Molecular group dynamics study on slip flow of thin fluid film based on the Hamaker hypotheses

Abstract

The thin fluid film was assumed to consist of a number of spherical fluid molecular groups and the attractive forces of molecular group pairs were calculated by the derived equation according to the three Hamaker homogeneous material hypotheses. Regarding each molecular group as a dynamics individual, the simulation method for the shearing motion of multilayer fluid molecular groups, which was initiated by two moving walls, was proposed based on the Verlet velocity iterative algorithm. The simulations reveal that the velocities of fluid molecular groups change about their respective mean velocities within a narrow range in steady state. It is also found that the velocity slips occur at the wall boundary and in a certain number of fluid film layers close to the wall. Because the dimension of molecular group and the number of group layers are not restricted, the hypothetical thickness of fluid film model can be enlarged from nanometer to micron by using the proposed simulation method. NomenclatureA: constant of repulsive force a: accelerated speed of molecular group, m s 2 B: constant of attractive force D: length of chain of attractive force, m e: strength factor of attractive force of molecular groups F 2 : total attractive force between groups M 1 and M 2 , N H: dimensionless distance between two walls L c : dimensionless cut-off length of attractive force L x : dimensionless center distance L 0 : dimensionless referential center distance l:distance between two molecules, m M: mass of molecular group, kg m: mass of molecular, kg N: number of molecular groups R x : dimensionless radius of spherical molecular group r x : dimensionless radius of molecular S: dimensionless displacement of molecular group t: time, s t: time step, s U: potential, J V: dimensionless velocity of molecular group V 1 : dimensionless velocity of molecular group m 1 V 2 : dimensionless velocity of molecular group m 2 V r : dimensionless velocity of upper wall V l : dimensionless velocity of lower wall v: velocity of molecular group, m s 1 : separation angle between central line and coordinate x, rad : ratio : potential parameter, J : separation angle between a line and coordinate y, rad : dimension parameter, m For dimensionless length L, L l .For dimensionless velocity V, V v m .