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.