Small-amplitude swimmers can self-propel faster in viscoelastic fluids

A computational approach to model gliding motion of an organism on a sticky slime layer over a solid substrate

Bacteria are microscopic single-celled microbes that can only be spotted via a microscope. They occur in a variety of shapes and sizes, and their dimensions are measured in micrometers (one-millionth of a meter). Bacterial categorization is based on a variety of features such as morphology, DNA sequencing, presence of flagella, cell structure, staining techniques, oxygen, and carbon-dioxide requirements. Due to these classifications, gliding bacteria are a miscellaneous class of rodlike microorganisms that cling and propel over ooze slime connected with a substrate. Without the assistance of flagella, which are essential parts of bacterial motility, the organism movement is adopted by waves streaming down the outer layer of this microorganism. To simulate the locomotion of such gliding microorganisms, a wavy sheet over Oldroyd-4 constant fluid is utilized. Under the long wavelength assumption, the equations regulating the flow of slime (modeled as Oldroyd-4 constant slime) beneath the cell/organism are developed. The quantities such as slime flow rate, cell speed, and propulsion power are computed by using bvp4c (MATLAB routine) integrated with the modified Newton-Rasphson technique. Furthermore, the flow patterns and velocity of the slime are graphically shown and thoroughly described using precise (calculated) values of the cell speed and velocity of the slime.

Autonomously Propelled Colloids for Penetration and Payload Delivery in Complex Extracellular Matrices

For effective treatment of diseases such as cancer or fibrosis, it is essential to deliver therapeutic agents such as drugs to the diseased tissue, but these diseased sites are surrounded by a dense network of fibers, cells, and proteins known as the extracellular matrix (ECM). The ECM forms a barrier between the diseased cells and blood circulation, the main route of administration of most drug delivery nanoparticles. Hence, a stiff ECM impedes drug delivery by limiting the transport of drugs to the diseased tissue. The use of self-propelled particles (SPPs) that can move in a directional manner with the application of physical or chemical forces can help in increasing the drug delivery efficiency. Here, we provide a comprehensive look at the current ECM models in use to mimic the in vivo diseased states, the different types of SPPs that have been experimentally tested in these models, and suggest directions for future research toward clinical translation of SPPs in diverse biomedical settings.

Three-dimensional simulations of undulatory and amoeboid swimmers in viscoelastic fluids

Microorganisms often move through viscoelastic environments, as biological fluids frequently have a rich microstructure owing to the presence of large polymeric molecules. Research on the effect of fluid elasticity on the swimming kinematics of these organisms has usually been focused on those that move via cilia or flagellum. Experimentally, Shen (X. N. Shen et al., Phys. Rev. Lett., 2011, 106, 208101) reported that the nematode C. elegans, a model organism used to study undulatory motion, swims more slowly as the Deborah number describing the fluid's elasticity is increased. This phenomenon has not been thoroughly studied via a fully resolved three-dimensional simulation; moreover, the effect of fluid elasticity on the swimming speed of organisms moving via euglenoid movement, such as E. gracilis, is completely unknown. In this study, we discuss the simulation of the arbitrary motion of an undulating or pulsating swimmer that occupies finite volume in three dimensions, with the ability to specify any differential viscoelastic rheological model for the surrounding fluid. To accomplish this task, we use a modified version of the Immersed Finite Element Method presented in a previous paper by Guido and Saadat in 2018 (A. Saadat et al., Phys. Rev. E, 2018, 98, 063316). In particular, this version allows for the simulation of deformable swimmers such that they evolve through an arbitrary set of specified shapes via a conformation-driven force. From our analysis, we observe several key trends not found in previous two-dimensional simulations or theoretical analyses for C. elegans, as well as novel results for the amoeboid motion. In particular, we find that regions of high polymer stress concentrated at the head and tail of the swimming C. elegans are created by strong extensional flow fields and are associated with a decrease in swimming speed for a given swimming stroke. In contrast, in two dimensions these regions of stress are commonly found distributed along the entire body, likely owing to the lack of a third dimension for polymer relaxation. A comparison of swim speeds shows that the calculations in two-dimensional simulations result in an over-prediction of the speed reduction. We believe that our simulation tool accurately captures the swimming motion of the two aforementioned model swimmers and furthermore, allows for the simulation of multiple deformable swimmers, as well as more complex swimming geometries. This methodology opens many new possibilities for future studies of swimmers in viscoelastic fluids.

Effect of body deformability on microswimming

In this work we consider the following question: given a mechanical microswimming mechanism, does increased deformability of the swimmer body hinder or promote the motility of the swimmer? To answer this we run immersed-boundary-lattice-Boltzmann simulations of a microswimmer composed of deformable beads connected with springs. We find that the same deformations in the beads can result in different effects on the swimming velocity, namely an enhancement or a reduction, depending on the other parameters. To understand this we determine analytically the velocity of the swimmer, starting from the forces driving the motion and assuming that the deformations in the beads are known as functions of time and are much smaller than the beads themselves. We find that to the lowest order, only the driving frequency mode of the surface deformations contributes to the swimming velocity, and comparison to the simulations shows that both the velocity-promoting and velocity-hindering effects of bead deformability are reproduced correctly by the theory in the limit of small bead deformations. For the case of active deformations we show that there are critical values of the spring constant - which for a general swimmer corresponds to its main elastic degree of freedom - which decide whether the body deformability is beneficial for motion or not.

SWIMMING DYNAMICS OF A MICRO-ORGANISM IN A COUPLE STRESS FLUID: A RHEOLOGICAL MODEL OF EMBRYOLOGICAL HYDRODYNAMIC PROPULSION

Mathematical simulations of embryological fluid dynamics are fundamental to improving clinical understanding of the intricate mechanisms underlying sperm locomotion. The strongly rheological nature of reproductive fluids has been established for a number of decades. Complimentary to clinical studies, mathematical models of reproductive hydrodynamics provide a deeper understanding of the intricate mechanisms involved in spermatozoa locomotion which can be of immense benefit in clarifying fertilization processes. Although numerous non-Newtonian studies of spermatozoa swimming dynamics in non-Newtonian media have been communicated, very few have addressed the micro-structural characteristics of embryological media. This family of micro-continuum models include Eringen’s micro-stretch theory, Eringen’s microfluid and micropolar constructs and V. K. Stokes’ couple stress fluid model, all developed in the 1960s. In the present paper we implement the last of these models to examine the problem of micro-organism (spermatozoa) swimming at low Reynolds number in a homogenous embryological fluid medium with couple stress effects. The micro-organism is modeled as with Taylor’s classical approach, as an infinite flexible sheet on whose surface waves of lateral displacement are propagated. The swimming speed of the sheet and rate of work done by it are determined as function of the parameters of orbit and the couple stress fluid parameter ([Formula: see text]). The perturbation solutions are validated with a Nakamura finite difference algorithm. The perturbation solutions reveal that the normal beat pattern is effective for both couple stress and Newtonian fluids only when the amplitude of stretching wave is small. The swimming speed is observed to decrease with couple stress fluid parameter tending to its Newtonian limit as alpha tends to infinity. However the rate of work done by the sheet decreases with [Formula: see text] and approaches asymptotically to its Newtonian value. The present solutions also provide a good benchmark for more advanced numerical simulations of micro-organism swimming in couple-stress rheological biofluids.

Microscale flow dynamics of ribbons and sheets

Numerical study of the hydrodynamics of thin sheets and ribbons presents difficulties associated with resolving multiple length scales. To circumvent these difficulties, asymptotic methods have been developed to describe the dynamics of slender fibres and ribbons. However, such theories entail restrictions on the shapes that can be studied, and often break down in regions where standard boundary element methods are still impractical. In this paper we develop a regularised stokeslet method for ribbons and sheets in order to bridge the gap between asymptotic and boundary element methods. The method is validated against the analytical solution for plate ellipsoids, as well as the dynamics of ribbon helices and an experimental microswimmer. We then demonstrate the versatility of this method by calculating the flow around a double helix, and the swimming dynamics of a microscale "magic carpet".

Bacterial gliding fluid dynamics on a layer of non-Newtonian slime: Perturbation and numerical study

Gliding bacteria are an assorted group of rod-shaped prokaryotes that adhere to and glide on certain layers of ooze slime attached to a substratum. Due to the absence of organelles of motility, such as flagella, the gliding motion is caused by the waves moving down the outer surface of these rod-shaped cells. In the present study we employ an undulating surface model to investigate the motility of bacteria on a layer of non-Newtonian slime. The rheological behavior of the slime is characterized by an appropriate constitutive equation, namely the Carreau model. Employing the balances of mass and momentum conservation, the hydrodynamic undulating surface model is transformed into a fourth-order nonlinear differential equation in terms of a stream function under the long wavelength assumption. A perturbation approach is adopted to obtain closed form expressions for stream function, pressure rise per wavelength, forces generated by the organism and power required for propulsion. A numerical technique based on an implicit finite difference scheme is also employed to investigate various features of the model for large values of the rheological parameters of the slime. Verification of the numerical solutions is achieved with a variational finite element method (FEM). The computations demonstrate that the speed of the glider decreases as the rheology of the slime changes from shear-thinning (pseudo-plastic) to shear-thickening (dilatant). Moreover, the viscoelastic nature of the slime tends to increase the swimming speed for the shear-thinning case. The fluid flow in the pumping (generated where the organism is not free to move but instead generates a net fluid flow beneath it) is also investigated in detail. The study is relevant to marine anti-bacterial fouling and medical hygiene biophysics.

Efficient nematode swimming in a shear thinning colloidal suspension

The swimming behavior of a nematode Caenorhabditis elegans (C. elegans) is investigated in a non-Newtonian shear thinning colloidal suspension. At the onset value (ϕ∼ 8%), the suspension begins to exhibit shear thinning behavior, and the average swimming speed of worms jumps by approximately 12% more than that measured in a Newtonian solution exhibiting no shear dependent viscosity. In the shear thinning regime, we observe a gradual yet significant improvement in swimming efficiency with an increase in ϕ while the swimming speed remains nearly constant. We postulate that this enhanced swimming can be explained by the temporal change in the stroke form of the nematode that is uniquely observed in a shear thinning colloidal suspension: the nematode features a fast and large stroke in its head to overcome the temporally high drag imposed by the viscous medium, whose effective viscosity (ηs) is shown to drop drastically, inversely proportional to the strength of its stroke. Our results suggest new insights into how nematodes efficiently maneuver through the complex fluid environment in their natural habitat.