The Casimir effect: from quantum to critical fluctuations

The Casimir effect in quantum electrodynamics (QED) is perhaps the best-known example of fluctuation-induced long-ranged force acting on objects (conducting plates) immersed in a fluctuating medium (quantum electromagnetic field in vacuum). A similar effect emerges in statistical physics, where the force acting, e.g., on colloidal particles immersed in a binary liquid mixture is affected by the classical thermal fluctuations occurring in the surrounding medium. The resulting Casimir-like force acquires universal features upon approaching a critical point of the medium and becomes long-ranged at criticality. In turn, this universality allows one to investigate theoretically the temperature dependence of the force via representative models and to stringently test the corresponding predictions in experiments. In contrast to QED, the Casimir force resulting from critical fluctuations can be easily tuned with respect to strength and sign by surface treatments and temperature control. We present some recent advances in the theoretical study of the universal properties of the critical Casimir force arising in thin films. The corresponding predictions compare very well with the experimental results obtained for wetting layers of various fluids. We discuss how the Casimir force between a colloidal particle and a planar wall immersed in a binary liquid mixture has been measured with femto-Newton accuracy, comparing these experimental results with the corresponding theoretical predictions.Comment: Talk delivered at the International Workshop "60 Years of Casimir Effect", Brasilia, 23-27 June 2008 (17 pages, 7 figures

Critical Casimir forces between homogeneous and chemically striped surfaces

Recent experiments have measured the critical Casimir force acting on a colloid immersed in a binary liquid mixture near its continuous demixing phase transition and exposed to a chemically structured substrate. Motivated by these experiments, we study the critical behavior of a system, which belongs to the Ising universality class, for the film geometry with one planar wall chemically striped, such that there is a laterally alternating adsorption preference for the two species of the binary liquid mixture, which is implemented by surface fields. For the opposite wall we employ alternatively a homogeneous adsorption preference or homogeneous Dirichlet boundary conditions, which within a lattice model are realized by open boundary conditions. By means of mean-field theory, Monte Carlo simulations, and finite-size scaling analysis we determine the critical Casimir force acting on the two parallel walls and its corresponding universal scaling function. We show that in the limit of stripe widths small compared with the film thickness, on the striped surface the system effectively realizes Dirichlet boundary conditions, which generically do not hold for actual fluids. Moreover, the critical Casimir force is found to be attractive or repulsive, depending on the width of the stripes of the chemically patterned surface and on the boundary condition applied to the opposing surface.Comment: 29 pages, 29 figures; v2: 29 pages, 31 figures, two new figures, added comparison with chemical-step estimate

Inter-cycle variability of ignition delay in an ethanol fumigated common rail diesel engine

An experimental study has been performed to investigate the ignition delay of a modern heavy-duty common-rail diesel engine run with fumigated ethanol substitutions up to 40% on an energy basis. The ignition delay was determined through the use of statistical modelling in a Bayesian framework this framework allows for the accurate determination of the start of combustion from single consecutive cycles and does not require any differentiation of the in-cylinder pressure signal. At full load the ignition delay has been shown to decrease with increasing ethanol substitutions and evidence of combustion with high ethanol substitutions prior to diesel injection have also been shown experimentally and by modelling. Whereas, at half load increasing ethanol substitutions have increased the ignition delay. A threshold absolute air to fuel ratio (mole basis) of above ~110 for consistent operation has been determined from the inter-cycle variability of the ignition delay, a result that agrees well with previous research of other in-cylinder parameters and further highlights the correlation between the air to fuel ratio and inter-cycle variability. Numerical modelling to investigate the sensitivity of ethanol combustion has also been performed. It has been shown that ethanol combustion is sensitive to the initial air temperature around the feasible operating conditions of the engine. Moreover, a negative temperature coefficient region of approximately 900{1050 K (the approximate temperature at fuel injection) has been shown with for n-heptane and n-heptane/ethanol blends in the numerical modelling. A consequence of this is that the dominate effect influencing the ignition delay under increasing ethanol substitutions may rather be from an increase in chemical reactions and not from in-cylinder temperature. Further investigation revealed that the chemical reactions at low ethanol substitutions are different compared to the high (> 20%) ethanol substitutions