Hydrodynamic Drag And Velocity Of Micro-bubbles In Dilute Paper Machine Suspensions
Free (open access)
343 - 354
A. Haapala, M. Honkanen, H. Liimatainen, T. Stoor & J. Niinimäki
This paper studies hydrodynamic drag forces acting on freely rising microbubbles in dilute paper machine suspensions under turbulent flow conditions. Dissolved, colloidal and numerous solid materials i.e. process chemicals, wood extractives, fillers and wood fibre fractions present in these suspensions disturb the rise of micro-bubbles increasing their drag. The aim of this study is to characterise the terminal velocities and drag coefficients of the bubbles as a function of their Reynolds number in several paper machine circulation waters, i.e. white waters, and in some model suspensions. Characterisation is performed experimentally with a high-speed CMOS camera and a submersed back-light illumination in a pressurised bubble column. Image sequences of bubbly flow are analysed with automatic image processing algorithms that measure not only the bubble size and velocity, but also the velocity of the fluid surrounding bubbles, revealing the initial slip velocity of each bubble. Bubbles are tracked in time to provide time series data for every bubble that passes the focal plane of the imaging system. Results show how some suspension properties – concentration, apparent viscosity and surface tension – affect the motion of micro-bubbles. Results also show the changes in micro-bubble formation with pressure drop and differences of bubble size distributions in a variety of suspensions and solutions. Finally, a mathematical model describing the bubble rise velocities and drag coefficients with respect to the bubble Reynolds number is developed for the investigated white waters. Keywords: bubble motion, drag coefficient, drag force, white water, papermaking, high-speed imaging, high-speed imaging, bubble sizing.
bubble motion, drag coefficient, drag force, white water, papermaking, high-speed imaging, high-speed imaging, bubble sizing