第36卷第5期 北京科技大学学报 Vol.36 No.5 2014年5月 Journal of University of Science and Technology Beijing May 2014 考虑固壁作用力的微可压缩流体纳微米圆管流动分析 张雪龄2，朱维耀”回，蔡强，刘启鹏)，王小锋”，娄钰” 1)北京科技大学土木与环境工程学院，北京1000832)清华大学材料科学与工程学院，北京100084 3)国土资源部油气资源战略研究中心，北京100034 ☒通信作者，E-mail:weiyaook@sina.com 摘要针对流体在纳微米尺度下的流体流动规律不符合泊肃叶规律的理论依据不足的难题，研究了纳微米圆管中流体的 流动，将流体的微可压缩和固壁对流体的作用同时考虑进来，并将固壁对流体的作用采用固壁作用力的形式引入到流体力学 方程，采用涡函数流函数将方程解耦，并用正则摄动法求得一阶精度的压力和速度的解析解。结果发现：固壁作用力导致零阶 径向压力的出现，一阶压力的增强和一阶速度的降低：量纲一的体积流量偏离了不可压缩流体的体积流量，偏离效应受流体 的微可压缩性和固壁作用力的共同影响.体积流量在同尺度下偏离泊肃叶流动的流量大小随着可压缩系数和流体中和壁面 产生作用的离子浓度增大而增大，随着纳微米圆管管径减小而增大，纳微米圆管管径低于某一尺寸时，流体将不能流动.通过 研究表明：纳微米尺度下产生微尺度效应的原因是流体的微可压缩性和壁面力的共同影响. 关键词纳微米管道：固壁作用力：可压缩流：涡函数：流函数：摄动法 分类号0357.3 Analysis of weakly compressible fluid flow in nano/micro-size circular tubes considering solid wall force ZHANG Xue-ling,ZHU Wei-yao,CAI Qiang,LIU Qi-peng,WANG Xiao-feng,LOU Yu 1)School of Civil and Environmental Engineering,University of Science and Technology Beijing,Beijing 100083,China 2)School of Material Science and Engineering,Tsinghua University,Beijing 100084,China 3)Strategie Research Center of Oil and Gas Resourees,Ministry of Land and Resourees,Beijing 100034,China Corresponding author,E-mail:weiyaook@sina.com ABSTRACT Aiming at the problem that fluid flow in nano/micro-size tubes deviates from the Hagen-Poiseuille law but the mecha- nism remains unclear to date,this paper focuses on fluid flowing in a nano/micro-size circular tube considering the weak compressibili- ty of the fluid and the tube wall action.The tube wall action was introduced into the momentum equations as a wall force,the hydrody- namic vorticity-stream equations were derived,and the first-order perturbation solutions of pressure and velocity were obtained.It is found that there exists zero-order radial pressure.Due to the influence of wall-fluid interaction,the first-order radial pressure increases and the first-order velocity decreases.The dimensionless volume flow rate deviates from an uncompressible fluid due to the compressi- bility of the fluid and the tube wall force.The deviation of the dimensionless volume flow rate from Poiseuille flow increases with the increasing of compressible coefficient and ion concentration in the liquid acted with the tube wall,and increases with the decreasing of the tube diameter.The liquid cannot flow when the tube diameter is less than a certain size.This paper reveals that the mirco-scale effect of nano/micro-size is resulted from the compressibility of the fluid and the tube wall force together. KEY WORDS nano/micro-size tubes:wall force:compressible flow:vorticity function:stream function:perturbation techniques 在纳微米孔道中的流体流动表现出微尺度效 应，即流速明显低于同尺度下的泊肃叶的流速，或者 收稿日期：2013-09-21 基金项目：国家重大基金资助项目(50934003,11372033)：教有部专项资金资助项目(FRF-MP-B12006B) DOI:10.13374/j.issn1001-053x.2014.05.001:http://journals.ustb.edu.cn第 36 卷 第 5 期 2014 年 5 月 北京科技大学学报 Journal of University of Science and Technology Beijing Vol． 36 No． 5 May 2014 考虑固壁作用力的微可压缩流体纳微米圆管流动分析 张雪龄1，2) ，朱维耀1) ，蔡 强2) ，刘启鹏1，3) ，王小锋1) ，娄 钰1) 1) 北京科技大学土木与环境工程学院，北京 100083 2) 清华大学材料科学与工程学院，北京 100084 3) 国土资源部油气资源战略研究中心，北京 100034  通信作者，E-mail: weiyaook@ sina． com 摘 要 针对流体在纳微米尺度下的流体流动规律不符合泊肃叶规律的理论依据不足的难题，研究了纳微米圆管中流体的 流动，将流体的微可压缩和固壁对流体的作用同时考虑进来，并将固壁对流体的作用采用固壁作用力的形式引入到流体力学 方程，采用涡函数流函数将方程解耦，并用正则摄动法求得一阶精度的压力和速度的解析解． 结果发现: 固壁作用力导致零阶 径向压力的出现，一阶压力的增强和一阶速度的降低; 量纲一的体积流量偏离了不可压缩流体的体积流量，偏离效应受流体 的微可压缩性和固壁作用力的共同影响． 体积流量在同尺度下偏离泊肃叶流动的流量大小随着可压缩系数和流体中和壁面 产生作用的离子浓度增大而增大，随着纳微米圆管管径减小而增大，纳微米圆管管径低于某一尺寸时，流体将不能流动． 通过 研究表明: 纳微米尺度下产生微尺度效应的原因是流体的微可压缩性和壁面力的共同影响． 关键词 纳微米管道; 固壁作用力; 可压缩流; 涡函数; 流函数; 摄动法 分类号 O 357. 3 Analysis of weakly compressible fluid flow in nano /micro-size circular tubes considering solid wall force ZHANG Xue-ling1，2) ，ZHU Wei-yao1)  ，CAI Qiang2) ，LIU Qi-peng1，3) ，WANG Xiao-feng1) ，LOU Yu1) 1) School of Civil and Environmental Engineering，University of Science and Technology Beijing，Beijing 100083，China 2) School of Material Science and Engineering，Tsinghua University，Beijing 100084，China 3) Strategic Ｒesearch Center of Oil and Gas Ｒesources，Ministry of Land and Ｒesources，Beijing 100034，China  Corresponding author，E-mail: weiyaook@ sina． com ABSTＲACT Aiming at the problem that fluid flow in nano /micro-size tubes deviates from the Hagen-Poiseuille law but the mecha￾nism remains unclear to date，this paper focuses on fluid flowing in a nano /micro-size circular tube considering the weak compressibili￾ty of the fluid and the tube wall action． The tube wall action was introduced into the momentum equations as a wall force，the hydrody￾namic vorticity-stream equations were derived，and the first-order perturbation solutions of pressure and velocity were obtained． It is found that there exists zero-order radial pressure． Due to the influence of wall-fluid interaction，the first-order radial pressure increases and the first-order velocity decreases． The dimensionless volume flow rate deviates from an uncompressible fluid due to the compressi￾bility of the fluid and the tube wall force． The deviation of the dimensionless volume flow rate from Poiseuille flow increases with the increasing of compressible coefficient and ion concentration in the liquid acted with the tube wall，and increases with the decreasing of the tube diameter． The liquid cannot flow when the tube diameter is less than a certain size． This paper reveals that the mirco-scale effect of nano /micro-size is resulted from the compressibility of the fluid and the tube wall force together． KEY WOＲDS nano /micro-size tubes; wall force; compressible flow; vorticity function; stream function; perturbation techniques 收稿日期: 2013--09--21 基金项目: 国家重大基金资助项目( 50934003，11372033) ; 教育部专项资金资助项目( FＲF-MP-B 12006B) DOI: 10． 13374 /j． issn1001--053x． 2014． 05． 001; http: / /journals． ustb． edu． cn 在纳微米孔道中的流体流动表现出微尺度效 应，即流速明显低于同尺度下的泊肃叶的流速，或者