Stokes Flow Before a Plane Boundary With Mixed Stick-Slip Boundary Conditions
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摘要: 对具有粘滑混合边界条件的平面边界,建立一个Stokes流动的一般性定理,利用双调和函数A与调和函数B,表示了3维Stokes流动的速度场和压力场.关于无滑动平面边界前Stokes流动的早期定理,成为该一般性定理的一个特例.进一步地,从一般性定理导出了一个推论,根据该Stokes流函数,给出了粘滑边界条件时刚性平面轴对称Stokes流动问题的解,得到了流体作用在边界上的牵引力和扭矩公式.给出了一个说明性的例子.Abstract: A general theorem for Stokes flow about a plane boundary with mixed stick-slip boundary conditions was established.This was done by making use of a representation for the velocity and pressure fields in three-dimensional Stokes flow,in terms of a biharmonic function A and a harmonic function B. The earlier theorem on Stokes flow before a no-slip plane boundary was shown to be a special case of the present theorem.Furthermore,a corollary of the theorem was also derived which offers the solution to a problem of axisymmetric Stokes flow about a rigid plane with stick-slip boundary conditions,in terms of the Stokes stream function.The formulae for the drag and torque exerted by the fluid on the boundary were found.An illustrative example was given.
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[1] 阿克塔 N,冉赫曼 F,森 S K. 平面边界前Stokes流动基本的奇异性[J]. 应用数学和力学,2004, 25(7): 729-734. (Akhtar N, Rahman F, Sen S K. Stokes flow due to fundamental singularities before a plane boundary[J]. Applied Mathematics and Mechanics(English Edition), 2004, 25(7): 799-805.) [2] Happel J, Brenner H. Low Reynolds Number Hydrodynamics[M]. 4th print. Dordrecht: Martinus Nijhoff Publishers, 1986: 71-77. [3] Collins W D. Note on a sphere theorem for the axisymmetric Stokes flow of a viscous fluid[J]. Mathematika, 1958, 5(2): 118-121. doi: 10.1112/S0025579300001431 [4] Aderogba K. On Stokeslets in a two-fluid space[J]. Journal of Engineering Mathematics, 1976, 10(2): 143-151. doi: 10.1007/BF01535657 [5] Padmavathi B S, Amaranath T, Nigam S D. Stokes flow past a sphere with mixed slip-stick boundary conditions[J]. Fluid Dynamics Research, 1993, 11(5): 229-234. doi: 10.1016/0169-5983(93)90113-O [6] Palaniappan D, Nigam S D, Amaranath T, Usha R. Lamb’s solution of Stokes’s equations: a sphere theorem[J]. The Quarterly Journal of Mechanics and Applied Mathematics, 1992, 45(1): 47-56. doi: 10.1093/qjmam/45.1.47 [7] Schmitz R, Felderhof B U. Creeping flow about a sphere[J]. Physica A, 1978, 92(3/4): 423-437. doi: 10.1016/0378-4371(78)90141-3 [8] Raja Sekhar G P, Tejeswara Rao K, Padmavathi B S, Amaranath T. Two-dimensional Stokes flows with slip-stick boundary conditions[J]. Mechanics Research Communications, 1995, 22(5): 491- 501. doi: 10.1016/0093-6413(95)00053-T [9] Palaniappan D, Daripa P. Interior Stokes flows with stick-slip boundary conditions[J]. Physica A, 2001, 297(1/2): 37-63. [10] Palaniappan D, Daripa P. Exterior Stokes flows with stick-slip boundary conditions[J]. Zeitschrift für Angewandte Mathematik und Physik, 2002, 53(2): 281-307. doi: 10.1007/s00033-002-8156-5 [11] Basset A B. A Treatise on Hydrodynamics[M]. Vol 2. New York: Dover, 1961: 271. [12] Lamb H. Hydrodynamics[M]. 6th ed. New York, Dover: Dover Publications, 1945: 576, 597-604. [13] Batchelor G K. An Introduction to Fluid Dynamics[M]. London, N W: Cambridge University Press, 1967, 1: 600-602. [14] Sneddon I N. Elements of Partial Differential Equations[M]. Singapore: McGraw-Hill Book Co, 1985: 159. [15] Stimson M, Jeffery G B. The motion of two spheres in a viscous fluid[J]. Proceedings of the Royal Society of London, Series A, 1926, 111(757): 110-116. doi: 10.1098/rspa.1926.0053 [16] Collins W D. A note on Stokes’s stream function for the slow steady motion of viscous fluid before plane and spherical boundaries[J]. Mathematika, 1954, 1(2): 125-130. doi: 10.1112/S0025579300000607 [17] Spiegel M R. Theory and Problems of Advanced Calculus[M]. McGraw Hill, Inc, 1963: 260-261.
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