Capillary imbibition in a square tube.

Area of Science:

• Fluid dynamics
• Capillary phenomena
• Materials science

Background:

• Liquid behavior in confined geometries like square tubes involves corner wetting and distinct bulk and finger-like wetted regions.
• Previous studies analyzed the growth of these bulk and finger parts of liquid imbibition separately.
• Understanding the interplay between these regions is crucial for predicting fluid transport in porous media.

Purpose of the Study:

• To analyze the coupled growth of bulk and finger regions during liquid imbibition in a square tube.
• To develop and propose coupled equations that account for the interaction between the two wetted regions.
• To investigate how this coupling affects the dynamics of liquid penetration.

Main Methods:

• Development of coupled mathematical equations for liquid imbibition in both bulk and finger regions.
• Theoretical analysis of the proposed coupled equations.
• Comparison of results with previous models that treated the regions independently.

Main Results:

• Both the bulk part (h0) and the finger part (h1) of the liquid penetration increase with time (t) following Lucas-Washburn's law (h ∼ t1/2).
• The coefficients governing the growth rate in the coupled model differ from those in uncoupled models.
• Explicitly accounting for the coupling modifies the predicted imbibition rates for both regions.

Conclusions:

• The growth dynamics of bulk and finger regions in liquid imbibition within square tubes are interconnected.
• Coupled equations provide a more accurate description of liquid imbibition compared to separate analyses.
• The findings highlight the importance of considering inter-region coupling for accurate modeling of capillary-driven fluid flow.