arXiv subjects
Publications and source records attributed to M. Schindler.
We study the properties of correlation matrices widely used in the characterisation of vibrational modes in colloidal materials. We show that the eigenvectors in the middle of the spectrum are strongly mixed, but that at both the top and the bottom of the spectrum it is possible to extract a good approximation to the true eigenmodes of an elastic system.
We consider the theory of fluctuations of a colloidal solid observed in a confocal slice. For a cubic crystal we study the evolution of the projected elastic properties as a function of the anisotropy of the crystal using numerical methods based on the fast Fourier transform. In certain situations of high symmetry we find exact analytic results for the projected fluctuations.
We investigate theoretically the onset of capillary-gravity waves created by a small object moving at the water-air interface. It is well established that, for straight uniform motion, no steady waves appear at velocities below the minimum phase velocity $c_\text{min} = 23 {\rm cm/s}$. At higher velocities the emission of capillary-gravity waves creates an additional drag force. The behavior of this force near the critical velocity is still poorly understood. A linear response theory where the object is replaced by an effective pressure source predicts a singular behavior for the wave drag. However, experimental data tends to indicate a more continuous transition. In this article, we show that a proper treatment of the flow equations around the obstacle can regularize wave emission, even in the linear wave approximation, thereby ensuring a continuous behavior of the drag force.
We propose a simple model to analyze the traffic of droplets in microfluidic ``dual networks''. Such functional networks which consist of two types of channels, namely those accessible or forbidden to droplets, often display a complex behavior characteristic of dynamical systems. By focusing on three recently proposed configurations, we offer an explanation for their remarkable behavior. Additionally, the model allows us to predict the behavior in different parameter regimes. A verification will clarify fundamental issues, such as the network symmetry, the role of the driving conditions, and of the occurrence of reversible behavior. The model lends itself to a fast numerical implementation, thus can help designing devices, identifying parameter windows where the behavior is sufficiently robust for a devices to be practically useful, and exploring new functionalities.
A finite-element algorithm for computing free-surface flows driven by arbitrary body forces is presented. The algorithm is primarily designed for the microfluidic parameter range where (i) the Reynolds number is small and (ii) force-driven pressure and flow fields compete with the surface tension for the shape of a stationary free surface. The free surface shape is represented by the boundaries of finite elements that move according to the stress applied by the adjacent fluid. Additionally, the surface tends to minimize its free energy and by that adapts its curvature to balance the normal stress at the surface. The numerical approach consists of the iteration of two alternating steps: The solution of a fluidic problem in a prescribed domain with slip boundary conditions at the free surface and a consecutive update of the domain driven by the previously determined pressure and velocity fields. ...
The flow profile in a capillary gap and the pumping efficiency of an acoustic micropump employing Surface Acoustic Waves is investigated both experimentally and theoretically. Such ultrasonic surface waves on a piezoelectric substrate strongly couple to a thin liquid layer and generate an internal streaming within the fluid. Such acoustic streaming can be used for controlled agitation during, e.g., microarray hybridization. We use fluorescence correlation spectroscopy and fluorescence microscopy as complementary tools to investigate the resulting flow profile. The velocity was found to depend on the applied power somewhat weaker than linearly and to decrease fast with the distance from the ultrasound generator on the chip.