Modeling problems in mucus viscoelasticity and mucociliary clearance

From the common cold and allergies to severe chronic and acute respiratory impairments, the function of the body\u27s mucociliary clearance mechanism plays a primary defense role. Mucus demonstrates numerous non-Newtonian behaviors which set it apart from viscous fluids. Among them: Bingham plastic behavior, shear-thinning, and elasticity on short time scales due to relaxation time. Experimental evidence suggests that certain rheologies promote effective transport. In an effort to reveal the mechanisms controlling transport, models are developed. Firstly, a steady state model which idealizes the mucus as a rigid body is created in order to bring together disparate bodies of experimental work from the literature. The force balance reveals that the force cilia are capable of exerting cannot be related, simply, to the velocity of mucus. That is, only a fraction of the force cilia are capable of exerting is required to steadily transport mucus at the velocities observed experimentally. Likewise, the velocities estimated by this model when cilia force is the input are overestimated by one to two orders of magnitude. This incongruity formally motivates the inclusion of one of mucus\u27s rheological behaviors, stress relaxation. The first viscoelastic problem considered is the response of the linear Maxwell fluid to an oscillating plate. Though a problem commonly discussed in textbooks on theoretical viscoelasticity, the complete analytical solutions are not provided. Here, solutions are found and graphed in terms of the phase and amplitude of the velocity field resultant from the oscillations of the plate; all derivations are shown in their entirety. The effects of stress relaxation (sometimes referred to as memory) and inertia on phase and amplitude are shown to have frequency dependence. Furthermore, it is shown that oscillatory shear perturbations to a viscoelastic Maxwell fluid always travel further and faster away from the source as Deborah number (a dimensionless parameter governing the importance of viscoelastic forces, De=0 corresponds to a Newtonian fluid) is increased. The limitation of the linear Maxwell fluid is illustrated by attempting to apply the constitutive equation to a thin film flow problem. It is found that the stress field of the solution only differs from the viscous case if the boundary conditions are transient; that is, the constitutive equation cannot account for the changes in stress that occur over space. The time derivative must be replaced by a Convected Derivative to achieve the proper Lagrangian to Eulerian coordinate transformation and is considered in a final set of problems. Three problems were completed using the Upper Convected Maxwell model for viscoelasticity. The first considers a purely unidirectional shear flow which, unlike a viscous fluid, possesses tensile stresses along streamlines. The model posits that these additional stresses are essential for transport by allowing regions which are actively sheared, to hold up inactive regions. A novel relationship between applied stress and relaxation time is developed; the model shows that increasing the relaxation time of mucus decreases the amount of stress that must be imparted by cilia. In the second two problems, the UCM equations are simplified via a perturbation series expansion for small Weissenberg number (also a dimensionless group governing the importance of viscoelastic forces). This technique allows the analytically solvable viscous (also referred to as the unperturbed or order one) solutions to be used to estimate the impact of small amounts of stress memory. It is found that elasticity increases the developing region of a viscous flow; all stress components are convected downstream due to flow memory. Likewise, in the sinusoidally varying stress case, the velocity field is always shifted further away from the phase of the applied stress as viscoelastic forces are increased. It is also found that the departure from the viscous solution is dramatically reduced if the stress distribution is moving at the same velocity as the mucal flow. This shows the benefit of an antiplectic wave speed (the physiologically relevant case in which the phase of the cilial beat is moving opposite to transport) as there is no danger that these two can be in phase with one another. Model restrictions prevent quantitative gauges of transport efficiency as a function of metachronal wave parameters and relaxation time to be made. Several additional problems are proposed to address unanswered modeling questions and experimental solutions for the lack of rheological data on tracheal mucus are suggested

Mechanochemical Topological Defects in an Active Nematic

We propose a reaction-diffusion system that converts topological information of an active nematic into chemical signals. We show that a curvature-dependent reaction dipole is sufficient for creating a system that dynamically senses topology by producing a scalar order parameter possessing local extrema coinciding with $\pm\frac{1}{2}$ defects. We consider two possible physical origins of such dipoles: (i) curved molecules that preferentially bind to nematic regions matching their curvature and (ii) nematic molecules that become reaction dipoles when deformed. We demonstrate the behavior of this system for stationary defects and in the presence of hydrodynamic flows as seen in active nematics. The model can help generate testable hypotheses for biological phenomena and motivate the creation of bioinspired materials that dynamically couple nematic structure with biochemistry

Self-organized dynamics and the transition to turbulence of confined active nematics

We study how confinement transforms the chaotic dynamics of bulk microtubule-based active nematics into regular spatiotemporal patterns. For weak confinements, multiple continuously nucleating and annihilating topological defects self-organize into persistent circular flows of either handedness. Increasing confinement strength leads to the emergence of distinct dynamics, in which the slow periodic nucleation of topological defects at the boundary is superimposed onto a fast procession of a pair of defects. A defect pair migrates towards the confinement core over multiple rotation cycles, while the associated nematic director field evolves from a distinct double spiral towards a nearly circularly symmetric configuration. The collapse of the defect orbits is punctuated by another boundary-localized nucleation event, that sets up long-term doubly-periodic dynamics. Comparing experimental data to a theoretical model of an active nematic, reveals that theory captures the fast procession of a pair of $+\frac{1}{2}$ defects, but not the slow spiral transformation nor the periodic nucleation of defect pairs. Theory also fails to predict the emergence of circular flows in the weak confinement regime. The developed confinement methods are generalized to more complex geometries, providing a robust microfluidic platform for rationally engineering two-dimensional autonomous flows

Optimal Control of Active Nematics

In this work we present the first systematic framework to sculpt active nematics systems, using optimal control theory and a hydrodynamic model of active nematics. We demonstrate the use of two different control fields, (1) applied vorticity and (2) activity strength, to shape the dynamics of an extensile active nematic that is confined to a disk. In the absence of control inputs, the system exhibits two attractors, clockwise and counterclockwise circulating states characterized by two co-rotating topological $+\frac{1}{2}$ defects. We specifically seek spatiotemporal inputs that switch the system from one attractor to the other; we also examine phase-shifting perturbations. We identify control inputs by optimizing a penalty functional with three contributions: total control effort, spatial gradients in the control, and deviations from the desired trajectory. This work demonstrates that optimal control theory can be used to calculate non-trivial inputs capable of restructuring active nematics in a manner that is economical, smooth, and rapid, and therefore will serve as a guide to experimental efforts to control active matter

From Disks to Channels: Dynamics of Active Nematics Confined to an Annulus

Confinement can be used to systematically tame turbulent dynamics occurring in active fluids. Although periodic channels are the simplest geometries to study confinement numerically, the corresponding experimental realizations require closed racetracks. Here, we computationally study 2D active nematics confined to such a geometry -- an annulus. By systematically varying the annulus inner radius and channel width, we bridge the behaviors observed in the previously studied asymptotic limits of the annulus geometry: a disk and an infinite channel. We identify new steady-state behaviors, which reveal the influence of boundary curvature and its interplay with confinement. We also show that, below a threshold inner radius, the dynamics are insensitive to topological constraints imposed by boundary conditions. We explain this insensitivity through a simple scaling analysis. Our work sheds further light on design principles for using confinement to control the dynamics of active nematics

Controlling nanowire growth through electric field-induced deformation of the catalyst droplet.

Semiconductor nanowires with precisely controlled structure, and hence well-defined electronic and optical properties, can be grown by self-assembly using the vapour-liquid-solid process. The structure and chemical composition of the growing nanowire is typically determined by global parameters such as source gas pressure, gas composition and growth temperature. Here we describe a more local approach to the control of nanowire structure. We apply an electric field during growth to control nanowire diameter and growth direction. Growth experiments carried out while imaging within an in situ transmission electron microscope show that the electric field modifies growth by changing the shape, position and contact angle of the catalytic droplet. This droplet engineering can be used to modify nanowires into three dimensional structures, relevant to a range of applications, and also to measure the droplet surface tension, important for quantitative development of strategies to control nanowire growth.European Research Council (Grant ID: 279342)This is the final version of the article. It first appeared from Nature Publishing Group via http://dx.doi.org/10.1038/ncomms1227

Making a Difference Matters: Impact Unlocks the Emotional Benefits of Prosocial Spending

When does giving lead to happiness? Here, we present two studies demonstrating that the emotional benefits of spending money on others (prosocial spending) are unleashed when givers are aware of their positive impact. In Study 1, an experiment using real charitable appeals, giving more money to charity led to higher levels of happiness only when participants gave to causes that explained how these funds are used to make a difference in the life of a recipient. In Study 2, participants were asked to reflect upon a time they spent money on themselves or on others in a way that either had a positive impact or had no impact. Participants who recalled a time they spent on others that had a positive impact were happiest. Together, these results suggest that highlighting the impact of prosocial spending can increase the emotional rewards of giving