A New Exponent Characterizing the Effect of Evaporation on Imbibition Experiments

We report imbibition experiments investigating the effect of evaporation on the interface roughness and mean interface height. We observe a new exponent characterizing the scaling of the saturated surface width. Further, we argue that evaporation can be usefully modeled by introducing a gradient in the strength of the disorder, in analogy with the gradient percolation model of Sapoval {\it et~al.}. By incorporating this gradient we predict a new critical exponent and a novel scaling relation for the interface width. Both the exponent value and the form of the scaling agree with the experimental results.Comment: 12 pages, REVTeX 3.0, figures on request (accepted for PRL

Path Crossing Exponents and the External Perimeter in 2D Percolation

2D Percolation path exponents $x^{\cal P}_{\ell}$ describe probabilities for traversals of annuli by $\ell$ non-overlapping paths, each on either occupied or vacant clusters, with at least one of each type. We relate the probabilities rigorously to amplitudes of $O(N=1)$ models whose exponents, believed to be exact, yield $x^{\cal P}_{\ell}=({\ell}^2-1)/12$. This extends to half-integers the Saleur--Duplantier exponents for $k=\ell/2$ clusters, yields the exact fractal dimension of the external cluster perimeter, $D_{EP}=2-x^{\cal P}_3=4/3$, and also explains the absence of narrow gate fjords, as originally found by Grossman and Aharony.Comment: 4 pages, 2 figures (EPSF). Revised presentatio

Three dimensional hysdrodynamic lattice-gas simulations of binary immiscible and ternary amphiphilic flow through porous media

We report the results of a study of multiphase flow in porous media. A Darcy's law for steady multiphase flow was investigated for both binary and ternary amphiphilic flow. Linear flux-forcing relationships satisfying Onsager reciprocity were shown to be a good approximation of the simulation data. The dependence of the relative permeability coefficients on water saturation was investigated and showed good qualitative agreement with experimental data. Non-steady state invasion flows were investigated, with particular interest in the asymptotic residual oil saturation. The addition of surfactant to the invasive fluid was shown to significantly reduce the residual oil saturation.Comment: To appear in Phys. Rev.

Viscous stabilization of 2D drainage displacements with trapping

We investigate the stabilization mechanisms due to viscous forces in the invasion front during drainage displacement in two-dimensional porous media using a network simulator. We find that in horizontal displacement the capillary pressure difference between two different points along the front varies almost linearly as function of height separation in the direction of the displacement. The numerical result supports arguments taking into account the loopless displacement pattern where nonwetting fluid flow in separate strands (paths). As a consequence, we show that existing theories developed for viscous stabilization, are not compatible with drainage when loopless strands dominate the displacement process.Comment: The manuscript has been substantially revised. Accepted in Phys. Rev. Let

Scaling properties of driven interfaces in disordered media

We perform a systematic study of several models that have been proposed for the purpose of understanding the motion of driven interfaces in disordered media. We identify two distinct universality classes: (i) One of these, referred to as directed percolation depinning (DPD), can be described by a Langevin equation similar to the Kardar-Parisi-Zhang equation, but with quenched disorder. (ii) The other, referred to as quenched Edwards-Wilkinson (QEW), can be described by a Langevin equation similar to the Edwards-Wilkinson equation but with quenched disorder. We find that for the DPD universality class the coefficient $\lambda$ of the nonlinear term diverges at the depinning transition, while for the QEW universality class either $\lambda = 0$ or $\lambda \to 0$ as the depinning transition is approached. The identification of the two universality classes allows us to better understand many of the results previously obtained experimentally and numerically. However, we find that some results cannot be understood in terms of the exponents obtained for the two universality classes {\it at\/} the depinning transition. In order to understand these remaining disagreements, we investigate the scaling properties of models in each of the two universality classes {\it above\/} the depinning transition. For the DPD universality class, we find for the roughness exponent $\alpha_P = 0.63 \pm 0.03$ for the pinned phase, and $\alpha_M = 0.75 \pm 0.05$ for the moving phase. For the growth exponent, we find $\beta_P = 0.67 \pm 0.05$ for the pinned phase, and $\beta_M = 0.74 \pm 0.06$ for the moving phase. Furthermore, we find an anomalous scaling of the prefactor of the width on the driving force. A new exponent $\varphi_M = -0.12 \pm 0.06$, characterizing the scaling of this prefactor, is shown to relate the values of the roughnessComment: Latex manuscript, Revtex 3.0, 15 pages, and 15 figures also available via anonymous ftp from ftp://jhilad.bu.edu/pub/abms/ (128.197.42.52

Reconstruction of individual cumulative radon exposures by low-level in vivo measurements and biokinetic modeling.

In vivo skull measurements of Pb-210 have been performed to assess the individual, chronic exposures of two persons living for 28 years in a house with a distinctly enhanced radon concentration of more than 10,000 Bq/m(3). A partial body counter consisting of 4 HPGe detectors, which were placed close to parietal positions of the head, was used in the study. The lower limit of detection of Pb-210 activity in the skeleton was found to be 40 Bq. Lead-210 activities of up to 152 Bq were found in the test persons, whereas no activity could be measured in an unexposed control person. The cumulative uptake of Pb-210 into the body was assessed for each single test person by using the ICRP respiratory tract and the biokinetic models. A fairly good agreement (within a factor of 2) between in vivo measurements and model was achieved for these two test persons. The technique used in the study may be a useful tool to evaluate assumptions, which have to be made for the reconstruction of individual, cumulative exposures to high radon concentrations