An official website of the United States government
A squirmer enclosed in a droplet represents a minimal model for some drug delivery systems. In the case of a spherical squirmer swimming with a spherical cage in a Newtonian fluid [Reigh et al., “Swimming with a cage: Low-Reynolds-number locomotion inside a droplet,” Soft Matter 13, 3161 (2017)], it was found that the squirmer and droplet always propelled in the same direction albeit at different speeds. We expand the model to include particles' shape and medium's heterogeneity, two biologically relevant features. Our results reveal a novel behavior: a configuration that consists of a spherical squirmer and a spheroidal droplet in highly heterogeneous media yields a backward motion of the droplet.
more »
« less
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.
more »
« less
- Award ID(s):
- 2211633
- PAR ID:
- 10431384
- Date Published:
- Journal Name:
- Journal of Fluid Mechanics
- Volume:
- 967
- ISSN:
- 0022-1120
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
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.more » « less
-
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.more » « less
-
null (Ed.)We investigate the self-propulsion of an inertial swimmer in a linearly density stratified fluid using the archetypal squirmer model which self-propels by generating tangential surface waves. We quantify swimming speeds for pushers (propelled from the rear) and pullers (propelled from the front) by direct numerical solution of the Navier–Stokes equations using the finite volume method for solving the fluid flow and the distributed Lagrange multiplier method for modelling the swimmer. The simulations are performed for Reynolds numbers ( $Re$ ) between 5 and 100 and Froude numbers ( $Fr$ ) between 1 and 10. We find that increasing the fluid stratification strength reduces the swimming speeds of both pushers and pullers relative to their speeds in a homogeneous fluid. The increase in the buoyancy force experienced by these squirmers due to the trapping of lighter fluid in their respective recirculatory regions as they move in the heavier fluid is one of the reasons for this reduction. With increasing the stratification, the isopycnals tend to deform less, which offers resistance to the flow generated by the squirmers around them to propel themselves. This resistance increases with stratification, thus, reducing the squirmer swimming velocity. Stratification also stabilizes the flow around a puller keeping it axisymmetric even at high $Re$ , thus, leading to stability which is otherwise absent in a homogeneous fluid for $Re$ greater than $O(10)$ . On the contrary, a strong stratification leads to instability in the motion of pushers by making the flow around them unsteady and three-dimensional, which is otherwise steady and axisymmetric in a homogeneous fluid. A pusher is a more efficient swimmer than a puller owing to efficient convection of vorticity along its surface and downstream. Data for the mixing efficiency generated by individual squirmers explain the trends observed in the mixing produced by a swarm of squirmers.more » « less
-
The hydrodynamic interactions between a sedimenting microswimmer and a solid wall have ubiquitous biological and technological applications. A plethora of gravity-induced swimming dynamics near a planar no-slip wall provide a platform for designing artificial microswimmers that can generate directed propulsion through their translation–rotation coupling near a wall. In this work, we provide exact solutions for a squirmer (a model swimmer of spherical shape with a prescribed slip velocity) facing either towards or away from a planar wall perpendicular to gravity. These exact solutions are used to validate a numerical code based on the boundary integral method with an adaptive mesh for distances from the wall down to 0.1 % of the squirmer radius. This boundary integral code is then used to investigate the rich gravity-induced dynamics near a wall, mapping out the detailed bifurcation structures of the swimming dynamics in terms of orientation and distance to the wall. Simulation results show that a squirmer may traverse the wall, move to a fixed point at a given height with a fixed orientation in a monotonic way or in an oscillatory fashion, or oscillate in a limit cycle in the presence of wall repulsion.more » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1017/jfm.2023.450
