When solute molecules in a liquid evaporate at the surface, concentration gradients can lead to surface tension gradients and provoke fluid convection at the interface, a phenomenon commonly known as the Marangoni effect. Here, we demonstrate that minute quantities of ethanol in concentrated sodium hydroxide solution can induce pronounced and long-lasting Marangoni flow upon evaporation at room temperature. By employing particle image velocimetry and gravimetric analysis, we show that the mean interfacial speed of the evaporating solution sensitively increases with the evaporation rate for ethanol concentrations lower than 0.5 mol %. Placing impermeable objects near the liquid-gas interface enforces steady concentration gradients, thereby promoting the formation of stationary flows. This allows for contact-free control of the flow pattern as well as its modification by altering the objects shape. Analysis of bulk flows reveals that the energy of evaporation in the case of stationary flows is converted to kinetic fluid energy with high efficiency, but reducing the sodium hydroxide concentration drastically suppresses the observed effect to the point where flows become entirely absent. Investigating the properties of concentrated sodium hydroxide solution suggests that ethanol dissolution in the bulk is strongly limited. At the surface, however, the co-solvent is efficiently stored, enabling rapid adsorption or desorption of the alcohol depending on its concentration in the adjacent gas phase. This facilitates the generation of large surface tension gradients and, in combination with the perpetual replenishment of the surface ethanol concentration by bulk convection, to the generation of long-lasting, self-sustaining flows.

Purpose: Inverse problems are often marked by highly dimensional state vectors. The high dimension affects the quality of the estimation result as well as the computational complexity of the estimation problem. This paper aims to present a state reduction technique based on prior knowledge. Design/methodology/approach: Ill-posed inverse problems require prior knowledge to find a stable solution. The prior distribution is constructed for the high-dimensional data space. The authors use the prior distribution to construct a reduced state description based on a lower-dimensional basis, which they derive from the prior distribution. The approach is tested for the inverse problem of electrical capacitance tomography. Findings: Based on a singular value decomposition of a sample-based prior distribution, a reduced state model can be constructed, which is based on principal components of the prior distribution. The approximation error of the reduced basis is evaluated, showing good behavior with respect to the achievable data reduction. Owing to the structure, the reduced state representation can be applied within existing algorithms. Practical implications: The full state description is a linear function of the reduced state description. The reduced basis can be used within any existing reconstruction algorithm. Increased noise robustness has been found for the application of the reduced state description in a back projection-type reconstruction algorithm. Originality/value: The paper presents the construction of a prior-based state reduction technique. Several applications of the reduced state description are discussed, reaching from the use in deterministic reconstruction methods up to proposal generation for computational Bayesian inference, e.g. Markov chain Monte Carlo techniques.

Pneumatic conveying is a standard transportation technique for bulk materials in various industrial fields. Flow metering is crucial for the efficient and reliable operation of such systems and for process control. Capacitive measurement systems are often proposed for this application. In this method, electrodes are placed on the conveyor systems transport line and capacitive signals are sensed. The design of the sensor with regard to the arrangement and the number of electrodes as well as the evaluation of the capacitive sensor signals can be divided into two categories. Calibration-based flow meters use regression methods for signal processing, which are parametrized from calibration measurements on test rigs. Their performance is limited by the extend of the calibration measurements. Electrical capacitance tomography based flow meters use model-based signal processing techniques to obtain estimates about the spatial material distribution within the sensor. In contrast to their calibration-based counterparts, this approach requires more effort with respect to modeling and instrumentation, as typically a larger number of measurement signals has to be acquired. In this work we present a comparative analysis of the two approaches, which is based on measurement experiments and a holistic system model for flow metering. For the model-based analysis Monte Carlo simulations are conducted, where randomly generated pneumatic conveying flow patterns are simulated to analyze the sensor and algorithm behavior. The results demonstrate the potential benefit of electrical capacitance tomography based flow meters over a calibration-based instrument design.

We investigated the long-term dynamics of a turbulent, submerged jet at Re = 16 400 to develop a strategy for data-assisted, fast calculations of passive species transport. We obtained our data from high-fidelity large eddy simulations LES, which we validated against in-house particle image velocimetry measurements. The flow was split into coherent and incoherent fields using the method of proper orthogonal decomposition (POD). Depending on the number of POD modes to construct coherent velocity fields, different patterns in the recurrence plot of the system were found. For low mode numbers, line segments parallel to the main diagonal were present, which indicated that close states evolved similarly for a finite duration. Strong turbulent fluctuations in the original velocity fields, on the other hand, hid any large-scale recurrences and caused a structureless recurrence statistics. Using an iterated method of analogs, we time-extrapolated a short time series of coherent, distinctly recurring velocity fields of $50\mathrm{s}$ to $250\mathrm{s}$ and performed a study of species transport. We found that coherent dynamics alone could not reproduce LES results due to the lack of turbulent, small-scale fluctuations, but already a small set of incoherent flow fields sufficed to cure this shortcoming considerably. Surprisingly, time extrapolation of the original database without decomposition and without any obvious recurrences led to the best results in very close agreement with LES but with high demands regarding memory. Our data-assisted simulations outperformed LES on the same computational mesh by a speed-up factor of 15.