We consider the stationary motion of a viscous incompressible fluid in a two-dimensional exterior domain; we prove that the problem has a solution for small values of the flux of the boundary datum through the boundary. (2000). 35Q30, 76D03, 76D05.
Mathematics Subject Classification
A new thermographic methodology for measuring the thermal diffusivity of a platelike sample is presented. In particular, the study of the time evolution of the spatial distribution of the surface temperature of the rear face of the plate (after heating its front surface by a flash Gaussian shaped source) enables to determine the in-plane thermal diffusivity. This technique is applied to an AISI304 stainless steel plate and the results are compared with literature value and with the value obtained on the same material by using Thermal Wave Interferometry.
A classical result of Amick (Acta Math 161:71-130, 1988) on the nontriviality of the symmetric Leray solutions of the steady-state Navier-Stokes equations in the plane is extended to Lipschitz domains. This results is compared with the famous Stokes paradox of linearized hydrodynamics and applied to a mixed problem of some interest in the applications.
Numerical simulations have unexplored potential in the study of droplet impact on non-uniform wettability surfaces. In this work, we compare numerical and experimental results to investigate the application potential of a Volume of Fluid method utilized in OpenFOAM®. The approach implements the Kistler model for the dynamic contact angle of impacting droplets. We begin with an investigation on the influence of the most important solver parameters in order to optimize the computational setup and reach the best compromise between computational cost and solution errors, as assessed in comparison to experimental results. Next, we verify the accuracy of the predictions for droplet impact on uniformly hydrophilic or superhydrophobic surfaces. Benchmarking the maximal spreading factor, contact and spreading times, as well as contact-line behavior, we show strong agreement between the present numerical results and the models of Pasandideh-Fard et al. (1996) and Clanét et al. (2004). Lastly, we demonstrate the capability of the model to accurately predict outcome behaviors of droplets striking distributed-wettability surfaces, which introduce 3-D outcome characteristics, even in orthogonal impact. The model successfully predicts droplet splitting and vectoring, as reported in the experiments of Schutzius et al. (2014). Finally, we demonstrate a configuration wherein a spreading droplet becomes arrested within a disc of higher wettability than its surrounding domain. The main contribution of the present work is a numerical model capable of accurately simulating droplet impact on spatially non-uniform wettability patterns of any foreseeable design.
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