During spontaneous imbibition, a wetting liquid is drawn into a porous medium by capillary forces. In systems with comparable pore length and diameter, such as paper and sand, the front of the propagating liquid forms a continuous interface. Sections of this interface advance in a highly correlated manner due to an effective surface tension, which restricts front broadening. Here we investigate water imbibition in a nanoporous glass (Vycor) in which the pores are much longer than they are wide. In this case, no continuous liquid-vapor interface with coalesced menisci can form. Anomalously fast imbibition front roughening is experimentally observed by neutron imaging. We propose a theoretical pore-network model, whose structural details are adapted to the microscopic pore structure of Vycor glass and show that it displays the same large-scale roughening characteristics as observed in the experiment. The model predicts that menisci movements are uncorrelated, indicating that despite the connectivity of the network the smoothening effect of surface tension on the imbibition front roughening is negligible. These results suggest a new universality class of imbibition behavior, which is expected to occur in any matrix with elongated, interconnected pores of random radii.liquid imbibition | interface roughening | porous media | neutron radiography | computer simulations M any everyday processes involve the flow of a liquid into a porous matrix, for instance, when we dunk a biscuit into coffee, clean the floor with a cloth, or get drenched with rain. The same process is also important in nature (e.g., for water to reach the tips of the tallest trees or to flow through soil) and crucial for different industrial processes, ranging from oil recovery and chromatography to food processing, agriculture, heterogeneous catalysis, and impregnation (for reviews see refs. 1-4).The above processes are examples of imbibition (Fig. 1). Imbibition of a liquid into a porous matrix is governed by the interplay of capillary pressure, viscous drag, volume conservation, and gravity. The porous matrix often has a complex topology. The inhomogeneities result in variations in the local bulk hydraulic permeability and in the capillary pressure at the moving interface. Nevertheless, the invasion front during solely capillarity-driven (i.e., spontaneous) imbibition advances in a simple square-rootof-time manner, according to the Lucas-Washburn law (5, 6). Such behavior is a result of the time-independent mean capillary pressure and the increasing viscous drag in the liquid column behind the advancing front. It is valid down to nanoscopic pore sizes (7-9) and particularly robust with regard to the geometrical complexity of the porous matrix (1, 4, 10, 11). The evolution of the invasion front displays universal scaling features on large length and timescales, which are independent of the microscopic details of the fluid and matrix (12-18), and which parallels the elegance of critical phenomena.Typically imbibition is studied using paper (14-16) or...

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The capillary rise of liquid in asymmetric channel junctions with branches of different radii can lead to long-lasting meniscus arrests in the wider channel, which has important implications for the morphology and dynamical broadening of imbibition fronts in porous materials with elongated pores. Using a microfluidic setup, we experimentally demonstrate the existence of arrest events in Y-shaped junctions, and measure their duration and compare them with theoretical predictions. For various ratios of the channel width and liquid viscosities and for different values of the feeding channel length, we find that the meniscus within the wider branch is arrested for a time that is proportional to the time that the meniscus needed to reach the junction, in very good quantitative agreement with theoretical predictions.

We present a scaling theory for the long time behavior of spontaneous imbibition in porous media consisting of interconnected pores with a large length-to-width ratio. At pore junctions, the meniscus propagation in one or more branches can come to a halt when the Laplace pressure of the meniscus exceeds the hydrostatic pressure within the junction. We derive the scaling relations for the emerging arrest time distribution and show that the average front width is proportional to the height, yielding a roughness exponent of exactly β = 1/2 and explaining recent experimental results for nanoporous Vycor glass. Extensive simulations of a pore network model confirm these predictions.

We theoretically study the transport properties of self-propelled particles on complex structures, such as motor proteins on filament networks. A general master equation formalism is developed to investigate the persistent motion of individual random walkers, which enables us to identify the contributions of key parameters: the motor processivity, and the anisotropy and heterogeneity of the underlying network. We prove the existence of different dynamical regimes of anomalous motion, and that the crossover times between these regimes as well as the asymptotic diffusion coefficient can be increased by several orders of magnitude within biologically relevant control parameter ranges. In terms of motion in continuous space, the interplay between stepping strategy and persistency of the walker is established as a source of anomalous diffusion at short and intermediate time scales.PACS numbers: 87.16. Ka, 87.16.Uv, 87.16.Nn Anomalous transport of self-propelled particles in biological environments has received much recent attention [1]. Of particular interest is the active motion of motor proteins along cytoskeletal filaments, which makes longdistance intracellular transport feasible [2]. The structural asymmetry of filaments results in a directed motion of motors with an effective processivity, denoting the tendency to move along the same filament. The processivity depends on the type of motor and filament [3] and it is strongly influenced by the presence of specific proteins or binding domains [4,5]. In the limit of small unbinding rates it has been shown [6] that a walker on simple lattice structures moves superdiffusively at short time scales followed by a normal diffusion at long times. Similar results were reported for single bead motion on radiallyorganized microtubule networks [7]. However, for general polarized cytoskeletal networks, the influence of structural complexity and motor processivity on the transport properties is not yet well understood. In this Rapid Communication, we introduce a coarse-grained perspective to the problem and show that the interplay between anisotropy and heterogeneity of the network and processivity leads to a rich transport phase diagram at short and intermediate time scales. The crossover times between different regimes and the asymptotic diffusion constant can vary by orders of magnitude when tuning the key parameters.More precisely, a general analytical framework is developed to study persistent walks with arbitrary steplength and turning-angle distributions. We obtain an exact analytical expression for the dynamical evolution of the mean square displacement (MSD), displaying anomalous diffusion on varying time scales. The results can be also interpreted within the context of random motion in continuous space, e.g. in crowded biological media where the origin of subdiffusive motion is highly debated [8][9][10][11][12][13].While subdiffusion in cytoplasm slows down the transfer of matter, it is beneficial for a variety of cellular functions [14-16], since they depend on th...