Study of wall effect on the flow of milk in capillary

Abstract

Dependence of the viscosity of milks on the bore-size of capillary viscometer has been studied at 25°C. Viscosity measurements were carried out with a Maron-Belner type low shear capillary viscometer with various capillary radii (0.0190–0.076 cm) within the shear stress range of 0.2–30 dynes/cm² at the capillary wall. Each milk showed non-Newtonian flow behavior and dependence on the size of the capillary. The viscosity of human fresh milk and cow’s fresh milk decreased with the decreases in the capillary bore-size within the range of shear stress studied, and the viscosity of homogenized milk, although similar phenomena as above were Observed in higher shear stress, decreased with the decrease in the capillary bore-size at the range of lower shear stress.

The difference in characteristics of capillary bore-size dependence on viscosity may be attributed to the difference in the behavior of fat droplets existing near the wall at which thermal motion of fat droplets will be hindered by the existence of capillary wall. The results were represented by the modified Ree-Eyring generalized flow formula for a flow system containing one Newtonian flow unit and one non-Newtonian flow unit which included additional terms dependent on the capillary bore-size. The viscosity equation suitable for analysing the dependence of viscosity on the capillary bore-size at entire ranges of rate of shear, was derived by assuming the wall layer. Composed of double layers (of thickness d_o and d_i - d_o) in the flowing liquid in capillary tube, and by combining this equation with the modified Ree-Eyring equation, the values of d_o and d_i were calculated.