Dynamics of Drying in 3D Porous Media

The drying dynamics in three dimensional porous media are studied with confocal microscopy. We observe abrupt air invasions in size from single particle to hundreds of particles. We show that these result from the strong flow from menisci in large pores to menisci in small pores during drying. This flow causes air invasions to start in large menisci and subsequently spread throughout the entire system. We measure the size and structure of the air invasions and show that they are in accord with invasion percolation. By varying the particle size and contact angle we unambiguously demonstrate that capillary pressure dominates the drying process.

Figure 1

Photographs of drying for $d=1.1\pm 0.1\mu \mathrm{m}$ colloidal suspension. (a) Drying images taken from above at six different times: 0 s (pict.1), 270 s (pict.2), 300 s (pict.3), 320 s (pict.4), 365 s (pict.5), and 410 s (pict.6). We divide the process into two stages: compacting stage (top row) and air invading stage (bottom row). (b) Interface between the packed region and free suspension, such as the small box area in pict.1. of (a). The left picture is a horizontal slice and the right is a vertical slice. In the right picture, a ceiling of closely packed particles near the air-liquid interface is clearly visible. (c) Image of one large burst. An area of 800 particle size (the highlighted area) is invaded within 0.07 s. (d) Cartoon illustrating the flow from large pore to small pore during drying.

Figure 2

Observation of strong flow from large pores to small pores. (a) $d=2\mu \mathrm{m}$ sample with $d=0.22\mu \mathrm{m}$ tracer particles. The tracer particles move randomly before the invading stage. (b) Tracer particle trajectories show a strong flow during invading stage. (c) One sample with small-pore and large-pore domains. The darker domain on the left is composed by $1.1\mu \mathrm{m}$ particles and the brighter domain on the right is by $2\mu \mathrm{m}$ particles. (d) $x\mathrm{\text{−}}y$ scans of the drying process of the two-domain sample. The large-pore domain is invaded first. Surprisingly, the invasion is restricted in the large-pore domain until it has been completely invaded. (e) $x\mathrm{\text{−}}z$ sections at a position similar to the dotted line in (d).

Figure 3

Size, structure, and dynamics of bursts. Main panel of (a), the probability, $P$, of finding a burst of size $s$ or $A$. Both the 2D (●) and 3D ($\circ$) size distributions are plotted. The 3D size, $s$, is computed from the 2D size, $A$, with the relationship $s\sim A^{D_f/2}$. The two fitting functions are: $P(A)\sim A^{-\alpha }\exp (-A/A^{*})$, with $\alpha =1.6\pm 0.1$, $A^{*}=850\pm 150\mu {\mathrm{m}}^2$ and $P(s)\sim s^{-{\tau }^{\prime }}\exp (-s/s^{*})$, with ${\tau }^{\prime }=1.5\pm 0.1$, $s^{*}=6500\pm 1000$. The smallest area in plot is limited by the image resolution. Lower inset, zoom-in picture of freshly invaded region. Only 15% pore space is filled by air. Upper inset, global pattern by many invasions. The field of view is $345\mu \mathrm{m}\times 345\mu \mathrm{m}$. (b) Liquid redistribution due to a burst. The 1st image is before the burst and The 2nd is after. An invasion occurs at the lower arrow spot, resulting in an obvious meniscus readjustment at the upper arrow spot. The 3rd picture traces the air-liquid interface of the first two images. The dotted curve is before the burst and the solid one is after. It shows menisci readjustments at several positions.

Figure 4

Variation of particle size and contact angle. (a) Completely dried samples of small ($d=0.22\mu \mathrm{m}$, left) and large ($d=2\mu \mathrm{m}$, right) particles. There are many cracks for $0.22\mu \mathrm{m}$ sample and no cracks for $2\mu \mathrm{m}$ one. (b) Rehydration of a dried sample. We see a smooth and continuous interface, in sharp contrast to the fractal pattern of drying.