Volume 3, Issue 3
Inverse Temperature Reconstruction in Thermocapillary-Driven Thin Liquid Films

MATHIEU SELLIER AND SATYANANDA PANDA

Int. J. Numer. Anal. Mod. B,3 (2012), pp. 285-296

Published online: 2012-03

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  • Abstract
A thin liquid film subject to a temperature gradient undergoes thermocapillary convection because of the non-uniform surface tension at the free surface. This induced flow perturbs the film free surface and generate a free surface velocity field. These observable consequences can be thought of as the “signature” of the imposed temperature field and this work investigates whether the temperature field can be reconstructed from this signature for general three-dimensional flows. Using a model based on the lubrication approximation, we show that one can explicitly formulate the partial differential equation which governs this inverse problem. This equation is solved using finite differences. We illustrates the feasibility of this reconstruction exercise on a set of “artificial” experimental data obtained by first solving the direct problem which consists in computing the free surface deformation and free surface velocity field for a given applied temperature field.
  • AMS Subject Headings

76T10 65L09

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COPYRIGHT: © Global Science Press

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@Article{IJNAMB-3-285, author = {MATHIEU SELLIER AND SATYANANDA PANDA}, title = {Inverse Temperature Reconstruction in Thermocapillary-Driven Thin Liquid Films}, journal = {International Journal of Numerical Analysis Modeling Series B}, year = {2012}, volume = {3}, number = {3}, pages = {285--296}, abstract = {A thin liquid film subject to a temperature gradient undergoes thermocapillary convection because of the non-uniform surface tension at the free surface. This induced flow perturbs the film free surface and generate a free surface velocity field. These observable consequences can be thought of as the “signature” of the imposed temperature field and this work investigates whether the temperature field can be reconstructed from this signature for general three-dimensional flows. Using a model based on the lubrication approximation, we show that one can explicitly formulate the partial differential equation which governs this inverse problem. This equation is solved using finite differences. We illustrates the feasibility of this reconstruction exercise on a set of “artificial” experimental data obtained by first solving the direct problem which consists in computing the free surface deformation and free surface velocity field for a given applied temperature field.}, issn = {}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnamb/284.html} }
TY - JOUR T1 - Inverse Temperature Reconstruction in Thermocapillary-Driven Thin Liquid Films AU - MATHIEU SELLIER AND SATYANANDA PANDA JO - International Journal of Numerical Analysis Modeling Series B VL - 3 SP - 285 EP - 296 PY - 2012 DA - 2012/03 SN - 3 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnamb/284.html KW - Inverse problem KW - Thin liquid film KW - Thermocapillary AB - A thin liquid film subject to a temperature gradient undergoes thermocapillary convection because of the non-uniform surface tension at the free surface. This induced flow perturbs the film free surface and generate a free surface velocity field. These observable consequences can be thought of as the “signature” of the imposed temperature field and this work investigates whether the temperature field can be reconstructed from this signature for general three-dimensional flows. Using a model based on the lubrication approximation, we show that one can explicitly formulate the partial differential equation which governs this inverse problem. This equation is solved using finite differences. We illustrates the feasibility of this reconstruction exercise on a set of “artificial” experimental data obtained by first solving the direct problem which consists in computing the free surface deformation and free surface velocity field for a given applied temperature field.
MATHIEU SELLIER AND SATYANANDA PANDA. (2012). Inverse Temperature Reconstruction in Thermocapillary-Driven Thin Liquid Films. International Journal of Numerical Analysis Modeling Series B. 3 (3). 285-296. doi:
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