Non-isothermal Capillary Imbibition of Power-law Fluids in a Hele-Shaw Cell: Scaling Laws and Governing Dimensionless Parameters

Non-isothermal capillary imbibition of non-Newtonian fluids in confined geometries is relevant to enhanced oil recovery, geothermal systems, microfluidics, and industrial transport in fracture-like channels. A lubrication-based framework is developed for capillary imbibition of power-law fluids in a Hele--Shaw cell under externally imposed temperature gradients. The temperature field is treated as a prescribed linear profile, and the energy equation is not solved. Two governing dimensionless parameters emerge naturally from the analysis: the Thermocapillary Gradient Number  and the Thermo-rheological Number , which characterize the competition between thermocapillary effects and thermo-rheological modulation. Their ratio depends exclusively on fluid properties and identifies the dominant transport mechanism. For the CMC solutions studied, For the CMC solutions studied, all experiments fall in the vicinity of the crossing regime 𝒩_TR ≈ |𝒩_TC|, where thermocapillary and thermo-rheological effects contribute with comparable magnitude. The analysis further demonstrates that the scaling exponent remains primarily governed by the flow behavior index, whereas thermal gradients strongly modify the imbibition prefactor and therefore the transport intensity. Scaling predictions are corroborated experimentally using CMC polymer solutions under isothermal, favorable, and adverse thermal gradients, with deviations below ۱۰%. The proposed dimensionless framework provides practical scaling criteria for thermally modulated capillary transport of generalized Newtonian fluids in confined geometries.

کلیدواژه ها:

Capillary imbibition ، Hele-Shaw cell ، Power-law fluids ، Lubrication theory ، Thermocapillary flow ، Non-isothermal flow ، Scaling laws ، Dimensionless parameters