Precursors of impregnation

– The progression of a liquid inside a porous medium often involves two macroscopic fronts: a main one, at the bottom, which saturates the medium; and a much thinner one, ahead, which propagates using the fine structures of the porous material. We discuss here different characteristics of this precursor. We show in particular how it can move faster than the main front, although it follows confined paths. We also describe its dynamics, and compare our results with different experimental situations. Diffuse fronts in impregnation experiments. – In many cases, the impregnation of a porous medium (such as paper, fabric, or powder) is well described by a diffusive-type law: the impregnated distance increases as the square root of time. This law also describes the progression of a liquid index in a capillary tube as long as gravity can be neglected, as shown in 1921 by Washburn [1]. Thus it has often been proposed to treat a porous medium as an array of parallel identical capillary tubes. But this very simple picture does not capture all the characteristics of the imbibition. For example, the front is generally not sharp (as it would be in an array of capillaries), but diffuse. This can be proved by measuring simultaneously the weight of the paper and the apparent position of the front (two very common types of measurement). We report in fig. 1 such an experiment, performed with a silicone oil (viscosity η = 16mPa s, surface tension γ = 20.6mN/m and density ρ = 950 kg/m3) impregnating a centimetric piece of paper (Whatman no. 4). At the end of the experiment, the whole paper is impregnated (on the centimetric height h0, to which there corresponds a mass m0). In fig. 1, the height of the visible front and the mass are scaled by h0 and m0, respectively. Both laws are diffusive (and we can find in the literature many similar results obtained by either one or the other of these techniques), but the diffusion coefficients which can be deduced from the experiment are different: we find a larger value (by typically 30%) for the visible front than for the mass of the liquid. This difference can be interpreted by considering that liquid precursors are progressing ahead (they darken the porous material, and thus are detected by the eye), while the large pores of the material (which provide most of the mass, once saturated with the liquid) are filled more slowly. J. Bico et al.: Precursors of impregnation 349 0 0.0 0.2 0.4 0.6 0.8 1.0 h/h0 m/m0 1/ 2 ( ) t s 20 40 60 80 100 visuel force Fig. 1 – Comparison between the progression of the liquid front (full diamonds) and the increase of the mass (line), in a piece of paper put at t = 0 in contact with a wetting silicone oil. h0 is the height of the sample, and m0 the mass of the liquid once the paper is fully impregnated. This suggests that the liquid front is wide, as shown by Williams for similar systems [2]. In Williams’ experiment, a long strip of paper is brought in contact with a bath of oil and removed before the front reaches the end of the strip (thus, for h < h0). The stripe is then cut up in small horizontal slices, which are weighed. Each mass is compared with the mass of a similar slice saturated with oil, which allows to reconstruct the filling rate of the porous along its length. Figure 2a shows the results of a similar experiment done with a paper in contact with a bath during 1700 s, 5500 s, 11700 s and a whole night, to which there correspond (apparently) impregnated lengths of 35mm, 53mm, 83mm and complete saturation, respectively. Close to the bath (z small), the paper is fully impregnated. Further, a diffuse front is observed, although a direct observation provides a very well-defined position h for the front. (In the case of an anisotropic porous medium, the front h is also observed to be rough in the direction perpendicular to the motion [3], which is not the case here.) The front width ∆h increases throughout the liquid progression, and is found in fig. 2b to be linear in h, which shows that both the laws are diffusive in time. If the porous medium could be simplified in an array of similar tubes, the front would be sharp. We propose here to study what happens when considering the polydispersity of the pores, and restrict to the simple case of a porous medium constituted of two types of pores interconnected with each other. This minimal description should mimic different practical cases: 0 0.2 0.4 0.6 0.8 1 1.2