Session R06: Transport in Biofluids

Fluid dynamics and mass transport driven by out-of-phase villi movements in the small intestine

The inner wall of the human small intestine is lined with columnar protrusions called villi. The movement of these villi generates micro-scale fluid motion, enhancing the transport of nutrients from the lumen to the epithelial cells on the villi surfaces for absorption. A high-fidelity numerical study using the lattice Boltzmann method has been conducted to investigate the fluid motion and mass transport induced by villous movement. The study found that grouping the villi arrays and making adjacent groups perform out-of-phase movements creates a micro-scale mixing layer. This mixing layer contains a series of eddies that not only facilitate the transport of nutrients from the upper bulk fluid to the villi surfaces through advection but also transport substances released from the villi surface back to the upper bulk fluid. Additionally, these eddies, interacting with the upper flow, travel downstream along the villi arrays, carrying fluid and dissolved substances downstream. The transport speed is influenced by the width of the villi groups and the frequency of their movements. This study provides a mechanistic foundation for how the human body can control the mixing and transport processes in the small intestine by regulating villi movement.   

Study of Cerebrospinal Fluid Flow and Mixing that Accounts for Non-Uniform Orientation of Cilia

Cerebrospinal fluid (CSF) within the brain ventricles serves an important physiological function of both a nutrient delivery and a waste removal. Complex CSF flow patterns created within the brain ventricles are generated by a synchronized motion of microscopic cilia. However, as opposed to conventional models of cilia carpets, where all cilia beat in the same direction, the ventricular walls display a complex anatomy with non-uniform cilia clustering and orientations. In order to understand the role of such physiologically-derived non-uniformities in cilia organization, we have developed a CSF flow model that takes non-uniform clustering and orientation of cilia into account. Flow patterns and mixing properties within the CSF fluid are studied, depending on several control parameters within the model, which include polarization properties of the ependymal cells, distribution in the deviation angles, and a percentage of dysfunctional cells. To study the effects of these parameters on the transport properties within the CSF flow, we introduce non-inertial Lagrangian particles into the simulations and track their motion within the fluid.   

Boundary conditions for the envelope of canopy interacting with two dimensional laminar flow

To reveal the mechanisms of collective motions of fibers clamped on a flat wall (i.e., canopy) subjected to fluid flow, boundary conditions at the envelope of canopy are proposed for synchronous and asynchronous motions of fibers, where fibers exhibit identical and individual motions, respectively. By assuming small deflection, the fibers are modeled as rigid bars installed with torsion springs. The effects of fluid forces on the fibers are expressed as the moments of fluid forces through averaging Navier-Stokes equations. The time-development of the envelope for synchronous motion of fibers is represented with mass-spring-damper system driven by the flow over the canopy. As the non-uniformity of fibers' motion is enhanced, the effects of fluid inertia in the wall-normal direction and diffusion of fiber velocities have more important role. The results of the simulations with our models are compared with those of fluid-structure interaction (FSI) simulations, which directly solve the interaction forces between the individual fluid and fibers, to assess the validity of the models. It is remarkable that the grid resolutions have such little influence on the results that one fluid mesh size can be set larger than inter-fibers.   

Assessing fluid transport in the periciliary layer through distinct measures of mixing

The mucociliary escalator in the respiratory system can become impaired due to disease and change morphologically, affecting fluid transport. In our study, we focus on flow only in the periciliary layer of the upper respiratory mucosal layer and calculate several distinct mixing measures (the mixing number, the finite-time Lyapunov exponent (FTLE) field, and the multiscale mix norm) to assess whether chaotic advection exists. We aim to visualize the mixing process over time and quantify the effect of selected parameters (beat frequency, domain length, height, metachronal wavelength, and inter-cilium spacing) on the flow field. The backward image trace methodology allows us to generate high-resolution visual maps of scalar transport in the periciliary layer. These compelling images, which provide a clear representation of the mixing process, are then analyzed heuristically by calculating the FTLE field of the flow. Then, we discuss our findings on the potential for chaotic advection by calculating both the mixing number and the multiscale mix-norm of the passive advection of a scalar. Interestingly, we see the emergence of two areas where mixing occurs at dissimilar rates. These two areas can be delineated using the FTLE field and are quantitatively evaluated using the mix norm. Finally, we present differences in the mixed state for various configuration parameters between a single cilium and a cilium patch.   

Enhanced transport in unsteady Stokes flows generated by beating cilia

Eukaryotic microorganisms use cilia for swimming, to transport nutrients, and to detect flows. While most of the generated flows occur at low Reynolds numbers, individual beating cilia are known to produce unsteady flows. We study how transport properties by individual and populations of beating cilia are modified when accounting for these transient unsteady effects, including near boundaries, using a combination of experiments, theory, and simulations.   

Feeders and Expellers, Two Types of Animalcules With Outboard Cilia, Have Distinct Surface Interactions

Within biological fluid dynamics, it is conventional to distinguish between 

"puller" and "pusher" microswimmers on the basis of the forward or aft 

location of the flagella relative to the cell body: typically, bacteria are

pushers and algae are pullers.  Here we note that since many pullers have 

"outboard" cilia or flagella displaced laterally from the cell centerline on both

sides of the organism, there are two important subclasses whose

far-field is that of a stresslet, but whose near field is qualitatively more complex.  

The ciliary beat creates not only a propulsive force

but also swirling flows that can be represented by paired rotlets with two possible

senses of rotation, either "feeders" that sweep fluid toward the cell apex, or 

"expellers" that push fluid away.  Experimental studies of the 

rotifer Brachionus plicatilis in combination with earlier work on the green algae 

Chlamydomonas reinhardtii show that the two classes have markedly

different interactions with surfaces.  When swimming near a surface, expellers such as 

C. reinhardtii scatter from the wall, 

whereas a feeder like B. plicatilis stably attaches.  This results in a stochastic "run-and-stick" locomotion, with periods of 

ballistic motion parallel to the surface interrupted by trapping at the surface.   

Carpet cleaning: Lagrangian transport by cilia

Cilia are hair-like appendages that protrude from the surface of a range of eukaryotic cells. Their deformation in a wavelike manner generates a flow in the surrounding fluid. This flow is important in a myriad of biological contexts, from mucus transport in the sinus to microorganism locomotion. The classical theoretical approach for fluid transport by cilia is Taylor's waving sheet model, where an asymptotic calculation in the sheet amplitude leads to a nonzero time-averaged Eulerian flow. We revisit this classical problem and calculate explicitly the Lagrangian transport of suspended tracers induced by small-amplitude deformations of the sheet. Using a multiple-scale analysis, we show that the Lagrangian drift transports particles on trajectories characterised by the superposition of a periodic orbit and a slower time horizontal drift, in a manner that, in contrast with the Eulerian flow, varies with the distance to the sheet. Our theoretical results are validated using numerical computations.   

Velocity fluctuations in sedimentation of particles stirred by bacterial suspensions

Interaction of passive particles with active matter is ubiquitous in environmental and biological processes. However, the effects of bacterial activity on the settling dynamics of passive particles remain elusive. To understand these effects, we built a custom-made experimental setup to explore the sedimentation dynamics of polystyrene particles in dilute E. coli suspensions. We showed that time-dependent concentration profiles at the macroscale (Singh et al., Soft Matter 2021) and mesoscale (Maldonando et al., Phys. Fluids 2022) are functions of bacterial activity. Probing the system at the microscale, we demonstrated that the sedimentation dynamics of passive colloids in an active bacterial bath exhibit a diffusion-to-bioconvection transition set by a critical bacterial concentration (Maldonado et al., J. Fluid Mech 2024). This transition from Stokes-Einstein diffusion dynamics to activity-driven convection is accompanied by fluctuations in sedimentation velocities. We characterize the statistics of these fluctuations,  in the components of sedimentation velocities parallel and orthogonal to the direction of the gravitational force, stoboscopically at the colloidal particle-scale and model them using a Hinch-blob type-model that accouts the effect of bacterial activity. This work provides a new perspective on underlying mechanism associated with the sedimentation dynamics of passive matter in an active bath.