Propulsion of a three-sphere microrobot in a porous medium.

Microorganisms and synthetic microswimmers often encounter complex environments consisting of networks of obstacles embedded into viscous fluids. Such settings include biological media, such as mucus with filamentous networks, as well as environmental scenarios, including wet soil and aquifers. A fundamental question in studying their locomotion is how the impermeability of these porous media impacts their propulsion performance compared with the case of that in a purely viscous fluid. Previous studies showed that the additional resistance due to the embedded obstacles leads to an enhanced propulsion of different types of swimmers, including undulatory swimmers, helical swimmers, and squirmers. In this paper, we employ a canonical three-sphere swimmer model to probe the impact of propulsion in porous media. The Brinkman equation is utilized to model a sparse network of stationary obstacles embedded into an incompressible Newtonian liquid. We present both a far-field theory and numerical simulations to characterize the propulsion performance of the swimmer in such porous media. In contrast to enhanced propulsion observed in other swimmer models, our results reveal that both the propulsion speed and efficiency of the three-sphere swimmer are largely reduced by the impermeability of the porous medium. We attribute the substantial reduction in propulsion performance to the screened hydrodynamic interactions among the spheres due to the more rapid spatial decays of flows in Brinkman media. These results highlight how enhanced or hindered propulsion in porous media is largely dependent on individual propulsion mechanisms. The specific example and physical insights provided here may guide the design of synthetic microswimmers for effective locomotion in porous media in their potential biological and environmental applications.

Flow-induced "waltzing" red blood cells: Microstructural reorganization and the corresponding rheological response.

We investigate flow-induced structural organization in a dilute suspension of tumbling red blood cells (RBCs) under confined shear flow. For small Reynolds (Re = 0.1) and capillary numbers (Ca), with fully coupled hydrodynamic interaction (HI) and without interparticle adhesion, we find that HI between the biconcave discoid particles prompts the formation of layered RBC chains and synchronized rotating RBC pairs, referred here as "waltzing doublets." As the volume fraction ϕ increases, more waltzing doublets appear in RBC files. Stronger shear stress disrupts structural arrangements at higher Ca. We find that the flow-induced organization of waltzing doublets changes how the suspension viscosity varies with ϕ qualitatively. The intrinsic viscosity is particularly sensitive to microstructural rearrangement, increasing (decreasing) with ϕ at low (high) Ca that correlates with the change in the fraction of doublets. We verified flow-induced collective motion with comparison to two-cell simulations in which the cell volume fraction is controlled by varying the domain volume.

Shear-induced non-monotonic viscosity dependence for model red blood cell suspensions in microvessels.

The cell-free layer thickness of an aggregating red blood cell (RBC) suspension in a rectangular microchannel is investigated by hybrid fluid-particle numerical modeling. Several factors affect the suspension viscosity, cell-free layer thickness, and the cell aggregate distribution. These include the hematocrit, vessel size, red cell stiffness, aggregation interaction, and shear rate. In particular, the effect of the shear rate on the cell-free layer thickness is controversial. We found that the suspension viscosity increases along with a decrease in the cell-free layer thickness as the shear rate increases for aggregating model RBCs at low shear rates. At moderate to high shear rates, the cell-free layer thickness increases with the increasing shear rate from medium to strong shear flow for both 10% and 20% red blood cell suspensions.

Modeling shear-induced particle ordering and deformation in a dense soft particle suspension.

We apply the lattice Boltzmann method and the bead-spring network model of deformable particles (DPs) to study shear-induced particle ordering and deformation and the corresponding rheological behavior for dense DP suspensions confined in a narrow gap under steady external shear. The particle configuration is characterized with small-angle scattering intensity, the real-space 2D local order parameter, and the particle shape factors including deformation, stretching and tilt angles. We investigate how particle ordering and deformation vary with the particle volume fraction ϕ (=0.45-0.65) and the external shear rate characterized with the capillary number Ca (=0.003-0.191). The degree of particle deformation increases mildly with ϕ but significantly with Ca. Under moderate shear rate (Ca = 0.105), the inter-particle structure evolves from string-like ordering to layered hexagonal close packing (HCP) as ϕ increases. A long wavelength particle slithering motion emerges for sufficiently large ϕ. For ϕ = 0.61, the structure maintains layered HCP for Ca = 0.031-0.143 but gradually becomes disordered for larger and smaller Ca. The correlation in particle zigzag movements depends sensitively on ϕ and particle ordering. Layer-by-layer analysis reveals how the non-slippery hard walls affect particle ordering and deformation. The shear-induced reconfiguration of DPs observed in the simulation agrees qualitatively with experimental results of sheared uniform emulsions. The apparent suspension viscosity increases with ϕ but exhibits much weaker dependence compared to hard-sphere suspensions, indicating that particle deformation and unjamming under shear can significantly reduce the viscous stress. Furthermore, the suspension shear-thins, corresponding to increased inter-DP ordering and particle deformation with Ca. This work provides useful insights into the microstructure-rheology relationship of concentrated deformable particle suspensions.

Bacterial colony from two-dimensional division to three-dimensional development.

On agar surface, bacterial daughter cells form a 4-cell array after the first two rounds of division, and this phenomenon has been previously attributed to a balancing of interactions among the daughter bacteria and the underneath agar. We studied further the organization and development of colony after additional generations. By confocal laser scanning microscopy and real-time imaging, we observed that bacterial cells were able to self-organize and resulted in a near circular micro-colony consisting of monolayer cells. After continuous dividing, bacteria transited from two-dimensional expansion into three-dimensional growth and formed two to multi-layers in the center but retained a monolayer in the outer ring of the circular colony. The transverse width of this outer ring appeared to be approximately constant once the micro-colony reached a certain age. This observation supports the notion that balanced interplays of the forces involved lead to a gross morphology as the bacteria divide into offspring on agar surface. In this case, the result is due to a balance between the expansion force of the dividing bacteria, the non-covalent force among bacterial offspring and that between bacteria and substratum.