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Volume 17, Issue 4
Stokes Flows Imposed Constant Navier Slip Length on Boundary for Domains of Simple Geometry

Zhan-Rui Qiu & Wei-Dong Su

Adv. Appl. Math. Mech., 17 (2025), pp. 1171-1203.

Published online: 2025-05

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  • Abstract

In micro-nano and even some macro-scale flows, the boundary slip cannot be ignored and has an important influence. We consider the most widely used Navier slip length model to investigate whether the solution of Stokes flow exists if a homogeneous slip is imposed as a boundary condition replacing the ordinary Dirichlet condition of velocity for some domains of simple geometries, including the two-dimensional channel, plane annulus and axisymmetric circular pipe. The Fourier series is employed to obtain the exact solutions formulated by the stream function. While a unique solution exists for most cases, it is found that yet occurs the cases of no solution under a certain slip length and infinitely multiple solutions under an infinitely discrete set of slip lengths, respectively.

  • AMS Subject Headings

76D07, 31A30, 35J40

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-17-1171, author = {Qiu , Zhan-Rui and Su , Wei-Dong}, title = {Stokes Flows Imposed Constant Navier Slip Length on Boundary for Domains of Simple Geometry}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2025}, volume = {17}, number = {4}, pages = {1171--1203}, abstract = {

In micro-nano and even some macro-scale flows, the boundary slip cannot be ignored and has an important influence. We consider the most widely used Navier slip length model to investigate whether the solution of Stokes flow exists if a homogeneous slip is imposed as a boundary condition replacing the ordinary Dirichlet condition of velocity for some domains of simple geometries, including the two-dimensional channel, plane annulus and axisymmetric circular pipe. The Fourier series is employed to obtain the exact solutions formulated by the stream function. While a unique solution exists for most cases, it is found that yet occurs the cases of no solution under a certain slip length and infinitely multiple solutions under an infinitely discrete set of slip lengths, respectively.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2023-0327}, url = {http://global-sci.org/intro/article_detail/aamm/24058.html} }
TY - JOUR T1 - Stokes Flows Imposed Constant Navier Slip Length on Boundary for Domains of Simple Geometry AU - Qiu , Zhan-Rui AU - Su , Wei-Dong JO - Advances in Applied Mathematics and Mechanics VL - 4 SP - 1171 EP - 1203 PY - 2025 DA - 2025/05 SN - 17 DO - http://doi.org/10.4208/aamm.OA-2023-0327 UR - https://global-sci.org/intro/article_detail/aamm/24058.html KW - Stokes flow, boundary condition, slip length, no solution, multiple solution. AB -

In micro-nano and even some macro-scale flows, the boundary slip cannot be ignored and has an important influence. We consider the most widely used Navier slip length model to investigate whether the solution of Stokes flow exists if a homogeneous slip is imposed as a boundary condition replacing the ordinary Dirichlet condition of velocity for some domains of simple geometries, including the two-dimensional channel, plane annulus and axisymmetric circular pipe. The Fourier series is employed to obtain the exact solutions formulated by the stream function. While a unique solution exists for most cases, it is found that yet occurs the cases of no solution under a certain slip length and infinitely multiple solutions under an infinitely discrete set of slip lengths, respectively.

Qiu , Zhan-Rui and Su , Wei-Dong. (2025). Stokes Flows Imposed Constant Navier Slip Length on Boundary for Domains of Simple Geometry. Advances in Applied Mathematics and Mechanics. 17 (4). 1171-1203. doi:10.4208/aamm.OA-2023-0327
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