TY - JOUR
T1 - Similarity solutions for early-time constant boundary flux imbibition in foams and soils
AU - Boakye-Ansah, Yaw Akyampon
AU - Grassia, Paul
PY - 2021/8/31
Y1 - 2021/8/31
N2 - The foam drainage equation and Richards equation are transport equations for foams and soils respectively. Each reduces to a nonlinear diffusion equation in the early stage of infiltration during which time, flow is predominantly capillary driven, hence is effectively capillary imbibition. Indeed such equations arise quite generally during imbibition processes in porous media. New early-time solutions based on the van Genuchten relative diffusivity function for soils are found and compared with the same for drainage in foams. The moisture profiles which develop when delivering a known flux into these various porous materials are sought. Solutions are found using the principle of self-similarity. Singular profiles that terminate abruptly are obtained for soils, a contrast with solutions obtained for node-dominated foam drainage which are known from literature (the governing equation being now linear is analogous to the linear equation for heat transfer). As time evolves, the moisture that develops at the top boundary when a known flux is delivered is greater in soils than in foams and is greater still in loamy soils than in sandstones. Similarities and differences between the various solutions for nonlinear and linear diffusion are highlighted.
AB - The foam drainage equation and Richards equation are transport equations for foams and soils respectively. Each reduces to a nonlinear diffusion equation in the early stage of infiltration during which time, flow is predominantly capillary driven, hence is effectively capillary imbibition. Indeed such equations arise quite generally during imbibition processes in porous media. New early-time solutions based on the van Genuchten relative diffusivity function for soils are found and compared with the same for drainage in foams. The moisture profiles which develop when delivering a known flux into these various porous materials are sought. Solutions are found using the principle of self-similarity. Singular profiles that terminate abruptly are obtained for soils, a contrast with solutions obtained for node-dominated foam drainage which are known from literature (the governing equation being now linear is analogous to the linear equation for heat transfer). As time evolves, the moisture that develops at the top boundary when a known flux is delivered is greater in soils than in foams and is greater still in loamy soils than in sandstones. Similarities and differences between the various solutions for nonlinear and linear diffusion are highlighted.
KW - similarity solutions
KW - early-time constant
KW - boundary flux inhibition
KW - foams
KW - soils
UR - https://www.springer.com/journal/10189?
U2 - 10.1140/epje/s10189-021-00112-y
DO - 10.1140/epje/s10189-021-00112-y
M3 - Article
VL - 44
JO - European Physical Journal E - Soft Matter
JF - European Physical Journal E - Soft Matter
SN - 1292-8941
IS - 9
M1 - 111
ER -