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Dynamical scaling of imbibition in columnar geometries

Journal: Physical Review E
Year: 2008   Volume: 77
Initial page: 57305  
Status: Published
In this status since: 9 May 2008
PDF file: 2008_pradas_pre.pdf
DOI: 10.1103/PhysRevE.77.056305
Pradas M., Hernandez-Machado A.,

Recent experiments on imbibition in columnar geometries show interfacial fluctuations whose dynamic scaling is not compatible with the usual nonlocal model governed by surface tension that results from a macroscopic description. To explore this discrepancy, we exhaustively analyze numerical integrations of a phase-field model with dichotomic columnar disorder. We find that two distinct behaviors are possible depending on the capillary contrast between the two values of disorder. In a high-contrast case, where interface evolution is mainly dominated by the disorder, an inherent anomalous scaling is always observed. Moreover, in agreement with experimental work, the interface motion has to be described through a local model. On the other hand, in a lower-contrast case, the interface is dominated by interfacial tension and can be well modeled by a nonlocal model. We have studied both spontaneous and forced-flow imbibition situations, giving a complete set of scaling exponents in each case, as well as a comparison to the experimental results.