Engineering topics
Aranson, I S
Publications and source records attributed to Aranson, I S.
Effective viscosity of bacterial suspensions: a three-dimensional PDE model with stochastic torque.
We present a PDE model for dilute suspensions of swimming bacteria in a three-dimensional Stokesian fluid. This model is used to calculate the statistically-stationary bulk deviatoric stress and effective viscosity of the suspension from the microscopic details of the interaction of an elongated body with the background flow. A bacterium is modeled as an impenetrable prolate spheroid with self-propulsion provided by a point force, which appears in the model as an inhomogeneous delta function in the PDE. The bacterium is also subject to a stochastic torque in order to model tumbling (random reorientation). Due to a bacterium's asymmetric shape, interactions with prescribed generic planar background flows, such as a pure straining or planar shear flow, cause the bacterium to preferentially align in certain directions. Due to the stochastic torque, the steady-state distribution of orientations is unique for a given background flow. Under this distribution of orientations, self-propulsion produces a reduction in the effective viscosity. For sufficiently weak background flows, the effect of self-propulsion on the effective viscosity dominates all other contributions, leading to an effective viscosity of the suspension that is lower than the viscosity of the ambient fluid. This is in qualitative agreement with recent experiments on suspensions of Bacillus subtilis.
Designing mechano-responsive microcapsules that undergo self-propelled motion.
Biological cells are capable of sensing mechanical cues and responding to these signals by undergoing morphological changes and directed motion. A significant challenge is creating cell-like objects that can translate mechanical stimuli into analogous behavior. Herein, we use computational modeling to design a simple mechanosensitive 'cell' that responds to mechanical deformation through a shape change that allows it to undergo self-sustained, directed movement. Our cellular object is formed from a nanoparticle-filled microcapsule that is located on an adhesive substrate in solution. In response to a locally applied force, the deformed capsule releases nanoparticles that bind to the surface and dynamically create adhesion gradients. Due to the self-generated gradients, the capsule moves autonomously from regions of less adhesion to greater adhesion. During the capsule's motion, new nanoparticles are released that both sustain and propagate the adhesion gradients and thus, the capsule sustains autonomous movement along its path (until it is depleted of nanoparticles). The self-sustained motion occurs only if the permeability of the capsule's shell depends on mechanical deformation. We isolate critical parameters that control the dynamic behavior of this mechano-responsive capsule. Our findings can facilitate the fabrication of devices that are powered by the autonomous movement of microscopic synthetic cells. Additionally, the capsules could serve as sensors for mechanical strain, indicating the presence of strain fields by their spontaneous motion and release of nanoparticles; the latter behavior could be exploited in the fabrication of self-healing materials.
Magnetic manipulation of self-assembled colloidal asters.
Self-assembled materials must actively consume energy and remain out of equilibrium to support structural complexity and functional diversity. Here we show that a magnetic colloidal suspension confined at the interface between two immiscible liquids and energized by an alternating magnetic field dynamically self-assembles into localized asters and arrays of asters, which exhibit locomotion and shape change. By controlling a small external magnetic field applied parallel to the interface, we show that asters can capture, transport, and position target microparticles. The ability to manipulate colloidal structures is crucial for the further development of self-assembled microrobots
Viscosity of bacterial suspensions: Hydrodynamic interactions and self-induced noise
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Motor-mediated microtubule self-organization in dilute and semi-dilute filament solutions.
We study molecular motor-induced microtubule self-organization in dilute and semi-dilute filament solutions. In the dilute case, we use a probabilistic model of microtubule interaction via molecular motors to investigate microtubule bundle dynamics. Microtubules are modeled as polar rods interacting through fully inelastic, binary collisions. Our model indicates that initially disordered systems of interacting rods exhibit an orientational instability resulting in spontaneous ordering. We study the existence and dynamic interaction of microtubule bundles analytically and numerically. Our results reveal a long term attraction and coalescing of bundles indicating a clear coarsening in the system; microtubule bundles concentrate into fewer orientations on a slow logarithmic time scale. In semi-dilute filament solutions, multiple motors can bind a filament to several others and, for a critical motor density, induce a transition to an ordered phase with a nonzero mean orientation. Motors attach to a pair of filaments and walk along the pair bringing them into closer alignment. We develop a spatially homogenous, mean-field theory that explicitly accounts for a force-dependent detachment rate of motors, which in turn affects the mean and the fluctuations of the net force acting on a filament. We show that the transition to the oriented state can be both continuous and discontinuous when the force-dependent detachment of motors is important.
Model for self-polarization and motility of keratocyte fragments.
Computational modeling of cell motility on substrates is a formidable challenge; regulatory pathways are intertwined and forces that influence cell motion are not fully quantified. Additional challenges arise from the need to describe a moving deformable cell boundary. Here, we present a simple mathematical model coupling cell shape dynamics, treated by the phase-field approach, to a vector field describing the mean orientation (polarization) of the actin filament network. The model successfully reproduces the primary phenomenology of cell motility: discontinuous onset of motion, diversity of cell shapes and shape oscillations. The results are in qualitative agreement with recent experiments on motility of keratocyte cells and cell fragments. The asymmetry of the shapes is captured to a large extent in this simple model, which may prove useful for the interpretation of experiments.
Model for dynamic self-assembled magnetic surface structures.
We propose a first-principles model for the dynamic self-assembly of magnetic structures at a water-air interface reported in earlier experiments. The model is based on the Navier-Stokes equation for liquids in shallow water approximation coupled to Newton equations for interacting magnetic particles suspended at a water-air interface. The model reproduces most of the observed phenomenology, including spontaneous formation of magnetic snakelike structures, generation of large-scale vortex flows, complex ferromagnetic-antiferromagnetic ordering of the snake, and self-propulsion of bead-snake hybrids.