Capillary forces can significantly contribute to the adhesion of biological and artificial micro- and nanoscale objects. In this paper, we study numerically the effect of meniscus size on the force between two homogeneous flat plates for different contact angles. The force distance curves show excellent quantitative agreement with previous investigations. The results for n menisci of equal total liquid volume reveal interesting scaling properties and an unexpected maximum force for moderately hydrophilic surfaces (i.e., contact angles around 70 degrees ). Further, we calculate the minimum solid-liquid area for multiple bridges, the cohesive stress (i.e., force per area) between the plates, and the work required to separate them. The results are presented in two-dimensional maps, which may be useful in the understanding of biological attachment structures and in the design of artificial contact systems.

A novel and versatile numerical form-finding procedure that requires only a minimal knowledge of the structure is presented. The procedure only needs the type of each member, i.e. either compression or tension, and the connectivity of the nodes to be known. Both equilibrium geometry and force densities are iteratively calculated. A condition of a maximal rank of the force density matrix and minimal member length, were included in the form-finding procedure to guide the search of a state of self-stress with minimal elastic potential energy. It is indeed able to calculate novel configurations, with no assumptions on cable lengths or cable-to-strut ratios. Moreover, the proposed approach compares favourably with all the leading techniques in the field. This is clearly exemplified through a series of examples.

Motivated by experimental results, we present numerical and analytical calculations of the capillary force exerted by a capillary bridge spanning the gap between two parallel flat plates of asymmetric wettability. Depending on whether the sum of the two contact angles is smaller or larger than 180 degrees, the capillary force is either attractive or repulsive at small separations D between the plates. In either cases the magnitude of the force diverges as D approaches zero. The leading order of this divergence is captured by an analytical expression deduced from the geometry of the meniscus of a flat capillary bridge. The results for substrates with different wettability reveal an interesting behavior: with the sum of the contact angles fixed, the magnitude of the capillary force and the rupture separation decreases as the asymmetry in contact angles is increased. In addition, we present the rupture separation, i.e., the maximal extension of a capillary bridge, as a function of the contact angles. Our results provide an extensive picture of surface wettability effects on capillary adhesion.

Arrays of elastic pillars are used in biophysical experiments as sensors for traction forces. The evaluation of the forces can be complicated if they are coupled to the pillar displacements over large distances. This is the case if many of the pillars are interconnected by elastic linkages as, for example, in fiber networks that are grown on top of pillars. To calculate the traction forces in such a network, we developed a set of nonlinear inhomogeneous equations relating the forces in the linking elements to the resulting pillar deflections. We chose a homogeneous, activated two-dimensional network of cytoskeletal actin filaments to illustrate that a pillar substrate is generally not a force sensor but a force-gradient sensor. In homogeneous networks the forces acting along the filaments can be approximated by analyzing only pillar deflections in the edge zones of the substrate and by integration over the corresponding force gradients.

The cytoskeleton is a complex polymer network that plays an essential role in the functionality of eukaryotic cells. It endows cells with mechanical stability, adaptability, and motility. To identify and understand the mechanisms underlying this large variety of capabilities and to possibly transfer them to engineered networks makes it necessary to have in vitro and in silico model systems of the cytoskeleton. These models must be realistic representatives of the cellular network and at the same time be controllable and reproducible. Here, an approach to design complementary experimental and numerical model systems of the actin cytoskeleton is presented and some of their properties discussed.

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Human epithelial cancer cells are known to exhibit a reorganization of their keratin cytoskeleton and an attendant change in their elastic stiffness upon incubation with a natural lipid. The change in the keratin network was modeled and the model structures were computationally deformed using a Finite Element Method. The simulation results show a marked difference in the mechanical behavior of the cells for tensile and compressive loading conditions. In the former case, the elastic compliance increases in agreement with experimental findings. We interpret this increase by applying principles of structural engineering and suggest that cells may generally use these principles to regulate their cytoskeletal architecture.

In living eukaryotic cells a crosslinked network of polymer fibers, the cytoskeleton, endows the cells with structural integrity and mechanical stability and flexibility. To understand the mechanisms that are at the base of these functions, it is important to know in what way the microstructure and the mechanical behavior of the cytoskeleton change as a function of the type and the density of crosslinking molecules. To address this issue, we have developed a new modeling approach based on the discretization of polymeric fibers that are modeled as homogeneous straight beams in a constant volume. Crosslinks between adjacent fibers are taken into account by creating additional beams between the fibers if their spacing is smaller than a meaningful upper bound. By varying their geometrical and mechanical properties, the influence of the crosslinks on the shear modulus of the network can be studied systematically. Our simulations predict interesting new scaling behaviors that depend on the degree of crosslinking.Mater. Res. Soc. Symp. Proc. Vol. 975