skip to main content
US FlagAn official website of the United States government
dot gov icon
Official websites use .gov
A .gov website belongs to an official government organization in the United States.
https lock icon
Secure .gov websites use HTTPS
A lock ( lock ) or https:// means you've safely connected to the .gov website. Share sensitive information only on official, secure websites.

Explore Research Products in the PAR
It may take a few hours for recently added research products to appear in PAR search results.


Title: Dynamics and steady state of squirmer motion in liquid crystal
We analyze a nonlinear partial differential equation system describing the motion of a microswimmer in a nematic liquid crystal environment. For the microswimmer’s motility, the squirmer model is used in which self-propulsion enters the model through the slip velocity on the microswimmer’s surface. The liquid crystal is described using the well-established Beris–Edwards formulation. In previous computational studies, it was shown that the squirmer, regardless of its initial configuration, eventually orients itself either parallel or perpendicular to the preferred orientation dictated by the liquid crystal. Furthermore, the corresponding solution of the coupled nonlinear system converges to a steady state. In this work, we rigorously establish the existence of the steady state and also the finite-time existence for the time-dependent problem in a periodic domain. Finally, we will use a two-scale asymptotic expansion to derive a homogenized model for the collective swimming of squirmers as they reach their steady-state orientation and speed.  more » « less
Award ID(s):
2005262
PAR ID:
10498931
Author(s) / Creator(s):
; ; ;
Publisher / Repository:
Cambridge University Press
Date Published:
Journal Name:
European Journal of Applied Mathematics
Volume:
35
Issue:
2
ISSN:
0956-7925
Page Range / eLocation ID:
225 to 266
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. ; ; ; ; (, Journal of Physics: Condensed Matter)
    Abstract The dynamics of active smectic liquid crystals confined on a spherical surface is explored through an active phase field crystal model. Starting from an initially randomly perturbed isotropic phase, several types of topological defects are spontaneously formed, and then annihilate during a coarsening process until a steady state is achieved. The coarsening process is highly complex involving several scaling laws of defect densities as a function of time where different dynamical exponents can be identified. In general the exponent for the final stage towards the steady state is significantly larger than that in the passive and in the planar case, i.e. the coarsening is getting accelerated both by activity and by the topological and geometrical properties of the sphere. A defect type characteristic for this active system is a rotating spiral of evolving smectic layering lines. On a sphere this defect type also determines the steady state. Our results can in principle be confirmed by dense systems of synthetic or biological active particles. 
    more » « less
  2. ; ; ; (, Journal of Fluid Mechanics)
    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
  3. ; (, Gochemical Society)
    none (Ed.)
    An obstacle to developing a general mechanical framework for magma mush is the emergence and complexity of a crystal fabric. To illuminate the conditions that produce a crystal fabric we performed time-dependent numerical simulations using a Computational-Fluid-Dynamics and Discrete-Element-Method (CFD-DEM) model in three dimensions. The specific focus was on the role of shear strain in the creation of a preferential orientation of crystals in mush. CFD-DEM method allows for the simultaneous coupling and frictional interactions of melt and crystals undergoing shear strain. The crystal shapes are represented using spheroids (either oblate or prolate). Simulations consist in imposing a compression stress (pressure) and a simple shear to a dense suspension of crystals in a viscous liquid, and monitoring the evolution of the orientation and strength of the shape fabrics. We ran a series of simulations by varying the size and aspect ratio of the particles. We considered samples in which all the solids have the same volume and shape, and cases including size and aspect ratio distributions. Results show that the strength of the shape fabric and the angle between the crystal preferential orientation and the compression plane both increase with the shear strain up to steady state values, which are primarily controlled by the aspect ratio of the particles. The stronger the aspect ratio, the greater the magnitude of the preferential orientation and the lower its angle relative to the compression plane. When introducing a distribution in the size of the crystals, we observed a decrease in the strength of the shape fabric and an increase in the angle between the preferential orientation of the crystals and the compression plane compared with samples composed of crystals having the same shape and size. Similarly, the distribution in the aspect ratio further decreases the strength of the shape fabric and increases the angle between the preferential orientation of the solids and the compression plane. Finally, we employed an alternative approach to quantify the amount of foliation and lineation and show that the samples always display a stronger foliation than lineation, although the shear strain increases both the foliation and the lineation. 
    more » « less
  4. ; ; (, Journal of Fluid Mechanics)
    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
  5. ; ; (, Journal of Biological Systems)
    A within-human-host malaria parasite model, integrating key variables that influence parasite evolution-progression-advancement, under innate and adaptive immune responses, is analyzed. The implicit role of immunity on the steady state parasite loads and parasitemia reproduction number ([Formula: see text]), a threshold parameter measuring the parasite’s annexing ability of healthy red blood cells (HRBCs), eventually rendering a human infectious to mosquitoes, is investigated. The impact of the type of recruitment function used to model HRBC growth is also investigated. The model steady states and [Formula: see text], both obtained as functions of immune system variables, are analyzed at snapshots of immune sizes. Model results indicate that the more the immune cells, innate and adaptive, the more efficient they are at inhibiting parasite development and progression; consequently, the less severe the malaria disease in a patient. Our analysis also illustrates the existence of a Hopf bifurcation leading to a limit cycle, observable only for the nonlinear recruitment functions, at reasonably large [Formula: see text]. 
    more » « less
  • Citation Formats
  • MLA
  • APA
  • Chicago
  • BibTeX
  • Save / Share this Record
  • Send to Email