Exact transverse macro dispersion coefficients for transport in heterogeneous porous media

We study transport through heterogeneous media. We derive the exact large scale transport equation. The macro dispersion coefficients are determined by additional partial differential equations. In the case of infinite Peclet numbers, we present explicit results for the transverse macro dispersion coefficients. In two spatial dimensions, we demonstrate that the transverse macro dispersion coefficient is zero. The result is not limited on lowest order perturbation theory approximations but is an exact result. However, the situation in three spatial dimensions is very different: The transverse macro dispersion coefficients are finite - a result which is confirmed by numerical simulations we performe

Pattern formation during the evaporation of a colloidal nanoliter drop: a numerical and experimental study

An efficient way to precisely pattern particles on solid surfaces is to dispense and evaporate colloidal drops, as for bioassays. The dried deposits often exhibit complex structures exemplified by the coffee ring pattern, where most particles have accumulated at the periphery of the deposit. In this work, the formation of deposits during the drying of nanoliter colloidal drops on a flat substrate is investigated numerically and experimentally. A finite-element numerical model is developed that solves the Navier-Stokes, heat and mass transport equations in a Lagrangian framework. The diffusion of vapor in the atmosphere is solved numerically, providing an exact boundary condition for the evaporative flux at the droplet-air interface. Laplace stresses and thermal Marangoni stresses are accounted for. The particle concentration is tracked by solving a continuum advection-diffusion equation. Wetting line motion and the interaction of the free surface of the drop with the growing deposit are modeled based on criteria on wetting angles. Numerical results for evaporation times and flow field are in very good agreement with published experimental and theoretical results. We also performed transient visualization experiments of water and isopropanol drops loaded with polystyrene microsphere evaporating on respectively glass and polydimethylsiloxane substrates. Measured evaporation times, deposit shape and sizes, and flow fields are in very good agreement with the numerical results. Different flow patterns caused by the competition of Marangoni loops and radial flow are shown to determine the deposit shape to be either a ring-like pattern or a homogeneous bump

Prediction of blood back spatter from a gunshot in bloodstain pattern analysis

A theoretical model for predicting and interpreting blood-spatter patterns resulting from a gunshot wound is proposed. The physical process generating a backward spatter of blood is linked to the Rayleigh-Taylor instability of blood accelerated toward the surrounding air, allowing the determination of the initial distribution of drop sizes and velocities. Then the motion of many drops in air is considered with governing equations accounting for gravity and air drag. Based on these equations, a numerical solution is obtained. It predicts the atomization process, the trajectories of the back-spatter drops of blood from the wound to the ground, the impact angle, and the impact Weber number on the ground, as well as the distribution and location of bloodstains and their shape and sizes. A parametric study is undertaken to predict patterns of backward blood spatter under realistic conditions corresponding to the experiments conducted in the present work. The results of the model are compared to the experimental data on back spatter generated by a gunshot impacting a blood-impregnated sponge

Effective velocity for transport in heterogeneous compressible flows with mean drift

Solving transport equations in heterogeneous flows might give rise to scale dependent transport behavior with effective large scale transport parameters differing from those found on smaller scales. For incompressible velocity fields, homogenization methods have proven to be powerful in describing the effective transport parameters. In this paper, we aim at studying the effective drift of transport problems in heterogeneous compressible flows. Such a study was done by Vergassola and Avellaneda in Physica D 106, 148 (1997). There, it was shown that for static compressible flow without mean drift, impacts on the large scale drift do not occur. We will first discuss the impact of a mean drift and show that static compressible flow with mean drift can produce a heterogeneity driven large scale drift (or ballistic transport). For the case of Gaussian stationary random processes, we derive explicit results for the large scale drift. Moreover, we show that the large scale or effective drift depends on the small scale diffusion coefficients and thus on the molecular weights of the particles. This study could be applied to weight-based particle separation. Numerical simulations are presented to illustrate these phenomena. © 2008 American Institute of Physics

Numerical simulation of blood flow and pressure drop in the pulmonary arterial and venous circulation

A novel multiscale mathematical and computational model of the pulmonary circulation is presented and used to analyse both arterial and venous pressure and flow. This work is a major advance over previous studies by Olufsen et al. (Ann Biomed Eng 28:1281–1299, 2012) which only considered the arterial circulation. For the first three generations of vessels within the pulmonary circulation, geometry is specified from patient-specific measurements obtained using magnetic resonance imaging (MRI). Blood flow and pressure in the larger arteries and veins are predicted using a nonlinear, cross-sectional-area-averaged system of equations for a Newtonian fluid in an elastic tube. Inflow into the main pulmonary artery is obtained from MRI measurements, while pressure entering the left atrium from the main pulmonary vein is kept constant at the normal mean value of 2 mmHg. Each terminal vessel in the network of ‘large’ arteries is connected to its corresponding terminal vein via a network of vessels representing the vascular bed of smaller arteries and veins. We develop and implement an algorithm to calculate the admittance of each vascular bed, using bifurcating structured trees and recursion. The structured-tree models take into account the geometry and material properties of the ‘smaller’ arteries and veins of radii ≥ 50 μ m. We study the effects on flow and pressure associated with three classes of pulmonary hypertension expressed via stiffening of larger and smaller vessels, and vascular rarefaction. The results of simulating these pathological conditions are in agreement with clinical observations, showing that the model has potential for assisting with diagnosis and treatment for circulatory diseases within the lung

Total Aortic Arch Replacement: Superior Ventriculo-Arterial Coupling with Decellularized Allografts Compared with Conventional Prostheses.

BACKGROUND: To date, no experimental or clinical study provides detailed analysis of vascular impedance changes after total aortic arch replacement. This study investigated ventriculoarterial coupling and vascular impedance after replacement of the aortic arch with conventional prostheses vs. decellularized allografts. METHODS: After preparing decellularized aortic arch allografts, their mechanical, histological and biochemical properties were evaluated and compared to native aortic arches and conventional prostheses in vitro. In open-chest dogs, total aortic arch replacement was performed with conventional prostheses and compared to decellularized allografts (n = 5/group). Aortic flow and pressure were recorded continuously, left ventricular pressure-volume relations were measured by using a pressure-conductance catheter. From the hemodynamic variables end-systolic elastance (Ees), arterial elastance (Ea) and ventriculoarterial coupling were calculated. Characteristic impedance (Z) was assessed by Fourier analysis. RESULTS: While Ees did not differ between the groups and over time (4.1+/-1.19 vs. 4.58+/-1.39 mmHg/mL and 3.21+/-0.97 vs. 3.96+/-1.16 mmHg/mL), Ea showed a higher increase in the prosthesis group (4.01+/-0.67 vs. 6.18+/-0.20 mmHg/mL, P<0.05) in comparison to decellularized allografts (5.03+/-0.35 vs. 5.99+/-1.09 mmHg/mL). This led to impaired ventriculoarterial coupling in the prosthesis group, while it remained unchanged in the allograft group (62.5+/-50.9 vs. 3.9+/-23.4%). Z showed a strong increasing tendency in the prosthesis group and it was markedly higher after replacement when compared to decellularized allografts (44.6+/-8.3dyn.sec.cm-5 vs. 32.4+/-2.0dyn.sec.cm-5, P<0.05). CONCLUSIONS: Total aortic arch replacement leads to contractility-afterload mismatch by means of increased impedance and invert ventriculoarterial coupling ratio after implantation of conventional prostheses. Implantation of decellularized allografts preserves vascular impedance thereby improving ventriculoarterial mechanoenergetics after aortic arch replacement

Money matters: a critique of 'informed financial consent'.

In recent years, concerns about the financial burdens of health care and growing recognition of the relevance of cost to decision making and patient experience have increasingly focused attention on financial 'transparency' and disclosure of costs to patients. In some jurisdictions, there have been calls not only for timely disclosure of costs information, but also for 'informed financial consent'. However, simply putting the 'financial' into 'informed consent' and invoking an informed consent standard for cost information encounters several ethical, legal, and practical difficulties. This article will examine the viability and desirability of 'informed financial consent', and whether it is possible to derive ideas from traditional informed consent that may improve decision making and the patient experience. We argue that, while there are important legal, ethical, and practical challenges to consider, some of the principles of informed consent to treatment can usefully guide financial communication. We also argue that, while medical practitioners (and their delegates) have an important role to play in bridging the gap between disclosure and enabling informed (financial) decision making, this must be part of a multi-faceted approach to financial communication that acknowledges the influence of non-clinical providers and other structural forces on discharging such obligations

What we talk about when we talk about uncertainty. Toward a unified, data-driven framework for uncertainty characterization in hydrogeology

In this manuscript, we compare and discuss different frameworks for hydrogeological uncertainty analysis. Since uncertainty is a property of knowledge, we base this comparison on purely epistemological concepts. In a detailed comparison between different candidates, we make the case for Bayesianism, i.e., the framework of reasoning about uncertainty using probability theory. We motivate the use of Bayesian tools, shortly explain the properties of Bayesian inference, prediction and decision and identify the most pressing current challenges of this framework. In hydrogeology, these challenges are the derivation of prior distributions for the parametric uncertainty, typically hydraulic conductivity values, as well as the most relevant paradigm for generating subsurface structures for assessing the structural uncertainty. We present the most commonly used paradigms and give detailed advice on two specific paradigms; Gaussian multivariate random fields as well as multiple-point statistics, both of which have benefits and drawbacks. Without settling for either of these paradigms, we identify the lack of open-access data repositories as the most pressing current impediment for the advancement of data-driven uncertainty analysis. We detail the shortcomings of the current situation and describe a number of steps which could foster the application of both the Gaussian as well as the multiple-point paradigm. We close the manuscript with a call for a community-wide initiative to create this necessary support

Effects of uncertainty in soil properties on simulated hydrological states and fluxes at different spatio-temporal scales

Soil properties show high heterogeneity at different spatial scales and their correct characterization remains a crucial challenge over large areas. The aim of the study is to quantify the impact of different types of uncertainties that arise from the unresolved soil spatial variability on simulated hydrological states and fluxes. Three perturbation methods are presented for the characterization of uncertainties in soil properties. The methods are applied on the soil map of the upper Neckar catchment (Germany), as an example. The uncertainties are propagated through the distributed mesoscale hydrological model (mHM) to assess the impact on the simulated states and fluxes. The model outputs are analysed by aggregating the results at different spatial and temporal scales. These results show that the impact of the different uncertainties introduced in the original soil map is equivalent when the simulated model outputs are analysed at the model grid resolution (i.e. 500 m). However, several differences are identified by aggregating states and fluxes at different spatial scales (by subcatchments of different sizes or coarsening the grid resolution). Streamflow is only sensitive to the perturbation of long spatial structures while distributed states and fluxes (e.g. soil moisture and groundwater recharge) are only sensitive to the local noise introduced to the original soil properties. A clear identification of the temporal and spatial scale for which finer-resolution soil information is (or is not) relevant is unlikely to be universal. However, the comparison of the impacts on the different hydrological components can be used to prioritize the model improvements in specific applications, either by collecting new measurements or by calibration and data assimilation approaches. In conclusion, the study underlines the importance of a correct characterization of uncertainty in soil properties. With that, soil maps with additional information regarding the unresolved soil spatial variability would provide strong support to hydrological modelling applications