The velocity slip of gas flow in a micron channel has been widely recognized. For pressure driven liquid flow in a macro pipe, the minute velocity slip at the wall boundary is usually neglected. With a decreasing scale in the cross section of the flow passage, the effect of velocity slip on flow and heat transfer behaviors becomes progressively more noticeable. Based on the three Hamaker homogeneous material hypotheses, the method for calculating the acting force between the solid and liquid molecular groups is established. By analyzing the forces exerted on the liquid group near the pipe wall, it is found that the active force arising from the rough solid wall can provide the component force to resist the shearing force and keep the liquid group immobile. Based on this a velocity slip criterion is proposed. Considering the force balance of a slipping liquid group, the frictional force caused by the solid wall can be obtained and then the velocity of the liquid group can be calculated using the derived coefficient of friction. The investigation reveals that, in a micron pipe, a small velocity slip may occur when the flow pressure gradient is relatively large, and will cause errors in the pipe flow estimates. velocity slip, pressure driven, liquid molecular group, coefficient of friction Citation:Zhou J F, Gu B Q, Shao C L. Boundary velocity slip of pressure driven liquid flow in a micron pipe.

A micromechanical model of short-fiber-reinforced elastomer matrix composite (SFRE) including the fiber, matrix and fiber-matrix interphase was established, in which main microstructural parameters, such as short fiber aspect radio, volume content and mechanic performances of main components, were taken into consideration, and the interphase was regard as a time-dependent viscoelastic component. The micromechanical stress transfer among short fiber, matrix and fiber-matrix interphase was studied. The equations expressing time-dependent tensile stress distribution on the fiber and the time-dependent shear stress distribution in the matrix and interphase were derived, and they were solved at the time t = 0 and t = + . A calculated example was carried out and the calculation results indicated that there existed the maximum fiber tensile stresses f (z, 0) and f (z, + ) at the fiber midpoint and both f (z, 0) and f (z, + ) equaled to zero at the fiber end, but the interphase shear stresses if (z, 0) and if (z, + ) reached to the maximum at the fiber end, and they equaled zero at the fiber midpoint.

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 .

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