We study the gravity driven flow of two fluid phases in a one dimensional homogeneous porous column when history dependence of the pressure difference between the phases (capillary pressure) is taken ...into account. In the hyperbolic limit, solutions of such systems satisfy the Buckley-Leverett equation with a non-monotone flux function. However, solutions for the hysteretic case do not converge to the classical solutions in the hyperbolic limit in a wide range of situations. In particular, with Riemann data as initial condition, stationary shocks become possible in addition to classical components such as shocks, rarefaction waves and constant states. We derive an admissibility criterion for the stationary shocks and outline all admissible shocks. Depending on the capillary pressure functions, flux function and the Riemann data, two cases are identified a priori for which the solution consists of a stationary shock. In the first case, the shock remains at the point where the initial condition is discontinuous. In the second case, the solution is frozen in time in at least one semi-infinite half. The predictions are verified using numerical results.
We analyze the motion of a sharp interface between fresh and salt groundwater in horizontal, confined aquifers of infinite extend. The analysis is based on earlier results of De Josselin de Jong ...(Proc Euromech 143:75–82,
1981
). Parameterizing the height of the interface along the horizontal base of the aquifer and assuming the validity of the Dupuit–Forchheimer approximation in both the fresh and saltwater, he derived an approximate interface motion equation. This equation is a nonlinear doubly degenerate diffusion equation in terms of the height of the interface. In that paper, he also developed a stream function-based formulation for the dynamics of a two-fluid interface. By replacing the two fluids by one hypothetical fluid, with a distribution of vortices along the interface, the exact discharge field throughout the flow domain can be determined. Starting point for our analysis is the stream function formulation. We derive an exact integro-differential equation for the movement of the interface. We show that the pointwise differential terms are identical to the approximate Dupuit–Forchheimer interface motion equation as derived by De Josselin de Jong. We analyze (mathematical) properties of the additional integral term in the exact interface motion formulation to validate the approximate Dupuit–Forchheimer interface motion equation. We also consider the case of flat interfaces, and we study the behavior of the toe of the interface. In particular, we give a criterion for finite or infinite speed of propagation.
The typical characteristic of a thin porous layer is that its thickness is much smaller than its in-plane dimensions. This often leads to physical behaviors that are different from three-dimensional ...porous media. The classical Richards equation is insufficient to simulate many flow conditions in thin porous media. Here, we have provided an alternative approach by accounting for the dynamic capillarity effect. In this study, we have presented a set of one-dimensional in-plane imbibition and subsequent drainage experiments in a thin fibrous layer. The X-ray transmission method was used to measure saturation distributions along the fibrous sample. We simulated the experimental results using Richards equation either with classical capillary equation or with a so-called dynamic capillarity term. We have found that the standard Richards equation was not able to simulate the experimental results, and the dynamic capillarity effect should be taken into account in order to model the spontaneous imbibition. The experimental data presented here may also be used by other researchers to validate their models.
Article Highlights
We have presented a set of one-dimensional in-plane imbibition and subsequent drainage experiments in a thin fibrous layer.
The experimental data were simulated using the Richards equation either with classical capillary equation or with a so-call dynamic capillarity term.
The dynamic capillarity effect should be taken into account in order to model the spontaneous imbibition.
Soil salinization is a major cause of soil degradation and hampers plant growth. For soils saturated with saline water, the evaporation of water induces accumulation of salt near the top of the soil. ...The remaining liquid gets an increasingly larger density due to the accumulation of salt, giving a gravitationally unstable situation, where instabilities in the form of fingers can form. These fingers can, hence, lead to a net downward transport of salt. We here investigate the appearance of these fingers through a linear stability analysis and through numerical simulations. The linear stability analysis gives criteria for onset of instabilities for a large range of parameters. Simulations using a set of parameters give information also about the development of the fingers after onset. With this knowledge, we can predict whether and when the instabilities occur, and their effect on the salt concentration development near the top boundary.
To analyze the diagnostic sensitivity and specificity of various brain-derived proteins (14-3-3, Tau, neuron specific enolase NSE, and S100b) in the CSF of patients with Creutzfeldt-Jakob disease ...(CJD) and to analyze biologic factors that modify these parameters.
CSF was tested for 14-3-3, Tau, NSE, and S100b in 1,859 patients with sporadic, genetic, iatrogenic, and variant CJD, and in 1,117 controls.
The highest sensitivity was achieved for 14-3-3 and Tau in sporadic CJD (85% and 86%), and a combined determination of 14-3-3 and Tau, S100b, or NSE increased the sensitivity to over 93%. A multivariate analysis showed that the sensitivity of all tests was highest in patients with the shortest disease duration, age at onset >40 years, and homozygosity at codon 129 of the prion protein gene. In a group of patients with repeated lumbar punctures, a second test also increased the diagnostic sensitivity.
The detection of elevated levels of brain-derived proteins in the CSF in patients with suspected Creutzfeldt-Jakob disease is a valuable diagnostic test. A second lumbar puncture may be of value in patients with atypical clinical course in whom the first test was negative.
This paper extends the work of van Duijn et al. (2018) where travelling wave solutions for wetting fronts were considered under the presence of only capillary hysteresis effect and only dynamic ...capillary effect. In this work, we investigate how the gravity driven wetting fronts behave while moving through long vertical homogeneous porous columns, under the combined effect of capillary hysteresis and dynamic capillarity. It is shown that the developed saturation profiles will exhibit non-monotone behaviour if certain parametric conditions are satisfied. The characteristics of the profiles are explained in detail for all the cases. Moreover, parametric conditions that inhibit the fronts from reaching full saturation are laid out. The analysis agrees well with experimental observations. Finally, numerical results are shown that confirm all the theoretical predictions.
Major mood disorders, which primarily include bipolar disorder and major depressive disorder, are the leading cause of disability worldwide and pose a major challenge in identifying robust risk ...genes. Here, we present data from independent large-scale clinical data sets (including 29 557 cases and 32 056 controls) revealing brain expressed protocadherin 17 (PCDH17) as a susceptibility gene for major mood disorders. Single-nucleotide polymorphisms (SNPs) spanning the PCDH17 region are significantly associated with major mood disorders; subjects carrying the risk allele showed impaired cognitive abilities, increased vulnerable personality features, decreased amygdala volume and altered amygdala function as compared with non-carriers. The risk allele predicted higher transcriptional levels of PCDH17 mRNA in postmortem brain samples, which is consistent with increased gene expression in patients with bipolar disorder compared with healthy subjects. Further, overexpression of PCDH17 in primary cortical neurons revealed significantly decreased spine density and abnormal dendritic morphology compared with control groups, which again is consistent with the clinical observations of reduced numbers of dendritic spines in the brains of patients with major mood disorders. Given that synaptic spines are dynamic structures which regulate neuronal plasticity and have crucial roles in myriad brain functions, this study reveals a potential underlying biological mechanism of a novel risk gene for major mood disorders involved in synaptic function and related intermediate phenotypes.
Mitochondrial DNA copy number (mtDNA-CN) measured from blood specimens is a minimally invasive marker of mitochondrial function that exhibits both inter-individual and intercellular variation. To ...identify genes involved in regulating mitochondrial function, we performed a genome-wide association study (GWAS) in 465,809 White individuals from the Cohorts for Heart and Aging Research in Genomic Epidemiology (CHARGE) consortium and the UK Biobank (UKB). We identified 133 SNPs with statistically significant, independent effects associated with mtDNA-CN across 100 loci. A combination of fine-mapping, variant annotation, and co-localization analyses was used to prioritize genes within each of the 133 independent sites. Putative causal genes were enriched for known mitochondrial DNA depletion syndromes (
p
= 3.09 × 10
–15
) and the gene ontology (GO) terms for mtDNA metabolism (
p
= 1.43 × 10
–8
) and mtDNA replication (
p
= 1.2 × 10
–7
). A clustering approach leveraged pleiotropy between mtDNA-CN associated SNPs and 41 mtDNA-CN associated phenotypes to identify functional domains, revealing three distinct groups, including platelet activation, megakaryocyte proliferation, and mtDNA metabolism. Finally, using mitochondrial SNPs, we establish causal relationships between mitochondrial function and a variety of blood cell-related traits, kidney function, liver function and overall (
p
= 0.044) and non-cancer mortality (
p
= 6.56 × 10
–4
).
Humans sleep approximately a third of their lifetime. The observation that individuals with either long or short sleep duration show associations with metabolic syndrome and psychiatric disorders ...suggests that the length of sleep is adaptive. Although sleep duration can be influenced by photoperiod (season) and phase of entrainment (chronotype), human familial sleep disorders indicate that there is a strong genetic modulation of sleep. Therefore, we conducted high-density genome-wide association studies for sleep duration in seven European populations (N=4251). We identified an intronic variant (rs11046205; P=3.99 × 10(-8)) in the ABCC9 gene that explains asymptotically =5% of the variation in sleep duration. An influence of season and chronotype on sleep duration was solely observed in the replication sample (N=5949). Meta-analysis of the associations found in a subgroup of the replication sample, chosen for season of entry and chronotype, together with the discovery results showed genome-wide significance. RNA interference knockdown experiments of the conserved ABCC9 homologue in Drosophila neurons renders flies sleepless during the first 3h of the night. ABCC9 encodes an ATP-sensitive potassium channel subunit (SUR2), serving as a sensor of intracellular energy metabolism.
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