Polymer solutions are demonstrated to have apparent viscosities in small pores which depend on pore diameter (or the mean diameter of porethroats in irregular pore diameter) and which, therefore, can be considerably different from viscosity of the same solution in unbounded media.
Several experimenter and scientist have given explanation as followings, the presence of a wall restricts the number of configurations available to macromolecules near the walls. Thereby reducing the contribution they make to the fluid stress.
The purpose of this study is to supply both theoretical and experimental analysis. First theoretical analysis was proceeded as followings, The local shear viscosity of the linear dumbbell polymer between two parallel plate with a rectilinear Poiseuille flow was given as a function of the laterial position $Z_c$(center of the mass coordinate of dumbbell) from the center of the channel. This was obtained by neglecting the brownian diffusion term of $Z_c$ as induced from the fact that the configurational probability distribution with respect to $Z_c$ is unchanged at steady state.
The average shear viscosity is increased as the channel size increases. But after reaching critical channel size, the average shear viscosity is not increasing with channel size.
The local fist normal stress coefficient was given as a function of the laterial position, too. But in the center of the channel its value has a infinite value, which should be corrected in the future.
Second the experimental analysis was proceeded as follows, Variation of apparent viscosity with pore size in both the Newtonian and shear thinning regimes has been studied in flow of xanthan and ployacrylamide water solution through well defined cylindrical pore. Shear viscosities of poymers were measured over a wide range og the shear rate. In the fine pores, Newtonian apparent viscosities were found to decrease with pore size and power law index is increasing with pore size. Such behavior is interpreted by the existence near the wall conformation restriction regime. Proposed data analysis of new rheometry and specially designated rheometer were successful.
