arXiv subjects

Alexander M. Leshansky

Publications and source records attributed to Alexander M. Leshansky.

10 recordsLinked to original sources

arXiv2025

Weak thermal fluctuations impede steering of chiral magnetic nanobots

Rotating magnetic field is an efficient method of actuation of synthetic colloids in liquids. In this Letter we theoretically study the effect of the thermal noise on torque-driven steering of magnetic nanohelices. Using a combination of numerical and analytical methods, we demonstrate that surprisingly a weak thermal noise can substantially disrupt the orientation and rotation of the nanohelix, severely impeding its propulsion. The results of Langevin simulations are in excellent agreement with the numerical solution of the Fokker-Planck equation and the analytical effective field approximation.

cond-mat.soft↗

arXiv2024

Slow linear shear flow past discrete particles adhered to a plane wall

Linear shear flow bounded by a plane wall is an idealization that occurs in microfluidic devices and many other applications. Perfect plane approximation neglects surface irregularities and discrete particles adsorbed at the surface. Here we study the disturbance to the linear shear flow due to the particle(s) rigidly attached to the surface. We first revisit the exact solution of O'Neill for a spherical particle in contact with an infinite plane boundary. While the original paper contains multiple typos and provides very few details of the derivation, we present detailed solution accompanied by an alternative and simpler derivation of the viscous force and the torque exerted on the particle. We further study the universal far-field behavior of the flow due to an arbitrary particle adhered to the surface, and demonstrate that it is controlled by the stress moment of magnitude depending on particle's volume and shape. Using the revised O'Neill solution, we compute the stress moment for a spherical particle. Using the far-field asymptotic form of the flow we estimate the net flow due to uniform and sparse layer of discrete adsorbates by superposition and demonstrate that it does not decay away from the plane.

physics.flu-dyn↗

arXiv2024

Quartz Crystal Microbalance frequency response to discrete adsorbates in liquids

Quartz Crystal Microbalance with Dissipation monitoring (QCM-D) has become a major tool in the analysis of adsorption of nanometric objects, such as proteins, viruses, liposomes and inorganic particles from the solution. While in vacuum extremely accurate mass measurements are possible, in a liquid phase the quantitative analysis is intricate due to the complex interplay of hydrodynamic and adhesion forces, varying with the physicochemical properties of adsorbent and the quartz resonator surfaces. In the present paper we dissect the role of hydrodynamics for the analytically tractable scenario of a stiff contact, whereas the adsorbed particles oscillate with the resonator as a whole without rotation. Under the assumption of the low surface coverage, we theoretically study the excess shear force exerted on the resonator due to presence of a single adsorbed particle. The excess shear force has two contributions: (i) the fluid-mediated force due to flow disturbance created by the particle and (ii) the viscous force exerted on the particle by the fluid and transmitted to the resonator via contact. We found that for small adsorbates, there is mutual cancellation of the above contributions to the excess shear force at the leading order approximation, reducing the overall effect of the hydrodynamics to the order-of-magnitude of the inertial force. However, accurate numerical solution shows that for small particles the viscous force dominates over the inertia force, rendering the standard Sauerbrey model inapplicable. These findings indicate that the accurate account of hydrodynamics in the analysis of QCM-D response is critical. The resulting dimensionless frequency and dissipation shifts and the corresponding acoustic ratio computed numerically, showing a fair agreement with previously published experimental results at low oscillation frequencies.

cond-mat.soft↗

arXiv2022

Excess shear force exerted on oscillating plate due to a nearby particle

In the present paper we theoretically study the shear force exerted on an infinite horizontal plane undergoing fast lateral oscillations in presence of a rigid particle suspended in the viscous liquid above the plate. The study is largely motivated by Quartz Crystal Microbalance (QCM-D) technique which relies on analyzing response (complex impedance) of fast oscillating (in MHz range) quartz crystal disk in the liquid medium due to small substances adsorbed at its surface. In fact, small substances suspended in the liquid medium in the vicinity of the oscillating crystal may also contribute to impedance, as they modify the local shear force the suspending liquid exerts on the quartz crystal. For a dilute suspension the contributions of individual particles are additive and, therefore, our analysis is restricted to the excess shear force due a single spherical particle located at arbitrary distance above the plane. Three distinct cases are considered: (i) limiting case of high solid inertia, whereas the heavy particle can be considered as stationary; (ii) a freely suspended particle of arbitrary mass, undergoing fluid-mediated time-periodic rotation and translation and (iii) an adsorbed particle moving with the plate as a whole without rotation. For small-amplitude plane oscillations the unsteady Stokes flow equations apply. We construct the series solution of these equations using the method of reflections, whereas its terms are written explicitly. Due to the exponential decay of the flow away from the oscillating plate, the truncated series containing only few low-order terms shows an excellent agreement with the rigorous numerical results for a wide range of particle sizes and separation distances. The present results support the notion that the hydrodynamic contribution of the suspended small substances to the measured impedance is non-negligible or even dominant.

physics.flu-dyn↗

arXiv2019

Unidirectional propulsion of planar magnetic nanomachines

Steering of magnetic nano-/microhelices by a rotating magnetic field is considered as a promising technique for controlled navigation of tiny objects through viscous fluidic environments. It has been recently demonstrated that simple geometrically achiral planar structures can also be steered efficiently. Such planar propellers are interesting for practical reasons, as they can be mass-fabricated using standard micro/nanolithography techniques. While planar magnetic structures are prone to in-plane magnetization, under the effect of an in-plane rotating magnetic field, they exhibit, at most, propulsion due to spontaneous symmetry breaking, i.e., they can propel either parallel or anti-parallel to the rotation axis of the field depending on their initial orientation. Here we demonstrate that actuation by a conically rotating magnetic field (i.e., superposition of in-plane rotating field and constant field orthogonal to it) can yield efficient unidirectional propulsion of planar and magnetized in-plane structures. In particular, we found that a highly symmetrical V-shape magnetized along its symmetry axis which exhibits no net propulsion in in-plane rotating field, exhibits unidirectional in-sync propulsion with a constant (frequency-independent) velocity when actuated by the conically rotating field.

physics.flu-dyn↗

arXiv2019

The role of symmetry in driven propulsion at low Reynolds number

We theoretically and experimentally investigate low-Reynolds-number propulsion of geometrically achiral planar objects that possess a dipole moment and that are driven by a rotating magnetic field. Symmetry considerations (involving parity, $\widehat{P}$, and charge conjugation, $\widehat{C}$) establish correspondence between propulsive states depending on orientation of the dipolar moment. Although basic symmetry arguments do not forbid individual symmetric objects to efficiently propel due to spontaneous symmetry breaking, they suggest that the average ensemble velocity vanishes. Some additional arguments show, however, that highly symmetrical ($\widehat{P}$-even) objects exhibit no net propulsion while individual less symmetrical ($\widehat{C}\widehat{P}$-even) propellers do propel. Particular magnetization orientation, rendering the shape $\widehat{C}\widehat{P}$-odd, yields unidirectional motion typically associated with chiral structures, such as helices. If instead of a structure with a permanent dipole we consider a polarizable object, some of the arguments have to be modified. For instance, we demonstrate a truly achiral ($\widehat{P}$- and $\widehat{C}\widehat{P}$-even) planar shape with an induced electric dipole that can propel by electro-rotation. We thereby show that chirality is not essential for propulsion due to rotation-translation coupling at low Reynolds number.

physics.flu-dyn↗

arXiv2014

Dynamics and polarization of superparamagnetic chiral nanomotors in a rotating magnetic field

Externally powered magnetic nanomotors are of particular interest due to the potential use for \emph{in vivo} biomedical applications. Here we develop a theory for dynamics and polarization of recently fabricated superparamagnetic chiral nanomotors powered by a rotating magnetic field. We study in detail various experimentally observed regimes of the nanomotor dynamic orientation and propulsion and establish the dependence of these properties on polarization and geometry of the propellers. Based on the proposed theory we introduce a novel "steerability" parameter $γ$ that can be used to rank polarizable nanomotors by their propulsive capability. The theoretical predictions of the nanomotor orientation and propulsion speed are in excellent agreement with available experimental results. Lastly, we apply slender-body approximation to estimate polarization anisotropy and orientation of the easy-axis of superparamagnetic helical propellers.

cond-mat.soft↗

arXiv2013

The chiral magnetic nanomotors

Propulsion of the chiral magnetic nanomotors powered by a rotating magnetic field is in the focus of the modern biomedical applications. This technology relies on strong interaction of dynamic and magnetic degrees of freedom of the system. Here we study in detail various experimentally observed regimes of the helical nanomotor orientation and propulsion depending on the actuation frequency, and establish the relation of these two properties with remanent magnetization and geometry of the helical nanomotors. The theoretical predictions for the transition between the regimes and nanomotor orientation and propulsion speed are in excellent agreement with available experimental data. The proposed theory offers a few simple guidelines towards the optimal design of the magnetic nanomotors. In particular, efficient nanomotors should be fabricated of hard magnetics, e.g., cobalt, magnetized transversally and have the geometry of a normal helix with a helical angle of 35-45 degrees.

cond-mat.soft↗

arXiv2008

How efficient is towing a cargo by a micro-swimmer?

We study the properties of arbitrary micro-swimmers towing a passive load through a viscous liquid. The simple close-form expression for the dragging efficiency of a general micro-swimmer dragging a distant load is found, and the leading order approximation for finite mutual separation is derived. We show that, while swimmer can be arbitrarily efficient, dragging efficiency is always bounded from above. It is also demonstrated, that opposite to Purcell's assumption, the hydrodynamic coupling can ''help" the swimmer to drag the load. We support our conclusions by rigorous numerical calculations for the "necklace-shaped" swimmer, towing a spherical cargo positioned at a finite distance.

physics.flu-dyn↗

arXiv2007

A frictionless microswimmer

We investigate the self-locomotion of an elongated microswimmer by virtue of the unidirectional tangential surface treadmilling. We show that the propulsion could be almost frictionless, as the microswimmer is propelled forward with the speed of the backward surface motion, i.e. it moves throughout an almost quiescent fluid. We investigate this swimming technique using the special spheroidal coordinates and also find an explicit closed-form optimal solution for a two-dimensional treadmiler via complex-variable techniques.

physics.flu-dyn↗