The framework for deriving tensorial interfacial dielectric profiles from bound charge distributions is established and applied to molecular dynamics simulations of water at hydrophobic and hydrophilic surfaces. In conjunction with a modified Poisson-Boltzmann equation, the trend of experimental double-layer capacitances is well reproduced. We show that the apparent Stern layer can be understood in terms of the dielectric profile of pure water.

We derive the theoretical framework to calculate the dielectric response tensor and determine its components for water adjacent to hydrophilic and hydrophobic surfaces using molecular dynamics simulations. For the nonpolarizable water model used, linear response theory is found to be applicable up to an external perpendicular field strength of ∼2 V/nm, which is well beyond the experimental dielectric breakdown threshold. The dipole contribution dominates the dielectric response parallel to the interface, whereas for the perpendicular component it is essential to keep the quadrupole and octupole terms. Including the space-dependent dielectric function in a mean-field description of the ion distribution at a single charged interface, we reproduce experimental values of the interfacial capacitance. At the same time, the dielectric function decreases the electrostatic part of the disjoining pressure between two charged surfaces, unlike previously thought. The difference in interfacial polarizability between hydrophilic and hydrophobic surfaces can be quantized in terms of the dielectric dividing surface. Using the dielectric dividing surface and the Gibbs dividing surface positions to estimate the free energy of a single ion close to an interface, ion-specific adsorption effects are found to be more pronounced at hydrophobic surfaces than at hydrophilic surfaces, in agreement with experimental trends.

Cell membranes are vital to shield a cell's interior from the environment. At the same time they determine to a large extent the cell's mechanical resistance to external forces. In recent years there has been considerable interest in the accurate computational modeling of such membranes, driven mainly by the amazing variety of shapes that red blood cells and model systems such as vesicles can assume in external flows. Given that the typical height of a membrane is only a few nanometers while the surface of the cell extends over many micrometers, physical modeling approaches mostly consider the interface as a two-dimensional elastic continuum. Here we review recent modeling efforts focusing on one of the computationally most intricate components, namely the membrane's bending resistance. We start with a short background on the most widely used bending model due to Helfrich. While the Helfrich bending energy by itself is an extremely simple model equation, the computation of the resulting forces is far from trivial. At the heart of these difficulties lies the fact that the forces involve second order derivatives of the local surface curvature which by itself is the second derivative of the membrane geometry. We systematically derive and compare the different routes to obtain bending forces from the Helfrich energy, namely the variational approach and the thin-shell theory. While both routes lead to mathematically identical expressions, so-called linear bending models are shown to reproduce only the leading order term while higher orders differ. The main part of the review contains a description of various computational strategies which we classify into three categories: the force, the strong and the weak formulation. We finally give some examples for the application of these strategies in actual simulations.

Red blood cells flowing through capillaries assume a wide variety of different shapes owing to their high deformability. Predicting the realized shapes is a complex field as they are determined by the intricate interplay between the flow conditions and the membrane mechanics. In this work we construct the shape phase diagram of a single red blood cell with a physiological viscosity ratio flowing in a microchannel. We use both experimental in vitro measurements as well as 3D numerical simulations to complement the respective other one. Numerically, we have easy control over the initial starting configuration and natural access to the full 3D shape. With this information we obtain the phase diagram as a function of initial position, starting shape and cell velocity. Experimentally, we measure the occurrence frequency of the different shapes as a function of the cell velocity to construct the experimental diagram which is in good agreement with the numerical observations. Two different major shapes are found, namely croissants and slippers. Notably, both shapes show coexistence at low (<1 mm s) and high velocities (>3 mm s) while in-between only croissants are stable. This pronounced bistability indicates that RBC shapes are not only determined by system parameters such as flow velocity or channel size, but also strongly depend on the initial conditions.

In this paper we study the transient surface cavity which is created by the controlled impact of a disk of radius h 0 on a water surface at Froude numbers below 200. The dynamics of the transient free surface is recorded by high-speed imaging and compared to boundary integral simulations giving excellent agreement. The flow surrounding the cavity is measured with high-speed particle image velocimetry and is found to also agree perfectly with the flow field obtained from the simulations.We present a simple model for the radial dynamics of the cavity based on the collapse of an infinite cylinder. This model accounts for the observed asymmetry of the radial dynamics between the expansion and the contraction phases of the cavity. It reproduces the scaling of the closure depth and total depth of the cavity which are both found to scale roughly as ∝ Fr 1/2 with a weakly Froude-number-dependent prefactor. In addition, the model accurately captures the dynamics of the minimal radius of the cavity and the scaling of the volume V bubble of air entrained by the process, namely, V bubble /h 3 0 ∝ (1 + 0.26Fr 1/2 )Fr 1/2 . † Present address: