Optimal feeding and swimming gaits of biflagellated organisms

Locomotion is widely observed in life at micrometric scales and is exhibited by many eukaryotic unicellular organisms. Motility of such organisms can be achieved through periodic deformations of a tail-like projection called the eukaryotic flagellum. Although the mechanism allowing the flagellum to deform is largely understood, questions related to the functional significance of the observed beating patterns remain unresolved. Here, we focus our attention on the stroke patterns of biflagellated phytoplanktons resembling the green alga Chlamydomonas. Such organisms have been widely observed to beat their flagella in two different ways - a breast-stroke and an undulatory stroke-both of which are prototypical of general beating patterns observed in eukaryotes. We develop a general optimization procedure to determine the existence of optimal swimming gaits and investigate their functional significance with respect to locomotion and nutrient uptake. Both the undulatory and the breaststroke represent local optima for efficient swimming. With respect to the generation of feeding currents, we found the breaststroke to be optimal and to enhance nutrient uptake significantly, particularly when the organism is immersed in a gradient of nutrients. Keywords: optimization; stroke kinematics; low Reynolds number; efficiencyNational Science Foundation (U.S.) (Grant CCF-0323672)National Science Foundation (U.S.) (Grant CTS-0624830

Structure evolution in electrorheological fluids flowing through microchannels

Enhanced knowledge of the transient behavior and characteristics of electrorheological (ER) fluids subject to time dependent electric fields offers the potential to advance the design of fast actuated hydraulic devices. In this study, the dynamic response of electrorheological fluid flows in rectilinear microchannels was investigated experimentally. Using high-speed microscopic imaging, the evolution of particle aggregates in ER fluids subjected to temporally stepwise electric fields was visualized. Nonuniform growth of the particle structures in the channel was observed and correlated to field strength and flow rate. Two competing time scales for structure growth were identified. Guided by experimental observations, we developed a phenomenological model to quantitatively describe and predict the evolution of microscale structures and the concomitant induced pressure gradient.United States. Defense Advanced Research Projects Agency. Maximum Mobility and Manipulation (M3) Progra

Yield Hardening of Electrorheological Fluids in Channel Flow

Electrorheological fluids offer potential for developing rapidly actuated hydraulic devices where shear forces or pressure-driven flow are present. In this study, the Bingham yield stress of electrorheological fluids with different particle volume fractions is investigated experimentally in wall-driven and pressure-driven flow modes using measurements in a parallel-plate rheometer and a microfluidic channel, respectively. A modified Krieger-Dougherty model can be used to describe the effects of the particle volume fraction on the yield stress and is in good agreement with the viscometric data. However, significant yield hardening in pressure-driven channel flow is observed and attributed to an increase and eventual saturation of the particle volume fraction in the channel. A phenomenological physical model linking the densification and consequent microstructure to the ratio of the particle aggregation time scale compared to the convective time scale is presented and used to predict the enhancement in yield stress in channel flow, enabling us to reconcile discrepancies in the literature between wall-driven and pressure-driven flows

Marangoni convection in droplets on superhydrophobic surfaces

We consider a small droplet of water sitting on top of a heated superhydrophobic surface. A toroidal convection pattern develops in which fluid is observed to rise along the surface of the spherical droplet and to accelerate downwards in the interior towards the liquid/solid contact point. The internal dynamics arise due to the presence of a vertical temperature gradient; this leads to a gradient in surface tension which in turn drives fluid away from the contact point along the interface. We develop a solution to this thermocapillary-driven Marangoni flow analytically in terms of streamfunctions. Quantitative comparisons between analytical and experimental results, as well as effective heat transfer coefficients, are presented.National Science Foundation (U.S.) (CTS-045609)National Science Foundation (U.S.) (CCF-0323672

The Design and Testing of RoboClam: A Machine Used to Investigate and Optimize Razor Clam-Inspired Burrowing Mechanisms for Engineering Applications

Razor clams (Ensis directus) are one of nature’s most adept burrowing organisms, able to dig to 70cm at nearly 1cm/s using only 0.21J/cm. Ensis reduces burrowing drag by using motions of its shell to fluidize a thin layer of substrate around its body. Although these shell motions have an energetic cost, moving through fluidized rather than packed soil results in exponentially lower overall energy consumption. This paper describes the design and testing of RoboClam, a device that mimics Ensis digging methods to understand the limits of razor clam-inspired burrowing, how they scale for different environments and conditions, and how they can be transferred into engineering applications. Using a genetic optimization solver, we found that RoboClam’s most efficient digging motion mimicked Ensis shell kinematics and yielded a power law relationship between digging energy and depth of n = 1.17, very close to the ideal value of n = 1. Pushing through static soil has a theoretical energy-depth power law of n = 2, which means that Ensis-inspired burrowing motions can provide exponentially higher energy efficiency and nearly depth-independent drag resistance.Battelle Memorial InstituteBluefin RoboticsChevron Corporatio

Two-Dimensional Self-Assembly in Diblock Copolymers

Diblock copolymers confined to a two-dimensional surface may produce uniform features of macromolecular dimensions (∼10–100  nm). We present a mathematical model for nanoscale pattern formation in such polymers that captures the dynamic evolution of a solution of poly(styrene)-b-poly(ethylene oxide), PS-b-PEO, in solvent at an air-water interface. The model has no fitting parameters and incorporates the effects of surface tension gradients, entanglement or vitrification, and diffusion. The resultant morphologies are quantitatively compared with experimental data

Razor clam to RoboClam: burrowing drag reduction mechanisms and their robotic adaptation

Estimates based on the strength, size, and shape of the Atlantic razor clam (Ensis directus) indicate that the animal's burrow depth should be physically limited to a few centimeters; yet razor clams can dig as deep as 70 cm. By measuring soil deformations around burrowing E. directus, we have found the animal reduces drag by contracting its valves to initially fail, and then fluidize, the surrounding substrate. The characteristic contraction time to achieve fluidization can be calculated directly from soil properties. The geometry of the fluidized zone is dictated by two commonly-measured geotechnical parameters: coefficient of lateral earth pressure and friction angle. Calculations using full ranges for both parameters indicate that the fluidized zone is a local effect, occurring between 1–5 body radii away from the animal. The energy associated with motion through fluidized substrate—characterized by a depth-independent density and viscosity—scales linearly with depth. In contrast, moving through static soil requires energy that scales with depth squared. For E. directus, this translates to a 10X reduction in the energy required to reach observed burrow depths. For engineers, localized fluidization offers a mechanically simple and purely kinematic method to dramatically reduce energy costs associated with digging. This concept is demonstrated with RoboClam, an E. directus-inspired robot. Using a genetic algorithm to find optimal digging kinematics, RoboClam has achieved localized fluidization burrowing performance comparable to that of the animal, with a linear energy-depth relationship, in both idealized granular glass beads and E. directus' native cohesive mudflat habitat.Battelle Memorial InstituteBluefin RoboticsChevron Corporatio

Multi-Substrate Burrowing Performance and Constitutive Modeling of RoboClam: A Biomimetic Robot Based on Razor Clams

The Atlantic razor clam (Ensis directus) reduces burrowing drag by using motions of its shell to fluidize a thin layer of substrate around its body. We have developed RoboClam, a robot that digs using the same mechanisms as Ensis, to explore how localized fluidization burrowing can be extended to engineering applications. In this work we present burrowing performance results of RoboClam in two distinctly different substrates: ideally granular 1mm soda lime glass beads and cohesive ocean mudflat soil. Using a genetic algorithm to optimize RoboClam’s kinematics, the machine was able to burrow in both substrates with a power law relationship between digging energy and depth of n = 1.17. Pushing through static soil has a theoretical energy-depth power law of n = 2, which means that Ensis-inspired burrowing motions can provide exponentially higher energy efficiency. We propose a theoretical constitutive model that describes how a fluidized region should form around a contracting body in virtually any type of saturated soil. The model predicts fluidization to be a relatively local effect, extending only two to three characteristic lengths away from the body, depending on friction angle and coefficient of lateral earth pressure, two commonly measured soil parameters.Battelle Memorial InstituteBluefin RoboticsChevron Corporatio

Design and analysis of a robust, low-cost, highly articulated manipulator enabled by jamming of granular media

Hyper-redundant manipulators can be fragile, expensive, and limited in their flexibility due to the distributed and bulky actuators that are typically used to achieve the precision and degrees of freedom (DOFs) required. Here, a manipulator is proposed that is robust, high-force, low-cost, and highly articulated without employing traditional actuators mounted at the manipulator joints. Rather, local tunable stiffness is coupled with off-board spooler motors and tension cables to achieve complex manipulator configurations. Tunable stiffness is achieved by reversible jamming of granular media, which-by applying a vacuum to enclosed grains-causes the grains to transition between solid-like states and liquid-like ones. Experimental studies were conducted to identify grains with high strength-to-weight performance. A prototype of the manipulator is presented with performance analysis, with emphasis on speed, strength, and articulation. This novel design for a manipulator-and use of jamming for robotic applications in general-could greatly benefit applications such as human-safe robotics and systems in which robots need to exhibit high flexibility to conform to their environments.United States. Defense Advanced Research Projects Agency (Maximum Mobility and Manipulation Program