Entrainment of magnetic fluid by a moving boundary of a plane gap

Abstract

A fluid mechanics problem is solved which technological prototype is a fluid acoustic contact that is an inherent element of ultrasonic non-destructive testing procedures. It is well known that the acoustic contact established with an ordinary fluid suffers from essential disadvantage that is the loss of stability due to the gravity-induced fluid leakage in the course of dynamic scanning. The use of magnetic fluid (MF) is one of the ways to resolve the issue. A compact portion of MF held in place by a permanent magnet enables one to maintain a stable acoustic contact (fluid bridge) under arbitrary orientation of the ultrasonic sensor and, simultaneously, to radically minimize the drain of the contact fluid. The model system under consideration comprises a MF bridge that fills a flat gap, one of whose boundaries moves with constant velocity. Due to its wetting by the fluid, the receding plane carries away a fluid film thus depleting the contact. Theoretical expressions are obtained which define the profile of the film in the dynamic regime and the dependencies of the magnetic fluid drain on the boundary velocity, gap height and configuration of the imposed magnetic field. On that basis the optimal parameters are evaluated which ensure effective retention of the fluid contact under minimal drain of the fluid from it.

Figures (6)

• Figure 1: Schematic illustration of the ultrasonic scanning process with an MF acoustic contact: (1) tested item, (2) ultrasonic sensor, (3) magnetic mounting, (4) magnetic fluid (fluid bridge).
• Figure 2: On the 2D problem of entrainment of MF by a moving wetted boundary of a plane gap; (1) lower boundary of the gap (moving), (2) magnetic fluid (fluid bridge), (3) upper boundary of the gap (fixed). Black dashed lines indicate that only a part of the whole scheme is shown.
• Figure 3: Surface profile of the film entrained by a moving boundary. Function $\mu(\lambda)$ is shown both in linear and logarithmic (inset) scales; symbols are the results of numerical evaluation, black lines render their interpolation; color lines show the dependencies corresponding to approximations: (\ref{['eq:A9']}) for the 'near' zone, (\ref{['eq:A11']}) for the 'far' zone after their splicing with the numerical solution, i.e., using the obtained values of $\alpha_{-1}$ and $\alpha_1$.
• Figure 4: Scheme of the fluid bridge (rear part); pane a) -- situation of arbitrary drain; b) -- situation of minimal drain: contact angle $\theta_0$ equals wetting angle $\theta_\ast$.
• Figure 5: Dimensionless drain $j/J_c$ as a function of the gap height $\xi=h_0/R_c$ for $\theta_\ast\approx41^\circ$ and $\theta_g=$0, 0.1, 0.2, 0.4 and 0.8 (from top to bottom); in the inset $\theta_g=$0.1, 0.4, 0.8. Solid lines show the exact solution (\ref{['eq:52']})--(\ref{['eq:53']}), dashed red lines in the inset show the results of approximation (\ref{['eq:33']}); vertical dashes indicate the border $\xi_\ast=\sqrt{1+\cos\theta_\ast}$, see (\ref{['eq:56']}); horizontal dashed lines show the maximal levels $j/J_c=0.5/\sqrt{1/\cos\theta_g-1}$ for non-zero $\theta_g$.