Models for thin viscous sheets

European Journal of Applied Mathematics - Tập 7 Số 4 - Trang 321-343 - 1996
P. D. Howell1
1Mathematical Institute, 24–29 St. Giles, Oxford, UK

Tóm tắt

Leading-order equations governing the dynamics of a two-dimensional thin viscous sheet are derived. The inclusion of inertia effects is found to result in an ill-posed model when the sheet is compressed, and the resulting paradox is resolved by rescaling the equations over new length-and timescales which depend on the Reynolds number of the flow and the aspect ratio of the sheet. Physically this implies a dominant lengthscale for transverse displacements during viscous buckling. The theory is generalized to give new models for fully three-dimensional sheets.

Từ khóa


Tài liệu tham khảo

10.1137/0150090

10.1017/S0022112096000055

10.1063/1.868260

10.1017/S0022112075001279

10.1122/1.549679

10.1017/S0022112092003094

10.1093/qjmam/47.4.541

Myers, 1995, OCIAM report

10.1063/1.857549

10.1137/S0036139993256138

10.1137/0149059

10.1017/S0022112088002502

10.1103/PhysRevLett.71.3458

10.1017/S002211209500156X

Kreyszig, 1959, Differential Geometry, 10.3138/9781487589455

Love, 1927, A Treatise on the Mathematical Theory of Elasticity

Howell P. D. (1994) Extensional thin layer flows. D.Phil, thesis, University of Oxford.

10.1017/S0022112070000010

10.1017/S0022112070001507

Thông tin
Thông tin xuất bản

European Journal of Applied Mathematics

Tập 7 Số 4

321-343

Thông tin tác giả