and in surfactant-covered drops.

Geometric confinements are frequently encountered in the biological world and strongly affect the stability, topology, and transport properties of active suspensions in viscous flow. Based on a far-field analytical model, the low-Reynolds-number locomotion of a self-propelled microswimmer moving inside a clean viscous drop or a drop covered with a homogeneously distributed surfactant, is theoretically examined. The interfacial viscous stresses induced by the surfactant are described by the well-established Boussinesq-Scriven constitutive rheological model. Moreover, the active agent is represented by a force dipole and the resulting fluid-mediated hydrodynamic couplings between the swimmer and the confining drop are investigated. We find that the presence of the surfactant significantly alters the dynamics of the encapsulated swimmer by enhancing its reorientation. Exact solutions for the velocity images for the Stokeslet and dipolar flow singularities inside the drop are introduced and expressed in terms of infinite series of harmonic components. Our results offer useful insights into guiding principles for the control of confined active matter systems and support the objective of utilizing synthetic microswimmers to drive drops for targeted drug delivery applications.

Effect of external shear flow on sperm motility.

The trajectory of sperm in the presence of background flow is of utmost importance for the success of fertilization, as sperm encounter background flow of different magnitude and direction on their way to the egg. Here, we have studied the effect of an unbounded simple shear flow as well as a Poiseuille flow on the sperm trajectory. In the presence of a simple shear flow, the sperm moves on an elliptical trajectory in the reference frame advecting with the local background flow. The length of the major-axis of this elliptical trajectory decreases with the shear rate. The flexibility of the flagellum and consequently the length of the major axis of the elliptical trajectories increases with the sperm number. The sperm number is a dimensionless number representing the ratio of viscous force to elastic force. The sperm moves downstream or upstream depending on the strength of background Poiseuille flow. In contrast to the simple shear flow, the sperm also moves toward the centerline in a Poiseuille flow. Far away from the centerline, the cross-stream migration velocity of the sperm increases as the transverse distance of the sperm from the centerline decreases. Close to the centerline, on the other hand, the cross-stream migration velocity decreases as the sperm further approaches the center. The cross-stream migration velocity of the sperm also increases with the sperm number.

Hydrodynamics-mediated trapping of micro-swimmers near drops.

In this paper, we investigate the swimming characteristics and dynamics of a model micro-swimmer in the vicinity of a clean drop, and of a surfactant covered drop. We model the swimmer as a force dipole and utilize the image-singularity system to study the dynamical behavior of the swimmer. Motivated by bacterial bio-remediation of insoluble hydrocarbons (HCs) released during oil spills, we report the 'trapping characteristics' - critical trapping radius, basin of attraction and trapping time distribution - of deterministic and stochastic swimmers, as a function of viscosity ratio, and dimensionless surface viscosity. We find that addition of surfactant reduces the critical trapping radius of a drop by ∼30%. The basin of attraction though, is not affected acutely for any combination in the parameter space of viscosity ratio and surface viscosity. We also carry out a dynamical system analysis of our problem, for deterministic swimmers, to clarify the aforementioned concepts. For hydrodynamics combined with diffusion based motion, we note increments ranging from ∼5-25% in the interface-retention times of surfactant-laden drops, as compared to clean drops. These differences occur for low values of surface viscosity, and saturate rapidly as the surface viscosity increases. With potential applications in bioremediation, our results highlight the importance of considering dispersant-addition in oil spills involving insoluble hydrocarbons.

Modeling of active swimmer suspensions and their interactions with the environment.

In this article, we review mathematical models used to study the behaviour of suspensions of micro-swimmers and the accompanying biophysical phenomena, with specific focus on stimulus response. The methods discussed encompass a range of interactions exhibited by the micro-swimmers; including passive hydrodynamic (gyrotaxis) and gravitational (gravitaxis) effects, and active responses to chemical cues (chemotaxis) and light intensities (phototaxis). We introduce the simplest models first, and then build towards more sophisticated recent developments, in the process, identifying the limitations of the former and the new results obtained by the latter. We comment on the accuracy/validity of the models adopted, based on the agreement between theoretical results and experimental observations. We conclude by identifying some of the open problems and associated challenges faced by researchers in the realm of active suspensions.

Collective Motion of Microorganisms in a Viscoelastic Fluid.

We study the collective motion of a suspension of rodlike microswimmers in a two-dimensional film of viscoelastic fluids. We find that the fluid elasticity has a small effect on a suspension of pullers, while it significantly affects the pushers. The attraction and orientational ordering of the pushers are enhanced in viscoelastic fluids. The induced polymer stresses break down the large-scale flow structures and suppress velocity fluctuations. In addition, the energy spectra and induced mixing in the suspension of pushers are greatly modified by fluid elasticity.

Fabrication of shape controllable Janus alginate/pNIPAAm microgels via microfluidics technique and off-chip ionic cross-linking.

A novel method to fabricate shape controllable alginate/pNIPAAm complex microgels is reported. Monodisperse alginate/pNIPAAm droplets are created via microfluidics and cross-linked in different concentrations of hot glycerol/barium acetate water solutions. By changing the initial droplet size and glycerol concentration of the collecting solution, the resultant microgel shape and surface details can be systematically tuned. High-speed imaging is used to visualize and explain the microgel formation process.

Low-Reynolds-number swimming at pycnoclines.

Microorganisms play pivotal functions in the trophic dynamics and biogeochemistry of aquatic ecosystems. Their concentrations and activities often peak at localized hotspots, an important example of which are pycnoclines, where water density increases sharply with depth due to gradients in temperature or salinity. At pycnoclines organisms are exposed to different environmental conditions compared to the bulk water column, including reduced turbulence, slow mass transfer, and high particle and predator concentrations. Here we show that, at an even more fundamental level, the density stratification itself can affect microbial ecology at pycnoclines, by quenching the flow signature, increasing the energetic expenditure, and stifling the nutrient uptake of motile organisms. We demonstrate this through numerical simulations of an archetypal low-Reynolds-number swimmer, the "squirmer." We identify the Richardson number--the ratio of buoyancy forces to viscous forces--as the fundamental parameter that quantifies the effects of stratification. These results demonstrate an unexpected effect of buoyancy on low-Reynolds-number swimming, potentially affecting a broad range of abundant organisms living at pycnoclines in oceans and lakes.

A multi-scale numerical study of monoclonal antibodies uptake by initial lymphatics after subcutaneous injection.

This paper studies the transport of monoclonal antibodies through skin tissue and initial lymphatics, which impacts the pharmacokinetics of monoclonal antibodies. Our model integrates a macroscale representation of the entire skin tissue with a mesoscale model that focuses on the papillary dermis layer. Our results indicate that it takes hours for the drugs to disperse from the injection site to the papillary dermis before entering the initial lymphatics. Additionally, we observe an inhomogeneous drug distribution in the interstitial space of the papillary dermis, with higher drug concentrations near initial lymphatics and lower concentrations near blood capillaries. To validate our model, we compare our numerical simulation results with experimental data, finding a good alignment. Our parametric studies on the drug molecule properties and injection parameters suggest that a higher diffusion coefficient increases the transport and uptake rate while binding slows down these processes. Furthermore, shallower injection depths lead to faster lymphatic uptake, whereas the size of the injection plume has a minor effect on the uptake rate. These findings advance our understanding of drug transport and lymphatic absorption after subcutaneous injection, offering valuable insights for optimizing drug delivery strategies and the design of biotherapeutics.