Dynamic
contact angle of bubble with an immersed-in-water spherical particle in
turbulent flow and its application to flotation

Abstract

Contact
angle is of great importance in measuring the wetting characteristics of mineral
particles which reflects the hydrophobicity level of the system. In mineral floatation
process, valuable mineral particles from the mixture of gangue particles are
recovered by altering the hydrophobicity level of the particles. The more
hydrophobic is the particle, the more tenaciously it clings to air, leading to
greater contact angle. With higher hydrophobicity, mineral particles attach to
the bubbles more easily than less hydrophobic gangue particles. Such attachment
which is critical for mineral recovery depends on the attractive capillary
force between the bubble and particle. Magnitude of this capillary force is
determined by the three parameters ? surface tension of the fluid, perimeter of
three phase contact line and the contact angle, and can be expressed as:

                                                                                                  (1)

where
particle radius is ,  is contact
angle,  is polar angle of three phase contact
on particle surface, and  is surface tension (Nguyen, 2003).        

The
above model is often used to determine capillary force magnitude for static
case under the assumption that contact angle is constant along the three phase
contact line. However, in a turbulent environment, such as mineral floatation
system, contact angle of the bubble on particle surface vary significantly and
use of static contact angle to predict the capillary force becomes questionable.
It is therefore essential to obtain knowledge of dynamic contact angle as a
function of system hydrodynamics to accurately predict the stability of the bubble-particle
aggregate.  

Nevertheless,
measuring dynamic contact angle in a fluctuating flow field is a rather
challenging task. Blake (1999) investigated hydrodynamic influence on the contact
angle measurement. Not only the wetting speed but also the whole flow field in
the vicinity of the moving contact line was found to be influential on the
dynamic nature of the contact angle. Pinning effect of contact line was found
to be affecting the capillary force. In industrial applications like flotation,
contact angle indeed has a spectrum of values ranging from advancing to
receding contact angle. To successfully predict the bubble-particle aggregate
stability, therefore, accurate measurement of the contact angle at the three
phase contact line is required to determine the correct magnitude of the
attaching capillary force. Acknowledging the dearth of knowledge in this area,
the present study aims at to quantify the dynamic nature of the contact angle
of bubble attached to particle in both fluctuating and shearing flow field.

To
quantify the variation of contact angle in a fluctuating flow field, in this
study, an oscillating grid turbulence generator was used to provide a nearly
homogeneous isotropic turbulence with zero mean flow (Fig.1). A channelled stainless
steel particle of 3 mm diameter was anchored on the tip of an 18G needle in the
centre of the transparent tank. Bubble was generated on the particle surface by
supplying controlled air flow from the syringe pump (Adelab Scientific
NE-1010).  

Fig.1
Schematic of the experimental setup for dynamic contact angle measurement in
turbulent field.

Oscillating grid
turbulence generator was operated at 4 Hz frequency providing fluctuating flow
with intensity high enough to detach the bubble. The dynamic contact angle was
measured by shadowgraphy imaging technique using a microscope lens connected to
a high speed camera (speedSense 9080) and microscope lens (Carl Zeiss Stemi
2000c) using a back light (3W white LED with collimating lens). High contrast
images were obtained with a magnification sufficient to measure the contact
angle (camera resolution: 3 μm/pixel).

 Fig.2 shows the transient
bubble detachment process in the oscillating grid generated homogeneous
turbulent field. Initially (t=0 ms), with no liquid motion, the bubble maintained
an axisyemmtric position on the particle surface. Once the grids were turned on,
the stationary bubble (t=0 ms) was perturbed with the turbulent liquid motion. It
can be seen that bubble shape was elongated due to the shearing action of the flow
field and contact angles on the both sides of the interface changed
subsequently (t=24 ms to 52 ms). The fluctuating flow field was found to be
strong enough to distort the bubble stretching it outside the image window
(t=60 ms).

It could be noticed
that with time, downstream (R) contact angle decreased, whereas, upstream contact
angle (L) increased. It was noted that when flow direction was from left to
right, three phase contact line retracted in the upstream (L) but it remained
pinned on the downstream side (R). Contact angle on the upstream side increased
gradually and conversely on the downstream side the angle decreased. Contact
line retraction continued on the upstream (L) side until a neck formed and
detachment occurred soon after it (t=60 ms).

Fig.2
Time series of bubble detachment in turbulent flow

The high
contrast shadow images obtained from the experiment were analysed to determine
the contact angles at the three phase contact line (TPCL). An in-house
edge-fitting code written in MATLAB R2011a was used to mark the profile of
bubble interface at TPCL. To obtain a very sharp interface, a threshold
gray-scale value of 150 was chosen on a scale of  0-255 and pixels of intensity
higher than this threshold value were set to zero resulting in a sharp boundary
of the bubble and the particle. The edge detected using the code was marked on
the bubble interface and presented in Fig.3 (b). Contact angle measured on the
left side (L) is θ₁ and contact angle on the right side (R) is
θ₂.

Fig.3
Bubble particle edge detection process: (a) raw image (b) edge detected

Fig.4 shows the
transient change in the magnitude of contact angles on the both sides of the
interface obtained from the images in relation with the instantaneous three
phase contact line diameter.

Fig.4 Contact angles (θ₁, θ₂)
changing with three phase contact line in bubble detachment process

In quiescent
case (t=0 ms), contact angle was measured to be 72^o which confirms
the reported static contact angle for stainless steel surface in the air water
system reported. In turbulent field, TPCL at the bubble base was perturbed by
the liquid motion and TPCL diameter was observed to decrease with time. However,
at lower grid operating frequency (<4 Hz), it was observed that TPCL
diameter remained unchanged due to relatively weak turbulence intensity, although
the contact angle dynamically changed on the both sides of the interface. It
can be seen from Fig.4 that contact angle (θ₂) on right side (R)
of the bubble gradually decreased from static value of 72^o to around
55^o while due to predominant flow from left to right direction,
contact angle (θ₁)grew abruptly and remained
constant at 104^o once reached the advancing contact angle state. The
larger hysteresis (difference between the two contact angles) compromised the
attaching capillary force finally leading to the bubble detachment. 

This study shows
the asymmetric magnitude of contact angles in a bubble-particle aggregate
system in a turbulent flow field. It was illustrated that hydrodynamics of the
system govern the contact angle magnitude significantly and use of static
contact angle is not adequate to describe the system dynamics. Future study
involves quantifying the variations of contact angle for increased level of
turbulence intensity by further varying the grid operating frequency. A
relationship between the u_rms (root means square velocity) of the
system and the associated contact angle variation would be established. Also,
the effect of unidirectional shear flow would be investigated in a two
dimensional water channel to explore the variation in contact angle and
associated bubble-particle aggregate stability in relation to the different liquid
velocity.

Reference

Blake,
T.D., Bracke, M., Shikhmurzaev, Y.D., 1999. Experimental evidence of nonlocal
hydrodynamic influence on the dynamic contact angle. Physics of Fluids
(1994-present), 11(8): 1995-2007.

Nguyen,
A.V., Schulze, H.J., 2004. colloidal science of flotation. Marcel Dekker, New
York, USA.