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3.3. Experimental section 35which has to be solved using the boundary conditions:{ 0 r = 0h r =cotan(θ) r = R , (3.10)where θ is the contact angle at the three-phase contact.3.2.3 Image analysisWe describe the image analysis procedure that we developed to derive the parameters γ 12and θ from the MRI images of the two-phase system. The images were acquired using T 1weighting such that the phases have the highest possible signal contrast. After selecting anappropriate region of interest for each time step the image analysis is performed to obtaina smooth interface representation, ¯h(x i ), i.e. the height of the interface as a functionof position x i in the images (x i is the horizontal coordinate of each column). Near thetwo-phase contact the vertical columns show a clear jump in signal. An arbitrary smoothfunction is fitted to the pixel values in each column. This procedure results in a smoothrepresentation of the interface. For convenience, we choose the following inverse tangentfunctionf(z) = A tan −1 ( z − z0ξ)+ B, (3.11)where A, z 0 , ξ and B are the amplitude, the inflection point, the steepness coefficientand the offset, respectively. Finally, exploiting the cylindrical symmetry of the problem,the horizontal center coordinate of ¯h(x i ) is determined, and the profile is split into twoparts. The left-hand-side and right-hand-side part of the profile are then regarded as twoseparate axisymmetric representations of the interface, i.e. ¯h L (r) and ¯h R (r), respectively.3.2.4 Optimization procedureThe second aspect of the IFT determination consist of the true optimization, which is aniterative process. Starting with an initial guess of the parameters γ 12 and θ the shapefunction h(r) is determined by solving the boundary value problem (BVP) given in Section3.2.2. The calculated function h(r) is simultaneously compared with the values of both¯h L (r) and ¯h R (r). This way the method is rather insensitive to image distortions. Basedon a least-square method the process is repeated automatically with improved values forγ 12 and θ. After about 200 iterations a satisfactory match of the calculated h(r) with¯h L (r) and ¯h R (r) is obtained.3.3 Experimental section3.3.1 MaterialsTetra-methyl-ortho-silicate, Si(OCH 3 ) 4 , was obtained from Aldrich (>99% pure). It wasdissolved in n-hexadecane (n-C 16 H 34 ), obtained from Merck (>99% pure), to form the oleicphase. For the aqueous phase we used double-demineralized water. Methanol (Merck, 99%