Search for: All records

We conducted a systematic numerical investigation of spherical, prolate and oblate particles in an inertial shear flow between two parallel walls, using smoothed particle hydrodynamics (SPH). It was previously shown that above a critical Reynolds number, spherical particles experience a supercritical pitchfork bifurcation of the equilibrium position in shear flow between two parallel walls, namely that the central equilibrium position becomes unstable, leading to the emergence of two new off-centre stable positions (Foxet al.,J. Fluid Mech., vol. 915, 2021). This phenomenon was unexpected given the symmetry of the system. In addition to confirming this finding, we found, surprisingly, that ellipsoidal particles can also return to the centre position from the off-centre positions when the particle Reynolds number is further increased, while spherical particles become unstable under this increased Reynolds number. By utilizing both SPH and the finite element method for flow visualization, we explained the underlining mechanism of this reverse of bifurcation by altered streamwise vorticity and symmetry breaking of pressure. Furthermore, we expanded our investigation to include asymmetric particles, a novel aspect that had not been previously modelled, and we observed similar trends in particle dynamics for both symmetric and asymmetric ellipsoidal particles. While further validation through laboratory experiments is necessary, our research paves the road for development of new focusing and separation methods for shaped particles. 

Soft objects squeezing through small apertures are crucial for many in vivo and in vitro processes. Red blood cell transit time through splenic inter-endothelial slits (IESs) plays a crucial role in blood filtration and disease progression, while droplet velocity through constrictions in microfluidic devices is important for effective manipulation and separation processes. As these transit phenomena are not well understood, we sought to establish analytical and numerical solutions of viscous droplet transit through a rectangular slit. This study extends from our former theory of a circular pore because a rectangular slit is more realistic in many physiological and engineering applications. Here, we derived the ordinary differential equations (ODEs) of a droplet passing through a slit by combining planar Poiseuille flow, the Young–Laplace equations, and modifying them to consider the lubrication layer between the droplet and the slit wall. Compared to the pore case, we used the Roscoe solution instead of the Sampson one to account for the flow entering and exiting a rectangular slit. When the surface tension and lubrication layer were negligible, we derived the closed-form solutions of transit time. When the surface tension and lubrication layer were finite, the ODEs were solved numerically to study the impact of various parameters on the transit time. With our solutions, we identified the impact of prescribed pressure drop, slit dimensions, and droplet parameters such as surface tension, viscosity, and volume on transit time. In addition, we also considered the effect of pressure drop and surface tension near critical values. For this study, critical surface tension for a given pressure drop describes the threshold droplet surface tension that prevents transit, and critical pressure for a given surface tension describes the threshold pressure drop that prevents transit. Our solutions demonstrate that there is a linear relationship between pressure and the reciprocal of the transit time (referred to as inverse transit time), as well as a linear relationship between viscosity and transit time. Additionally, when the droplet size increases with respect to the slit dimensions, there is a corresponding increase in transit time. Most notably, we emphasize the initial antagonistic effect of surface tension which resists droplet passage but at the same time decreases the lubrication layer, thus facilitating passage. Our results provide quantitative calculations for understanding cells passing through slit-like constrictions and designing droplet microfluidic experiments. 

The splenic interendothelial slits fulfill the essential function of continuously filtering red blood cells (RBCs) from the bloodstream to eliminate abnormal and aged cells. To date, the process by which 8 $\mathrm{\mu }$m RBCs pass through 0.3 $\mathrm{\mu }$m-wide slits remains enigmatic. Does the slit caliber increase during RBC passage as sometimes suggested? Here, we elucidated the mechanisms that govern the RBC retention or passage dynamics in slits by combining multiscale modeling, live imaging, and microfluidic experiments on an original device with submicron-wide physiologically calibrated slits. We observed that healthy RBCs pass through 0.28 $\mathrm{\mu }$m-wide rigid slits at 37 °C. To achieve this feat, they must meet two requirements. Geometrically, their surface area-to-volume ratio must be compatible with a shape in two tether-connected equal spheres. Mechanically, the cells with a low surface area-to-volume ratio (28% of RBCs in a 0.4 $\mathrm{\mu }$m-wide slit) must locally unfold their spectrin cytoskeleton inside the slit. In contrast, activation of the mechanosensitive PIEZO1 channel is not required. The RBC transit time through the slits follows a $-$1 and $-$3 power law with in-slit pressure drop and slip width, respectively. This law is similar to that of a Newtonian fluid in a two-dimensional Poiseuille flow, showing that the dynamics of RBCs is controlled by their cytoplasmic viscosity. Altogether, our results show that filtration through submicron-wide slits is possible without further slit opening. Furthermore, our approach addresses the critical need for in vitro evaluation of splenic clearance of diseased or engineered RBCs for transfusion and drug delivery. 

Abstract The nuclear lamina is widely recognized as the most crucial component in providing mechanical stability to the nucleus. However, it is still a significant challenge to model the mechanics of this multilayered protein network. We developed a constitutive model of the nuclear lamina network based on its microstructure, which accounts for the deformation phases at the dimer level, as well as the orientational arrangement and density of lamin filaments. Instead of relying on homology modeling in the previous studies, we conducted molecular simulations to predict the force‐extension response of a highly accurate lamin dimer structure obtained through X‐ray diffraction crystallography experimentation. Furthermore, we devised a semiflexible worm‐like chain extension‐force model of lamin dimer as a substitute, incorporating phases of initial stretching, uncoiling of the dimer coiled‐coil, and transition of secondary structures. Subsequently, we developed a 2D network continuum model for the nuclear lamina by using our extension‐force lamin dimer model and derived stress resultants. By comparing with experimentally measured lamina modulus, we found that the lamina network has sharp initial strain‐hardening behavior. This also enabled us to carry out finite element simulations of the entire nucleus with an accurate microstructure‐based nuclear lamina model. Finally, we conducted simulations of transendothelial transmigration of a nucleus and investigated the impact of varying network density and uncoiling constants on the critical force required for successful transmigration. The model allows us to incorporate the microstructure characteristics of the nuclear lamina into the nucleus model, thereby gaining insights into how laminopathies and mutations affect nuclear mechanics. 

We derived equations and closed-form solutions of transit time for a viscous droplet squeezing through a small circular pore with a finite length at microscale under constant pressures. Our analyses were motivated by the vital processes of biological cells squeezing through small pores in blood vessels and sinusoids and droplets squeezing through pores in microfluidics. First, we derived ordinary differential equations (ODEs) of a droplet squeezing through a circular pore by combining Sampson flow, Poiseuille flow, and Young–Laplace equations and took into account the lubrication layer between the droplet and the pore wall. Second, for droplets wetting the wall with small surface tension, we derived the closed-form solutions of transit time. For droplets with finite surface tension, we solved the original ODEs numerically to predict the transit time. After validations against experiments and finite element simulations, we studied the effects of pressure, viscosity, pore/droplet dimensions, and surface tension on the transit time. We found that the transit time is inversely linearly proportional to pressure when the surface tension is low compared to the critical surface tension for preventing the droplet to pass and becomes nonlinear when it approaches the critical tension. Remarkably, we showed that when a fixed percentage of surface tension to critical tension is applied, the transit time is always inversely linearly proportional to pressure, and the dependence of transit time on surface tension is nonmonotonic. Our results provided a quick way of quantitative calculations of transit time for designing droplet microfluidics and understanding cells passing through constrictions. 

Abstract Particle migration dynamics in viscoelastic fluids in spiral channels have attracted interest in recent years due to potential applications in the 3D focusing and label-free sorting of particles and cells. Despite a number of recent studies, the underlying mechanism of Dean-coupled elasto-inertial migration in spiral microchannels is not fully understood. In this work, for the first time, we experimentally demonstrate the evolution of particle focusing behavior along a channel downstream length at a high blockage ratio. We found that flow rate, device curvature, and medium viscosity play important roles in particle lateral migration. Our results illustrate the full focusing pattern along the downstream channel length, with side-view imaging yielding observations on the vertical migration of focused streams. Ultimately, we anticipate that these results will offer a useful guide for elasto-inertial microfluidics device design to improve the efficiency of 3D focusing in cell sorting and cytometry applications. 

The regulation of polymorphonuclear leukocyte (PMN) function by mechanical forces encountered during their migration across restrictive endothelial cell junctions is not well understood. Using genetic, imaging, microfluidic, and in vivo approaches, we demonstrated that the mechanosensor Piezo1 in PMN plasmalemma induced spike-like Ca2+ signals during trans-endothelial migration. Mechanosensing increased the bactericidal function of PMN entering tissue. Mice in which Piezo1 in PMNs was genetically deleted were defective in clearing bacteria, and their lungs were predisposed to severe infection. Adoptive transfer of Piezo1-activated PMNs into the lungs of Pseudomonas aeruginosa-infected mice or exposing PMNs to defined mechanical forces in microfluidic systems improved bacterial clearance phenotype of PMNs. Piezo1 transduced the mechanical signals activated during transmigration to upregulate nicotinamide adenine dinucleotide phosphate (NADPH) oxidase 4, crucial for the increased PMN bactericidal activity. Thus, Piezo1 mechanosensing of increased PMN tension, while traversing the narrow endothelial adherens junctions, is a central mechanism activating the host-defense function of transmigrating PMNs. 

Growth of the microfluidics field has triggered numerous advances in focusing and separating microparticles, with such systems rapidly finding applications in biomedical, chemical, and environmental fields. The use of shear-thinning viscoelastic fluids in microfluidic channels is leading to evolution of elasto-inertial focusing. Herein, we showed that the interplay between the elastic and shear-gradient lift forces, as well as the secondary flow transversal drag force that is caused by the non-zero second normal stress difference, lead to different particle focusing patterns in the elasto-inertial regime. Experiments and 3D simulations were performed to study the effects of flowrate, particle size, and the shear-thinning extent of the fluid on the focusing patterns. The Giesekus constitutive equation was used in the simulations to capture the shear-thinning and viscoelastic behaviors of the solution used in the experiments. At low flowrate, with Weissenberg number Wi ~ O(1), both the elastic force and secondary flow effects push particles towards the channel center. However, at a high flowrate, Wi ~ O(10), the elastic force direction is reversed in the central regions. This remarkable behavior of the elastic force, combined with the enhanced shear-gradient lift at the high flowrate, pushes particles away from the channel center. Additionally, a precise prediction of the focusing position can only be made when the shear-thinning extent of the fluid is correctly estimated in the modeling. The shear-thinning also gives rise to the unique behavior of the inertial forces near the channel walls which is linked with the ‘warped’ velocity profile in such fluids.