TY - JOUR
T1 - Variational approach for Stokes flow through a two-dimensional non-uniform channel
AU - Banerjee, Abhishek
AU - Oron, Alexander
AU - Agnon, Yehuda
N1 - Publisher Copyright:
© The Author(s) 2024.
PY - 2024/12
Y1 - 2024/12
N2 - A variational approach is proposed to study the Stokes flow in a two-dimensional non-uniform channel. By using the stationarity of the Lagrangian, the Euler-Lagrange equations are established which leads to a simple set of ordinary differential equations to provide an estimate for the average pressure drop explicitly in terms of the channel shape function. The results for the pressure drop show an excellent agreement with the second-order extended lubrication theory. A higher-order formulation further improves the accuracy of the results for the pressure drop along the channel.
AB - A variational approach is proposed to study the Stokes flow in a two-dimensional non-uniform channel. By using the stationarity of the Lagrangian, the Euler-Lagrange equations are established which leads to a simple set of ordinary differential equations to provide an estimate for the average pressure drop explicitly in terms of the channel shape function. The results for the pressure drop show an excellent agreement with the second-order extended lubrication theory. A higher-order formulation further improves the accuracy of the results for the pressure drop along the channel.
KW - Euler-Lagrange equation
KW - Finite volume method
KW - Stokes flow
KW - Variational calculus
UR - http://www.scopus.com/inward/record.url?scp=85197716797&partnerID=8YFLogxK
U2 - 10.1038/s41598-024-66500-4
DO - 10.1038/s41598-024-66500-4
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AN - SCOPUS:85197716797
SN - 2045-2322
VL - 14
JO - Scientific Reports
JF - Scientific Reports
IS - 1
M1 - 15689
ER -