水力学相互作用对虎克哑铃分子模型稀溶液流变性质的影响
The Effect of the Hydrodynamic Interaction on the Rheological Properties of Hookean Dumbbell Suspensions in Steady State Shear Flow
-
摘要: 本文用伽辽金方法求解定常剪切流中计及水力学相互作用的虎克哑铃分子模型位形空间分布函数的扩散方程,并计算了其稀溶液的剪切粘度、第一、二正应力差系数和分子的平均相对拉伸.结果表明,微观分子模型中的水力学相互作用,对虎克哑铃分子模型稀溶液的流变性质有重要的影响:粘度和第一正应力差系数不再为常数,而随着剪切率的增加而减少;第二正应力差系数不再为零,而是绝对值很小的负值;分子的平均相对拉伸增加.与自治平均法(Self-Cosistent Average Method)相比,两种方法所得到的粘度函数和第一正应力差系数定性地相符;而自洽平均法得到的第二正应力差系数与数值解和实验不符.Abstract: The diffusion equation for the configurational distribution function of Hookean dumbbell suspensions with the hydrodynamic interaction(HI) was solved, in terms of Galerkin's method, in steady state shear flow;and viscosity,first and second normal-stress coefficients and molecular stretching were then calculated. The results indicate that the HI included in a microscopic model of molecules gives rise to a significant effect on the macroscopic properties of Hookean dumbbell suspensions. For example, the viscosity and the first normal stress coefficient, decreasing as shear rate increases, are no longer constant;the second normal-stress coefficient, being negative with small absolute value and shear-rate dependent, is no longer zero;and an additional stretching of dumbbells is yielded by the HI. The viscosity function and the first normal-stress coefficient calculated from this method are in agreement with those predicted from the self-consistent average method qualitatively, while the negative second normal-stress coefficient from the former seems to be more reasonable than the positive one from the latter.
-
[1] Kirkwood,J.G.and J.Riseman,The intrinsic viscosities and diffusion constants of flexible macromolecules in solution,J.Chem.Phys.,16(1948),565-573. [2] Bird,R.B.,O.Hassager,R.C.Armstrong and C.F.Curtiss,Dynamic of Polymeric Liquids,Vol.2,Kinetic Theory,Wiley,New York(1977). [3] Zimm,B.H.Theory of the non-Newtonian viscosity of high polymer solution,Ann.N.Y.Acad.Sci.,89(1961),670-671. [4] Pyun,C.W.and M.Fixman,Intrinsic viscosity of polymer chains,J.Chem.Phys.,42(1965),3838-3844. [5] Fixman,M.,Inclusion of hydrodynamic interaction in polymer dynamical simulations,Macromolecules,14,(1981),1710-1717. [6] Öttinger,H.C.,Consistently averaged hydrodynamic interaction for rouse dumbbells,J.Chen.Phys.,83,(1985),6535-6536. [7] Fan,X.J.,Viscosity,first normal-stress coefficient,and molecular stretching in dilute polymer solutions,J.Non-Newtonian Fluid Mech.,17(1985),125-144;Viscosity,first and second normal-stress coefficients,and molecular stretching in concentrated solutions and melts,ibid,17(1985),251-265. [8] Lieberstein,H.M.,《偏微分方程理论》(蒋定华译,林建祥校),高等教育出版社(1984),. [9] Öttinger,H.C.,Private Communication. -
点击查看大图
计量
- 文章访问数: 1696
- HTML全文浏览量: 82
- PDF下载量: 473
- 被引次数: 0
下载:
