Study of the Flow Characteristics of Pumped Media in the Confined Morphology of a Ferrofluid Pump With Annular Microscale Constraints

The driving mechanism of ferrofluid micropumps under the constraints of an annular microscale morphology is not fully understood. The gap between microfabrication technology and the fundamental theory of microfluidics has become a substantial obstacle to the development and application of ferrofluid micropumps. In this study, we first theoretically analyzed the Knudsen numbers of millimeter-scale microfluids using Jacobson's molecular hard sphere model, obtaining the initial conclusion that liquid flow conforms to the continuum hypothesis in geometric morphologies with characteristic dimensions greater than 7 × 10⁻⁸ m. Subsequently, using a microscopic lens combined with the particle image velocimetry optical measurement method, the flow patterns in millimeter-scale annular flow channels were captured and we observed wall slip phenomena in which the slip length of the millimeter-scale channel approached the micron level. The slip velocity and flowrate through the cross section of the microscale channel followed a logarithmic function relationship and could be divided into rapid growth, slow growth, and stable stages. As the characteristic scale of the channel was further reduced, the linear relationship between the slip velocity and cross-sectional flowrate in the rapid growth stage was broken, and the nonlinear relationship approximated an exponential function. Finally, a theoretical model for the flow behavior of the driving fluid in a ferrofluid micropump was established using slip boundary conditions. The flow patterns in microscale ring flow under slip conditions conformed to a quadratic function.