Schedule for: 18w5123 - Complex Fluids in Biological Systems

A buffet dinner is served daily between 5:30pm and 7:30pm in the Vistas Dining Room, the top floor of the Sally Borden Building.

Breakfast is served daily between 7 and 9am in the Vistas Dining Room, the top floor of the Sally Borden Building.

A brief introduction to BIRS with important logistical information, technology instruction, and opportunity for participants to ask questions.

With endoskeletal droplets, it is possible to design delivery vehicles that deposit efficiently to a target surface and can then be removed through shape change. In addition, by introducing magnetic nanoparticles to the droplets, we demonstrate that reconfiguration and response can be driven with external fields. This study is the first evidence of novel routes to controlling the shape, stability, and dynamics of multifunctional emulsions with applications for designing materials that respond to changes in their surroundings.

We present a model that probes a particular mechanism for cancer-cell extravasation from blood vessels. Microfluidic-based assays suggest that a cancer cell extends a filopodium through the endothelium that adheres to the extracellular matrix through a focal adhesion. Contraction of myosin motors on the stress fibers then pulls the cell body, including the relatively stiff nucleus, through the narrow opening between endothelial cells. Our model accounts for the positive feedback among myosin attachment, contraction force in the stress fiber and buildup of the focal adhesion. By dynamic simulations that couple the fluid and solid mechanics of the cells and tissues, we demonstrate that under appropriate conditions, the myosin contraction in the stress fibers can produce sufficient elastic deformation in the endothelium and the cell nucleus to effect extravasation.

Lunch is served daily between 11:30am and 1:30pm in the Vistas Dining Room, the top floor of the Sally Borden Building.

Meet in the Corbett Hall Lounge for a guided tour of The Banff Centre campus.

Meet in foyer of TCPL to participate in the BIRS group photo. The photograph will be taken outdoors, so dress appropriately for the weather. Please don't be late, or you might not be in the official group photo!

The huge population of bacteria in the digestive tract (gut microbiota) play important roles in digestion, health, and immune response. In the large intestine, the spatial distribution of species varies both along the intestine as well as radially; with some species primarily found only in the lumen of the intestine rather than colonizing the wall. Many of these bacteria are immotile, and even motile bacteria swim too slowly to swim upstream against the flow. This raises the question of how the population of bacteria is maintained in the face of the constant peristaltic flow moving contents through the intestine. Using analytical and numerical calculations we investigate how peristalsis, motility, flow, and diffusion lead to bacterial population maintenance. We find that it is likely that a dominant factor leading to population maintenance in the human intestine is Taylor dispersion.

The three-dimensional spatiotemporal organization of genetic material inside the cell nucleus remains an open question in cellular biology. During the time between two cell divisions, the functional form of DNA in cells, known as chromatin, fills the cell nucleus in its uncondensed polymeric form, which allows the transcriptional machinery to access DNA. Recent in vivo imaging experiments have cast light on the existence of coherent chromatin motions inside the nucleus, in the form of large-scale correlated displacements on the scale of microns and lasting for seconds. To elucidate the mechanisms for such motions, we have developed a coarse-grained active polymer model where chromatin is represented as a confined flexible chain acted upon by active molecular motors, which perform work and thus exert dipolar forces on the system. Numerical simulations of this model that account for steric and hydrodynamic interactions as well as internal chain mechanics demonstrate the emergence of coherent motions in systems involving extensile dipoles, which are accompanied by large-scale chain reconfigurations and local nematic ordering. Comparisons with experiments show good qualitative agreement and support the hypothesis that long-ranged hydrodynamic couplings between chromatin-associated active motors are responsible for the observed coherent dynamics.

Many representations of cellular behavior rely on abstractions that do not account for how molecules are organized within cells. For example, linear algebra-, differential equation-, and stochastic simulation algorithm-based models typically do not represent individual molecules or their spatial positioning and motion. For many questions in biology and medicine these simpler models have been sufficient. However, there are fundamental gaps in physical understanding of cells that cannot be easily resolved. Here we discuss our progress in adapting and advancing modeling and simulation tools developed for spherically confined colloidal suspensions, for use in studying cellular systems, so that biomolecules and their interactions can be represented individually and explicitly. By developing a more robust and fundamentally well-grounded physics model for how macromolecules interact within cells we can contribute to a more physically complete representation of living matter. A primary challenge in the development of models for such confined systems is the accurate and efficient representation of many- body hydrodynamic interactions, Brownian motion, and confinement. To this end, we developed new hydrodynamic mobility functions for spherically confined colloids and implemented them in a Stokesian dynamics framework. The method accounts for all many-body particle/particle and particle/cavity interactions. Utilizing this model, we studied short- and long-time self-diffusion at equilibrium. We find that confinement produces qualitative changes in transport, such as a position dependent and anisotropic diffusion and entrainment. Connections to underlying structure are made, and consequences for cellular behavior are discussed.

A buffet dinner is served daily between 5:30pm and 7:30pm in the Vistas Dining Room, the top floor of the Sally Borden Building.

Biological cilia are used for feeding, locomotion, particulate transport, sensing, and other vital functions. Due to their small size, cilia operate in low Reynolds number environments, where a non-reciprocal beating is required to transport fluid. In this talk, I will discuss how to design arrays of ferromagnetic elastic cilia that effectively mimic beating of natural cilia when subject to a rotating magnetic field. We characterize cilia motion in terms of relevant dimensionless parameters, and probe fluid pumping, mixing, and particle capture by arrays of magnetically-actuated cilia. We design ciliary arrays that exhibit metachronal beating and show how to selectively immobilize individual cilia by using electrostatics to control beating pattern.

An important class of fluid-structure problems involve the dynamics of ordered arrays of immersed, flexible fibers. While specialized numerical methods have been developed to study fiber-fluid systems, they become infeasible when there are many, rather than a few, fibers present, and do not lend themselves to analytical calculation. In this talk I will introduce a coarse-grained continuum model, based on local-slender body theory for elastic fibers immersed in a viscous Newtonian fluid. We will explore some of the basic properties of these systems subjected to steady and oscillatory shear flows; and then show how qualitatively different phenomenon can emerge in some systems as the fiber density is varied. Finally, we will show how the model can be used to study pumping in beds of actuated cilia.

In 1851 Stokes analyzed the oscillatory translation of a rigid spherical particle in unsteady creeping flow: he demonstrated that the hydrodynamic force on the particle is a quadratic function of the square root of its frequency of oscillation. The force has a much more complicated dependence on frequency for an anisotropic particle (e.g. Lawrence and Weinbaum, JFM 1986). Here, we consider the unsteady motion of an elongated particle of revolution: specifically, we utilize slender-body theory to derive an asymptotic approximation to the frequency-dependent force for oscillatory translations parallel and perpendicular to the axis of rotational symmetry of the particle. We also discuss the steady translation of an elongated particle at non-zero Reynolds number (Re). Here, slender-body theory is used to develop an analytic approximation to the force on the particle, which is in surprisingly good agreement with the force computed from numerical solution of the Navier-Stokes equations at moderate Re.

In this work a two-phase flow model is constructed to study the combined effects of interfacial slip, permeability and elasticity of the porous skeleton inside a viscous drop under simple linear flows. This two-phase flow model describes a viscous fluid filling a deformable elastic skeleton inside a drop whose interface deforms according to the balance of traction on the interface. When the viscous dissipation of the interior porous flow is negligible (compared to the friction between the fluid and the skeleton), the two-phase flow is reduced to a poroelastic Darcy fluid instead. At the interface between such an interior poroelastic fluid and an exterior Stokesian fluid, both slip and permeability are taken into account. The permeating flow induces dissipation that depends on the elastic stress of the interior solid. Small-deformation analysis leads to a set of linear ODE's of which the eigenvalues can be used to find parameter regimes where small-deformation is reasonable. By exploring the interfacial slip, permeability and interior elasticity various flow patterns are found at equilibrium of these slightly deformed poroelastic drops. These results shed light on the rheology of a suspension of poroelastic spherical particles, and give insight to possible flow patterns of a system of self-propelling swimmers with porous flow (such as intracellular cytosol) inside.

There is a lot of interest in characterizing the mechanics of complex interfaces that compose biological systems such as cells. In this talk, we discuss some of our recent work on the micromechanics of vesicles, i.e., sacs of fluid of ~20 microns containing a phospholipid bilayer. Here, we focus on how these systems behave in extensional flows, probing the conditions under which they become mechanically unstable and break up. We find that vesicles exhibit qualitatively different shape transitions than droplets under flow due to the bending and dilatational resistance of the phospholipid bilayer. We discuss the microfluidic experiments and boundary element simulations to quantify the different shape transitions, and describe how flow type and flow history alters these dynamics. In the second half of the talk, we discuss more general problems on how shear and dilatational resistance of a membrane alter the dynamics of droplet-like systems found in biology. We develop analytical theories to quantify how linear shear and dilatational surface moduli alter droplet translation, shape, breakup, and particle lift. We find that one can use simple symmetry/scaling arguments to illuminate how interfacial shear viscosity alters the translational speed of a droplet.

We consider the Brownian motion of a small spherical particle in viscoelastic flow. Even in absence of external flow or forcing the particle resistance is frequency-dependent which establishes a link between observed Brownian displacements and the linear rheology of the fluid [Mason, T.G., Weitz, D.A., 1995. PRL. 74, 1250.] Under external flow or forcing the frequency-dependent particle resistance may become anisotropic and non-symmetric due to fluid elasticity. We derive the Brownian mean-square displacements as function of time under the usual assumptions of statistical stationarity and equipartition. We also derive explicit results for the particle resistance via perturbation theory of the time-dependent Oldroyd-B model. We discuss potential applications of our results to Taylor dispersion and microrheology.

Complex fluids have long been characterized by two functions that summarize the fluid’s elastic and viscous properties, the storage and loss moduli. Information about these bulk fluid properties can be inferred from the path statistics of immersed, fluctuating microparticles. In this talk, we describe a systematic study of this multi-step protocol and we analyze errors and uncertainties intrinsic to it. Particle velocities are assumed to be well-described by the Generalized Langevin Equation uniquely characterized by a memory kernel, which is hypothesized to be inherited from the surrounding fluid. We present a rigorous justification for a key relationship between a particle’s Mean Squared Displacement and its memory kernel central to passive microrheology. Finally, we show that, despite the fact that certain parameters are essentially unidentifiable on their own, the protocol is remarkably effective in reconstructing the storage and loss moduli in a range that corresponds to the experimentally observable regime.

Superhydrophobic surfaces, formed by air entrapment within the cavities of a hydrophobic solid substrate, are ubiquitous in nature. As these surfaces exhibit a promising potential for drag reduction in small-scale flows, they have attracted the attention of fluid mechanists for quite some time. While low-drag configurations are typically associated with singular limits, most of the existing analysis in the literature is based upon numerical schemes. I will discuss the application of singular perturbations to several of the canonical problems in the field.

Active matter systems often show intriguing phenomena in large spatial scales and long time scales, due to various interactions between the building-block particles. The long-range interactions are usually through Stokes flow and electrostatic field, while steric interaction is usually the dominant effect at short-range. We develop an extension to the Kernel Independent Fast Multipole Method to allow adaptive and flexible treatment of long-range interactions with various boundary conditions. We demonstrate the application of this algorithm with a new Stokeslet image system for half-space Stokes flow. To handle the short-range steric interactions, we propose a new method based on constrained minimization to circumvent the stiffness of pairwise repulsive potential. All the proposed algorithms are parallel and scalable, and we demonstrate the applications with a few active matter systems, including microtubule network and growing and dividing cells.

Recent experiments show that bacterial and other active suspensions in confined geometries can self-organize into persistent flow structures that exhibit spontaneously broken mirror symmetry. To describe such observations within a minimal theoretical framework, we consider generalized Navier-Stokes (GNS) equations that combine a generic linear instability mechanism with a conventional advective nonlinearity. This phenomenological model is analytically tractable and reproduces several experimentally observed phenomena, including spontaneous flows and viscosity reduction in active suspensions. Triad analysis and numerical simulations of the GNS equations predict that 3D active flows can realize chiral Beltrami vector fields that support inverse energy transport from smaller to larger scales.

Even without external forcing active systems are out of equilibrium, which gives rise to interesting properties in both small and large concentrations of the particles. These properties have been observed in experiments as well as simulation/modeling approaches. It is important to understand how hydrodynamic interactions between active colloids cause and/or alter the suspension properties including enhanced transport and mixing. One of the most successful approaches has been a mean field theory. However, in some situations the mean field theory makes predictions that differ significantly from experiments and direct (agent or particle based) simulations. There are also some quantities that cannot be calculated by the mean field theory. We will describe our new approach which uses a stochastic field to overcome the limitations of the mean field assumption. It allows us to calculate how interactions between organisms alter the correlations and mixing even in conditions where there is no large-scale group behavior.

The locomotion of flagellated bacteria in viscous fluid provides the blueprint for a number of micro-scale engineering applications. The elasticities of both the hook protein (connecting cell body and flagellum) and the flagella themselves play a key role in determining the stability of locomotion. We use a coarse-grained discretization of elastic flagella connected to a rigid cell body to examine trajectories and flow fields for free swimmers. We indeed find that hook and/or flagellar buckling occurs above a critical flexibility relative to the swimmer’s torque input. This renders straight swimming ineffective, though not necessarily undesirable in practice. Simulations with two flagella show bundling greatly stabilize the buckling effect. We also examine the impact of higher flagellar multiplicity on locomotion, finding that while the straight swimming speed is quite similar to the uniflagellar case, multiflagellar swimming is robust to random placement and resists buckling as well. Ultimately our results may provide insight on how swimmers move through complex environments and how to design microrobotic swimmers for specific applications.

Artificial microswimmers are a new technology with promising microfluidics and biomedical applications, such as directed cargo transport, microscale assembly, and targeted drug delivery. A fundamental barrier to realising this potential is the ability to independently control the trajectories of multiple individuals within a large group. A promising navigation mechanism for "fuel-based" microswimmers, for example autophoretic Janus particles, entails modulating the local environment to guide the swimmer, for instance by etching grooves in microchannels. However, such techniques are currently limited to bulk guidance. I will show (theoretically) that by manufacturing microswimmers from phoretic filaments of flexible shape-memory polymer, elastic transformations can modulate swimming behaviour, allowing precision navigation of selected individuals within a group through complex environments. I will then discuss the experimental implementation of this work, and future directions including potential uses in the manufacture of photorheological fluids.

For Brownian motion in bounded domains there are a variety of "exit time problems," where the goal is to estimate the expected time for a Brownian particle to reach some part of the domain, called the exit. When the exit is small, there are analytical techniques available to estimate the exit time. These techniques can be extended to include a swimming velocity. We use these techniques, as well as numerical simulations, to investigate the time required for a rod-like microswimmer to reverse direction in a tight channel. This is joint work with Jacob Gloe.

Interactions between motile microorganisms and solid boundaries play an important role in many biological and industrial processes. I will discuss recent advances in experiments and simulations that aim to understand the motion of micro-swimmers such as bacteria, micro-algae or spermatozoa in confinements or structured environments. Our results highlight the complex interplay of the fluidic and contact interactions of the individuals with each-other and the boundaries to give rise to intricate behavior.

We investigate the swimming dynamics of motile bacteria outside both clean and surfactant-laden-drops. The micro-organism locomotion outside the drop is solved by modeling it as a force dipole, and obtaining the solution for its image singularity with respect to the drop. The bacterium gets hydrodynamically trapped around the drop, if the drop radius is larger than a critical trapping radius. In cases where the bacteria diffusive motion is strong, they escape the drops after some interface-retention time. This retention time is considerably higher for surfactant-laden drops, as compared to clean drops. We then investigate the combined influence of hydrodynamics and chemotaxis on the distribution of micro-organisms around nutrient sources like crude oil drops. The results of our studies are expected to provide vital information and fertile ground for research in the field of bacterial bioremediation of subsurface oil-spills.

Numerical simulations of micro-organism locomotion in viscoelastic fluids have demonstrated highly localized, large elastic stresses near the tips of flagella for large amplitude strokes. The physical origin of these stresses is not understood, nor is their effect on locomotion. The motion of long, thin objects moving in Newtonian fluids has been studied extensively. Surprisingly little is known about the dynamics of cylindrical objects moving in viscoelastic fluids, and previous analytic work has focused small relaxation time limit in which the nonlinearities of viscoelasticity are small. We examine the limit of small elastic stiffness which retains the nonlinearities responsible for the large localized stresses. We examine the steady flow around cylinders translating in a viscoelastic fluids with different orientations. This analysis predicts a critical Weissenberg above which large elastic tip stresses appear, and it shows that the elastic tip stresses are larger for cylinders moving in the direction tangential to their long axis than for cylinder moving orthogonal to their long axis. Finally we present numerical simulations of different kinds of swimmers which demonstrate the implications of these tip stresses on locomotion.

We ask the question: Why is the fluid response to small amplitude and large amplitude strokes different in viscoelastic fluids? It is well known that elastic stresses accumulate in viscoelastic fluids and where stretching outpaces relaxation. For example, large fluid stresses develop at steady extensional points for sufficiently large Weissenberg number. It is more difficult to understand how stress accumulates near swimmer bodies in part because the flows around moving micro-organisms, or waving cilia, cannot be characterized by a single Weissenberg number. In addition, it is not currently possible to measure the fluid elastic stress near motile cells in viscoelastic fluids. We use theory and numerical simulations to guide our intuition on where elastic stresses develop in the flows around organisms. By examining the flows around idealized undulating flagella or waving cilia in our numerical simulations we find that fluid regions near tips of these objects experience an effective oscillating extensional point from which we can define a local Weissenberg number. This can help us quantify what high amplitude means in terms of large stress accumulation around the body.

We will discuss the dynamics of hydrodynamically interacting motile and non-motile stress-generating swimmers or particles as they invade a surrounding viscous fluid. Colonies of aligned pusher particles are shown to elongate in the direction of particle orientation and undergo a cascade of transverse concentration instabilities. Colonies of aligned puller particles instead are found to elongate in the direction opposite the particle orientation and exhibit dramatic splay as the group moves into the bulk. A linear stability analysis of concentrated line distributions of particles is performed and growth rates are found, using an active slender-body approximation, to match the results of numerical simulations. Thin concentrated bands of aligned pusher particles are always unstable, while bands of aligned puller particles can either be stable (immotile particles) or unstable (motile particles) with a growth rate which is non monotonic in the force dipole strength. We also prove a surprising "no-flow theorem": a distribution initially isotropic in orientation loses isotropy immediately but in such a way that results in no fluid flow anywhere at any time.

5-day workshop participants are welcome to use BIRS facilities (BIRS Coffee Lounge, TCPL and Reading Room) until 3 pm on Friday, although participants are still required to checkout of the guest rooms by 12 noon.