Ken Tore Tallakstad

Local dynamics of a randomly pinned crack front during creep and forced propagation: an experimental study.

We have studied the propagation of a crack front along the heterogeneous weak plane of a transparent poly(methyl methacrylate) (PMMA) block using two different loading conditions: imposed constant velocity and creep relaxation. We have focused on the intermittent local dynamics of the fracture front for a wide range of average crack front propagation velocities spanning over four decades. We computed the local velocity fluctuations along the fracture front. Two regimes are emphasized: a depinning regime of high velocity clusters defined as avalanches and a pinning regime of very low-velocity creeping lines. The scaling properties of the avalanches and pinning lines (size and spatial extent) are found to be independent of the loading conditions and of the average crack front velocity. The distribution of local fluctuations of the crack front velocity are related to the observed avalanche size distribution. Space-time correlations of the local velocities show a simple diffusion growth behavior.

Evolution of the average avalanche shape with the universality class

A multitude of systems ranging from the Barkhausen effect in ferromagnetic materials to plastic deformation and earthquakes respond to slow external driving by exhibiting intermittent, scale-free avalanche dynamics or crackling noise. The avalanches are power-law distributed in size, and have a typical average shape: these are the two most important signatures of avalanching systems. Here we show how the average avalanche shape evolves with the universality class of the avalanche dynamics by employing a combination of scaling theory, extensive numerical simulations and data from crack propagation experiments. It follows a simple scaling form parameterized by two numbers, the scaling exponent relating the average avalanche size to its duration and a parameter characterizing the temporal asymmetry of the avalanches. The latter reflects a broken time-reversal symmetry in the avalanche dynamics, emerging from the local nature of the interaction kernel mediating the avalanche dynamics.

History independence of steady state in simultaneous two-phase flow through two-dimensional porous media.

It is well known that the transient behavior during drainage or imbibition in multiphase flow in porous media strongly depends on the history and initial condition of the system. However, when the steady-state regime is reached and both drainage and imbibition take place at the pore level, the influence of the evolution history and initial preparation is an open question. Here, we present an extensive experimental and numerical work investigating the history dependence of simultaneous steady-state two-phase flow through porous media. Our experimental system consists of a Hele-Shaw cell filled with glass beads which we model numerically by a network of disordered pores transporting two immiscible fluids. From measurements of global pressure evolution, histograms of saturation, and cluster-size distributions, we find that when both phases are flowing through the porous medium, the steady state does not depend on the initial preparation of the system or on the way it has been reached.

Film flow dominated simultaneous flow of two viscous incompressible fluids through a porous medium

We present an experimental study of two-phase flow in a quasi-two-dimensional porous medium. The two phases, a water-glycerol solution and a commercial food grade rapeseed/canola oil, having an oil to water-glycerol viscosity ratio of 1.3, are injected simultaneously into a Hele-Shaw cell with a mono-layer of randomly distributed glass beads. The two liquids are injected into the model from alternating point inlets. Initially, the porous model is filled with the water-glycerol solution. We observe that after an initial transient state, an overall static cluster configuration is obtained. While the oil is found to create a connected system spanning cluster, a large part of the water-glycerol clusters left behind the initial invasion front is observed to remain immobile throughout the rest of the experiment. This could suggest that the water-glycerol flow-dynamics is largely dominated by film flow. The flow pathways are thus given through the dynamics of the initial invasion. This behavior is quite different from that observed in systems with large viscosity differences between the two fluids, and where compressibility plays an important part of the process.

Direct velocity measurement of a turbulent shear flow in a planar Couette cell.

In a plane Couette cell a thin fluid layer consisting of water is sheared between the sides of a transparent band at Reynolds numbers ranging from 300 to 1400. The length of the cells flow channel is large compared to the film separation. To extract the flow velocity in the experiments, a correlation image velocimetry method is used on pictures recorded with a high-speed camera. The flow is recorded at a resolution that allows us to analyze flow patterns similar in size to the film separation. The fluid flow is then studied by calculating flow velocity autocorrelation functions. The turbulent patterns that arise on this scale above a critical Reynolds number of Re=360 display characteristic patterns that are proven by use of the calculated velocity autocorrelation functions. The patterns are metastable and reappear at different positions and times throughout the experiments. Typically these patterns are turbulent rolls which are elongated in the stream direction, which is the direction in which the band is moving. Although the flow states are metastable they possess similarities to the steady Taylor vortices known to appear in circular Taylor Couette cells.