Cell stiffness is a sensitive indicator of physiological and pathological changes in cells, with many potential applications in biology and medicine. A new method, real-time deformability cytometry, probes cell stiffness at high throughput by exposing cells to a shear flow in a microfluidic channel, allowing for mechanical phenotyping based on single-cell deformability. However, observed deformations of cells in the channel not only are determined by cell stiffness, but also depend on cell size relative to channel size. Here, we disentangle mutual contributions of cell size and cell stiffness to cell deformation by a theoretical analysis in terms of hydrodynamics and linear elasticity theory. Performing real-time deformability cytometry experiments on both model spheres of known elasticity and biological cells, we demonstrate that our analytical model not only predicts deformed shapes inside the channel but also allows for quantification of cell mechanical parameters. Thereby, fast and quantitative mechanical sampling of large cell populations becomes feasible.

Springtails (Collembola) are wingless arthropods adapted to cutaneous respiration in temporarily rain-flooded habitats. They immediately form a plastron, protecting them against suffocation upon immersion into water and even low-surface-tension liquids such as alkanes. Recent experimental studies revealed a high-pressure resistance of such plastrons against collapse. In this work, skin sections of Orthonychiurus stachianus are studied by transmission electron microscopy. The micrographs reveal cavity side-wall profiles with characteristic overhangs. These were fitted by polynomials to allow access for analytical and numerical calculations of the breakthrough pressure, that is, the barrier against plastron collapse. Furthermore, model profiles with well-defined geometries were used to set the obtained results into context and to develop a general design principle for the most robust surface structures. Our results indicate the decisive role of the sectional profile of overhanging structures to form a robust heterogeneous wetting state for low-surface-tension liquids that enables the omniphobicity. Furthermore, the design principles of mushroom and serif T structures pave the way for omniphobic surfaces with a high-pressure resistance irrespective of solid surface chemistry.

The measurement of cell stiffness is an important part of biological research with diverse applications in biology, biotechnology and medicine. Real-time deformability cytometry (RT-DC) is a new method to probe cell stiffness at high throughput by flushing cells through a microfluidic channel where cell deformation provides an indicator for cell stiffness (Otto et al. Real-time deformability cytometry: on-the-fly cell 725 mechanical phenotyping. Nat. Methods 2015, 12, 199−202). Here, we propose a full numerical model for single cells in a flow channel to quantitatively relate cell deformation to mechanical parameters. Thereby the cell is modeled as a viscoelastic material surrounded by a thin shell cortex, subject to bending stiffness and cortical surface tension. For small deformations our results show good agreement with a previously developed analytical model that neglects the influence of cell deformation on the fluid flow (Mietke et al.

SUMMARY Diffuse interface models for incompressible two‐phase flow with large density ratios are tested on benchmark configurations for a two‐dimensional bubble rising in liquid columns. The benchmark quantities circularity, center of mass, and mean rise velocity are compared with reference solutions from Hysing et al. Copyright © 2011 John Wiley & Sons, Ltd.

Springtails (Collembola) are wingless arthropods adapted to cutaneous respiration in temporarily rain-flooded and microbially contaminated habitats by a non-wetting and antiadhesive skin surface that is mechanically rather stable. Recapitulating the robust and effectively repellent surface characteristics of springtail skin in engineered materials may offer exciting opportunities for demanding applications, but it requires a detailed understanding of the underlying design principles. Towards this aim and based on our recent analysis of the structural features of springtail skin, we developed a tunable polymer replication process to dissect the contributions of different structural elements and surface chemistry to the omniphobic performance of the cuticle. The Cassie-Wenzel transition at elevated pressures was explored by in situ plastron collapse experiments and by numerical FEM simulations. The results obtained unravel the decisive role of nanoscopic cuticle structures for the protection of springtails against wetting, and explain how the evolved nanotopography enables the production of omniphobic surfaces even from intrinsically hydrophilic polymer materials.

We present a new diffuse interface model for the dynamics of inextensible vesicles in a viscous fluid with inertial forces. A new feature of this work is the implementation of the local inextensibility condition in the diffuse interface context. Local inextensibility is enforced by using a local Lagrange multiplier, which provides the necessary tension force at the interface. We introduce a new equation for the local Lagrange multiplier whose solution essentially provides a harmonic extension of the multiplier off the interface while maintaining the local inextensibility constraint near the interface. We also develop a local relaxation scheme that dynamically corrects local stretching/compression errors thereby preventing their accumulation. Asymptotic analysis is presented that shows that our new system converges to a relaxed version of the inextensible sharp interface model. This is also verified numerically. To solve the equations, we use an adaptive finite element method with implicit coupling between the Navier-Stokes and the diffuse interface inextensibility equations. Numerical simulations of a single vesicle in a shear flow at different Reynolds numbers demonstrate that errors in enforcing local inextensibility may accumulate and lead to large differences in the dynamics in the tumbling regime and smaller differences in the inclination angle of vesicles in the tank-treading regime. The local relaxation algorithm is shown to prevent the accumulation of stretching and compression errors very effectively. Simulations of two vesicles in an extensional flow show that local inextensibility plays an important role when vesicles are in close proximity by inhibiting fluid drainage in the near contact region.

Colloids that are partially wetted by two immiscible fluids can become confined to fluid-fluid interfaces. At sufficiently high volume fractions, the colloids may jam and the interface may crystallize. Examples include bicontinuous interfacially jammed emulsion gels (bijels), which were proposed in this study by Stratford et al. [Science 309, 2198 (2005)] as a hypothetical new class of soft materials in which interpenetrating, continuous domains of two immiscible viscous fluids are maintained in a rigid state by a jammed layer of colloidal particles at their interface. We develop a continuum model for such a system that is capable of simulating the long-time evolution. A Navier-Stokes-Cahn-Hilliard model for the macroscopic two-phase flow system is combined with a surface phase-field-crystal model for the microscopic colloidal system along the interface. The presence of colloids introduces elastic forces at the interface between the two immiscible fluid phases. An adaptive finite element method is used to solve the model numerically. Using a variety of flow configurations in two dimensions, we demonstrate that as colloids jam on the interface and the interface crystallizes, the elastic force may be strong enough to make the interface sufficiently rigid to resist external forces, such as an applied shear flow, as well as surface tension induced coarsening in bicontinuous structures.

In this paper, we develop a novel phase-field model for fluid-structure interaction (FSI), that is capable to handle very large deformations as well as topology changes like contact of the solid to the domain boundary. The model is based on a fully Eulerian description of the velocity field in both, the fluid and the elastic domain. Viscous and elastic stresses in the Navier-Stokes equations are restricted to the corresponding domains by multiplication with their characteristic functions. To obtain the elastic stress, an additional Oldroyd-B -like equation is solved. Thermodynamically consistent forces are derived by energy variation. The convergence of the derived equations to the traditional sharp interface formulation of fluid-structure interaction is shown by matched asymptotic analysis. The model is evaluated in a challenging benchmark scenario of an elastic body traversing a fluid channel. A comparison to reference values from Arbitrary Lagrangian Eulerian (ALE) simulations shows very good agreement. We highlight some distinct advantages of the new model, like the avoidance of re-triangulations and the stable inclusion of surface tension. Further, we demonstrate how simple it is to include contact dynamics into the model, by simulating a ball bouncing off a wall. We extend this scenario to include adhesion of the ball, which to our knowledge, cannot be simulated with any other FSI model. While we have restricted simulations to fluid-structure interaction, the model is capable to simulate any combination of viscous fluids, visco-elastic fluids and elastic solids.