Many environmental and industrial processes depend on how fluids displace each other in porous materials. However, the flow dynamics that govern this process are still poorly understood, hampered by the lack of methods to measure flows in optically opaque, microscopic geometries. We introduce a 4D microvelocimetry method based on high-resolution X-ray computed tomography with fast imaging rates (up to 4 Hz). We use this to measure flow fields during unsteady-state drainage, injecting a viscous fluid into rock and filter samples. This provides experimental insight into the nonequilibrium energy dynamics of this process. We show that fluid displacements convert surface energy into kinetic energy. The latter corresponds to velocity perturbations in the pore-scale flow field behind the invading fluid front, reaching local velocities more than 40 times faster than the constant pump rate. The characteristic length scale of these perturbations exceeds the characteristic pore size by more than an order of magnitude. These flow field observations suggest that nonlocal dynamic effects may be long-ranged even at low capillary numbers, impacting the local viscous-capillary force balance and the representative elementary volume. Furthermore, the velocity perturbations can enhance unsaturated dispersive mixing and colloid transport and yet, are not accounted for in current models. Overall, this work shows that 4D X-ray velocimetry opens the way to solve long-standing fundamental questions regarding flow and transport in porous materials, underlying models of, e.g., groundwater pollution remediation and subsurface storage of CO ₂ and hydrogen.

Fluid flow through intricate confining geometries often exhibits complex behaviors, certainly in porous materials, e.g., in groundwater flows or the operation of filtration devices and porous catalysts. However, it has remained extremely challenging to measure 3D flow fields in such micrometer-scale geometries. Here, we introduce a new 3D velocimetry approach for optically opaque porous materials, based on time-resolved x-ray micro-computed tomography (CT). We imaged the movement of x-ray tracing micro-particles in creeping flows through the pores of a sandpack and a porous filter, using laboratory-based CT at frame rates of tens of seconds and voxel sizes of 12 μm. For both experiments, fully three-dimensional velocity fields were determined based on thousands of individual particle trajectories, showing a good match to computational fluid dynamics simulations. Error analysis was performed by investigating a realistic simulation of the experiments. The method has the potential to measure complex, unsteady 3D flows in porous media and other intricate microscopic geometries. This could cause a breakthrough in the study of fluid dynamics in a range of scientific and industrial application fields.

Maintaining chemical and physical stability of the product during freeze-drying is important but challenging. In addition, freeze-drying is typically associated with long process times. Therefore, mechanistic models have been developed to maximize drying efficiency without altering the chemical or physical stability of the product. Dried product mass transfer resistance ( $R_p$ ) is a critical input for these mechanistic models. Currently available techniques to determine $R_p$ only provide an estimation of the mean $R_p$ and do not allow measuring and determining essential local (i.e., intra-vial) $R_p$ differences. In this study, we present an analytical method, based on four-dimensional micro-computed tomography (4D- $\mathsf{\mu }$ CT), which enables the possibility to determine intra-vial $R_p$ differences. Subsequently, these obtained $R_p$ values are used in a mechanistic model to predict the drying time distribution of a spin-frozen vial. Finally, this predicted primary drying time distribution is experimentally verified via thermal imaging during drying. It was further found during this study that 4D- $\mathsf{\mu }$ CT uniquely allows measuring and determining other essential freeze-drying process parameters such as the moving direction(s) of the sublimation front and frozen product layer thickness, which allows gaining accurate process knowledge. To conclude, the study reveals that the variation in the end of primary drying time of a single vial could be predicted accurately using 4D- $\mathsf{\mu }$ CT as similar results were found during the verification using thermal imaging.

Time-resolved high-resolution X-ray Computed Tomography (4D $\mu$CT) is an imaging technique that offers insight into the evolution of dynamic processes inside materials that are opaque to visible light. Conventional tomographic reconstruction techniques are based on constructing a sequence of 3D images from radiographic projections, recorded during time-frames that represent global sample states. This frame-based approach limits the temporal resolution compared to dynamic radiography experiments, and it leads to an inflation of the amount of data. This results in costly post-processing computations to quantify the dynamic behaviour from the sequence of time-frames, hereby often ignoring the temporal correlations of the sample structure. Our proposed 4D $\mu$CT reconstruction technique, named DYRECT, estimates individual attenuation evolution profiles for each position in the sample with time resolution down to the single projection level. This leads to a novel memory-efficient event-based representation for samples that display sudden, irreversible transitions over time. As little as three image volumes suffice for a broad range of applications: the initial attenuations, the final attenuations and the local transition times. This third volume represents spatially distributed events on a continuous timescale instead of the discrete global time-frames. We propose a method to iteratively reconstruct the transition times and the attenuation volumes. The dynamic reconstruction technique was validated on synthetic ground truth data and experimental data, and was found to effectively pinpoint the transition times in the synthetic dataset with a time resolution corresponding to less than a tenth of the amount of projections required to reconstruct traditional $\mu$CT time-frames.