9 research outputs found
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Ciliary propulsion through non-uniform flows
The classical paper by Lighthill (Commun. Pure Appl. Maths, vol. 109, 1952, p. 118) on the propulsion of ciliated microorganisms has become the reference against which many modern studies on swimming in low Reynolds number are compared. However, Lighthill’s study was limited to propulsion in a uniform flow, whereas several biologically relevant microorganisms experience non-uniform flows. Here we propose a benchmark for ciliary propulsion in paraboloidal flows. We first consider the axisymmetric problem, with the microorganisms on the centreline of the background flow, and derive exact analytical solutions for the flow field. Our results reveal flow features, swimming characteristics and performance metrics markedly different from those generated in a uniform flow. In particular, the background paraboloidal flow introduces a Stokes quadrupole singularity at the leading-order flow field, generating vortices. Moreover, we determine the necessary conditions on the strength of the background flow for optimal power dissipation and swimming efficiency. We then consider the more general case of a microorganism off the centreline of the background flow. In this case, the squirmer experiences a paraboloidal, linear shear and uniform flows due to its position relative to the flow’s centreline. Our findings show that while the linear shear flow does not affect the translational and rotational velocities of the squirmer, it does influence the velocity field and, therefore, the power dissipation
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The effect of particle geometry on squirming in a heterogeneous medium
Biological microorganisms and artificial micro-swimmers often locomote in heterogeneous viscous environments consisting of networks of obstacles embedded into viscous fluid media. In this work, we use the squirmer model and present a numerical investigation of the effects of shape on swimming in a heterogeneous medium. Specifically, we analyse the microorganism’s propulsion speed as well as its energetic cost and swimming efficiency. The analysis allows us to probe the general characteristics of swimming in a heterogeneous viscous environment in comparison with the case of a purely viscous fluid. We found that a spheroidal microorganism always propels faster, expends less energy and is more efficient than a spherical microorganism in either a homogeneous fluid or a heterogeneous medium. Moreover, we determined that above a critical eccentricity, a spheroidal microorganism in a heterogeneous medium can swim faster than a spherical microorganism in a homogeneous fluid. Based on an analysis of the forces acting on the squirmer, we offer an explanation for the decrease in the squirmer’s speed observed in heterogeneous media compared with homogeneous fluids
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Influence of heterogeneity or shape on the locomotion of a caged squirmer
The development of novel drug delivery systems, which are revolutionizing modern medicine, is benefiting from studies on microorganisms’ swimming. In this paper we consider a model microorganism (a squirmer) enclosed in a viscous droplet to investigate the effects of medium heterogeneity or geometry on the propulsion speed of the caged squirmer. We first consider the squirmer and droplet to be spherical (no shape effects) and derive exact solutions for the equations governing the problem. For a squirmer with purely tangential surface velocity, the squirmer is always able to move inside the droplet (even when the latter ceases to move as a result of large fluid resistance of the heterogeneous medium). Adding radial modes to the surface velocity, we establish a new condition for the existence of a co-swimming speed (where squirmer and droplet move at the same speed). Next, to probe the effects of geometry on propulsion, we consider the squirmer and droplet to be in Newtonian fluids. For a squirmer with purely tangential surface velocity, numerical simulations reveal a strong dependence of the squirmer’s speed on shapes, the size of the droplet and the viscosity contrast. We found that the squirmer speed is largest when the droplet size and squirmer’s eccentricity are small, and the viscosity contrast is large. For co-swimming, our results reveal a complex, non-trivial interplay between the various factors that combine to yield the squirmer’s propulsion speed. Taken together, our study provides several considerations for the efficient design of future drug delivery systems.U.A. and H.N. gratefully acknowledge funding support from the National Science Foundation, grant no. 2211633. H.N. also acknowledges support from a Jess and Mildred Fisher Endowed Professor of Mathematics from the Fisher College of Science and Mathematics at Towson Universit
Electrohydrodynamic phenomena
This work is a review article focused on exploring the interactions between external and induced electric fields and fluid motion, in the presence of embedded charges. Such interactions are generally termed electrohydrodynamics (EHD), which encompasses a vast range of flows stemming from multiscale physical effects. In this review article we shall mainly emphasize on two mechanisms of particular interest to fluid dynamists and engineers, namely electrokinetic flows and the leaky dielectric model. We shed light on the underlying physics behind the above mentioned phenomena and subsequently demonstrate the presence of a common underpinning pattern which governs any general electrohydrodynamic motion. Hence we go on to show that the seemingly unrelated fields of electrokinetics and the leaky dielectric models are indeed closely related to each other through the much celebrated Maxwell stresses, which have long been known as stresses caused in fluids in presence of electric and magnetic fields. Interactions between Maxwell Stresses and charges (for instance, in the form of ions) present in the fluid generates a body force on the same and eventually leads to flow actuation. We show that the manifestation of the Maxwell stresses itself depends on the charge densities, which in turn is dictated by the underlying motion of the fluid. We demonstrate how such inter-related dynamics may give rise intricately coupled and non-linear system of equations governing the dynamical state of the system. This article is mainly divided into two parts. First, we explore the realms of electrokinetics, wherein the formation and the structure of the so-called electrical double layer (EDL) is delineated. Subsequently, we review EDL’s relevance to electroosmosis and streaming potential with the key being the presence and absence of an applied pressure gradient. We thereafter focus on the leaky dielectric model, wherein the fundamental governing equations and its main difference with electrokinetics are described. We limit our attentions to the leaky dielectric motion around droplets and flat surfaces and subsequent interface deformation. To this end, through a rigorous review of a number of previous articles, we establish that the interface shapes can be finely tailored to achieve the desired geometrical characteristics by tuning the fluid properties. We further discuss previous studies, which have shown migration of droplets in the presence of strong electric fields. Finally, we describe the effects of external agents such as surface impurities on leaky dielectric motion and attempt to establish a qualitative connection between the leaky dielectric model and EDLs. We finish off with some pointers for further research activities and open questions in this field.by Aditya Bandopadhyay and Uddipta Ghos