(531i) Deformation Based On Interfacial Tension During Microfiltration of Oil Drops On a Slotted Pore Membrane

Deformation
based on interfacial tension during microfiltration of oil drops on a slotted
pore membrane

A. Ullah

Department of Chemical
Engineering Loughborough University, Leicestershire LE11 3TU, UK

Abstract

The effect of interfacial tension between two fluids, on the
passage and rejection of oil droplets through slotted pore membranes is
investigated. A mathematical model was developed in order to predict conditions
for 100% cut-off of oil droplets through the membrane as a function of permeate
flux rate. Good agreement of theoretical predictions with experimental data
shows that the model can be applied to the filtration of deformable droplets
through slotted pore membranes.  At high
interfacial tension (40 mN/m)
with lower flux (200 l m^-2 hr^-1) droplets of crude oil
(27^oAPI) were 100% rejected at droplet radius 4.3 µm using a 4 µm
slotted pore membrane. At lower interfacial tension (5 mN/m), with the
same flux rate, 100% rejection occurred at 10 µm droplet diameter using the
same membrane.  It was also found that
the droplet rejection efficiency below the 100% cut-off was roughly linear with
drop size, down to zero rejection at zero drop diameter.  Hence, the model, coupled with this
approximate correlation, can be used to predict dispersed oil drop
concentration from a known feed drop size distribution.

Static force (F_cx) is the
force responsible for the rejection of drops, given as follows [1]:

                                                             (1)

Where
is interfacial tension between oil/water,
 is the radius of the
drop, and
 is the half width of slot of the
membrane and
.

While drag force tries to pass the drops through the membrane and
expressed as [2]:

                                                                                                    
              (2)

where
 is a wall correction
factor,
 is viscosity of the fluid,
is the radius of the spherical droplet and
is the velocity of the fluid. 
The droplet is under steady state conditions inside the pore, when
becomes equal to
 and the droplets will be captured in
this position. The droplet will deform and will pass through the membrane when
 and it will be
rejected by the membrane in the case of
 [1].

A 4 µm slot
width membrane was used for filtration experiments using the dead-end candle
microfiltration system as illustrated in Fig.1.

Fig.1. Schematic view of dead-end microfiltration system.

Fig.2.
illustrates the comparison of 100% cut-off (rejections) points of all the
droplets obtained from experimental measurements and theoretical predications.
The static force was obtained using eq (1), and drag
force from eq (2). A satisfactory agreement between
theoretical points and the experimental measured points shows that this model
can be used to predict the 100% cut-off values of the oil types tested
here.  

Fig.2. Experimental measurements and predicted points of 100% cut-off
during filtering vegetable oil droplets with various surfactants (Silica + gum
Arabic, Gum Arabic, PVA, Tween20, Crude oil (31^oAPI) and crude oil
(27^oAPI) with different flux rates (200, 400 and 600 l m^-2
hr^-1).

References

[1] A. Ullah, R.G. Holdich, M. Naeem,
V.M. Starov, Stability and deformation of oil drops
during microfiltration on a slotted pore membrane, J Membrane Sci 401-402 (2012), 118-124.

[2] H.J. Keh,
Y. Chen Po, slow motion of a droplet between two parallel walls, Chem Eng Sci
56 (2001) 6863-6871.