Hydrodynamics of particles embedded in a flat surfactant layer overlying a subphase of finite depth
Hydrodynamics of particles embedded in a flat surfactant layer overlying a subphase of finite depth
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DOI：
10.1017/s0022112098001980
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发表时间：
1998-08-25
影响因子：
3.7
通讯作者：
Ajdari, A
中科院分区：
文献类型：
--
作者：
Stone, HA;Ajdari, A
膜结合物体的运动在生物学和物理化学的许多方面都具有重要意义。Saffman&Delbruck(1975)提出了这种F构型的流体力学模型，并将其推广到研究有限深度H流体表面粘性膜中圆盘状物体的平移问题，得到了流动问题的数值解。对于描述该系统的两个无量纲参数的整个范围，给出了物体的摩擦系数的结果：子层(ETA)与膜(ETA(M))的粘度之比，Lambda=Eta R/Eta(M)h(其中R和h分别是物体的半径和表面膜的厚度)，以及子层厚度比H/R。给出了基于在问题中出现的不同长度尺度的比较来预测摩擦系数变化的标度变元：几何长度尺度H和R，自然出现的长度尺度L(M)=eta(M)h/eta，中间长度尺度L(H)=(eta(M)hh/eta)(1/2)。对于Lambda远小于1和Lambda远大于1的两个极限，根据这些长度尺度的不同可能顺序，识别出八个不同的渐近区域。此外，还建立了可用近似的有效域。最后，给出了一些具有代表性的表面速度场，并简要讨论了这些结果对表征与有限深度亚层相邻的膜结合蛋白质之间的流体动力学相互作用的意义。
The motion of membrane-bound objects is important in many aspects of biology and physical chemistry. A hydrodynamic model for this Fconfiguration was proposed by Saffman & Delbruck (1975) and here it is extended to study the translation of a disk-shaped object in a viscous surface film overlying a fluid of finite depth H. A solution to the flow problem is obtained in the form of a system of dual integral equations that are solved numerically. Results for the friction coefficient of the object are given for a complete range of the two dimensionless parameters that describe the system: the ratio of the sublayer (eta) to membrane (eta(m)) viscosities, Lambda = eta R/eta(m)h (where R and h are the object radius and thickness of the surface film, respectively), and the sublayer thickness ratio, H/R. Scaling arguments are presented that predict the variation of the friction coefficient based upon a comparison of the different length scales that appear in the problem: the geometric length scales H and R, the naturally occurring length scale l(m) = eta(m)h/eta, and an intermediate length scale l(H) = (eta(m)hH/eta)(1/2). Eight distinct asymptotic regimes are identified based upon the different possible orderings of these length scales for each of the two limits Lambda much less than 1 and Lambda much greater than 1. Moreover, the domains of validity of available approximations are established. Finally, some representative surface velocity fields are given and the implication of these results for the characterization of hydrodynamic interactions among membrane-bound proteins adjacent to a finite-depth sublayer is discussed briefly.