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A linear regime of hysteresis for calculating the dynamic contact angle under low capillary numbers with displacement
Menggang Wen1, Da Lei1, Yun Li1
1School of Chemical Engineering and Technology, Xi'an Jiaotong University, Xi'an, Shaanxi 710049, China.
Hypothesis:
Determining capillary pressures and permeation resistances of multiphase seepage in porous-type reservoirs is crucial. The dynamic contact angle (CA) is one of the critical parameters used to calculate capillary pressures and permeation resistances. Under reservoir conditions, dynamic CAs are rate-independent of the triple-phase contact line velocity. Calculating rate-independent dynamic CAs remains challenging and is the main focus of this paper.
Experiments:
An experimental system was designed to capture the dynamic CAs of liquid-fluid displacements in microscale polydimethylsiloxane (PDMS) microchannels. These microchannels were 20 × 80 μm or 20 × 40 μm in height and width. The capillary numbers (Ca) were controlled to satisfy the conditions of Ca < 4 × 10-5 for liquid-air displacements and Ca < 3.5 × 10-7 for liquid-liquid displacements.
Findings:
Since pinning forces were consistent at the receding interface and the advancing interface, energy barriers exhibited symmetry. However, CA hysteresis exhibited asymmetry. Based on our experiments, a linear regime of hysteresis was developed and verified to be consistent with others' experiments. The relation can be used to calculate hysteresis strengths and rate-independent CAs. This model was also compared with the fractal model. The hysteresis factor in this model can be derived using the Wenzel factor r and the Cassie fraction ϕs.
