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.

Standardized polyacrylamide microgel beads as novel tools to calibrate experiments in biomechanics and to measure stresses in complex tissues.

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.

The wetting of deformable elastic structures has been recently shown to comprise a rich variety of new physical phenomena (stick-slip motion, durotaxis, Shuttleworth effect, etc.) whose fundamental understanding demands for numerical simulation tools. In this article, we develop a novel unified model and numerical method for this problem. As special features, the method includes exact incompressibility and a linear monolithic assembly of the Navier-Stokes and Cahn-Hilliard equations which stabilizes dominant surface tension at small interface lengths. Also, solid viscosity is included which offers the opportunity to simulate the surfing behavior of droplets on viscoelastic substrates for the first time. We show that the method is highly accurate and more robust than most previous approaches and illustrate its potential by numerical simulation examples. K E Y W O R D S binary fluid structure interaction, elasto-capillarity, moving contact line, phase field method, soft wetting This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.