In a recent paper [Yiotis et al., Phys. Rev. E 85, 046308 (2012)] we developed a model for the drying of porous media in the presence of gravity. It incorporated effects of corner film flow, internal and external mass transfer, and the effect of gravity. Analytical results were derived when gravity opposes drying and hence leads to a stable percolation drying front. In this paper, we test the theory using laboratory experiments. A series of isothermal drying experiments in glass bead packings saturated with volatile hydrocarbons is conducted. The transparent glass cells containing the packing allow for the visual monitoring of the phase distribution patterns below the surface, including the formation of liquid films, as the gaseous phase invades the pore space, and for the control of the thickness of the diffusive mass boundary layer over the packing. The experimental results agree very well with theory, provided that the latter is generalized to account for the effects of corner roundness in the film region (which was neglected in the theoretical part). We demonstrate the existence of an early constant rate period (CRP), which lasts as long as the films saturate the surface of the packing, and of a subsequent falling rate period (FRP), which begins practically after the detachment of the film tips from the external surface. During the CRP, the process is controlled by diffusion within the stagnant gaseous phase in the upper part of the cells, yielding a Stefan tube problem solution. During the FRP, the process is controlled by diffusion within the packing, with a drying rate inversely proportional to the observed position of the film tips in the cell. Theoretical and experimental results compare favorably for a specific value of the roundness of the films, which is found to be constant and equal to 0.2 for various conditions, and verify the theoretical dependence on the capillary Ca(f), Bond Bo, and Sherwood Sh numbers.

We develop a mathematical model for the drying of porous media in the presence of gravity. The model incorporates effects of corner flow through macroscopic liquid films that form in the cavities of pore walls, mass transfer by diffusion in the dry regions of the medium, external mass transfer over the surface, and the effect of gravity. We consider two different cases: when gravity opposes liquid flow in the corner films and leads to a stable percolation drying front, and when it acts in the opposite direction. In this part, we develop analytical results when the problem can be cast as an equivalent continuum and described as a one-dimensional (1D) problem. This is always the case when gravity acts against drying by opposing corner flow, or when it enhances drying by increasing corner film flow but it is sufficiently small. We obtain results for all relevant variables, including drying rates, extent of the macroscopic film region, and the demarkation of the two different regimes of constant rate period and falling rate period, respectively. The effects of dimensionless variables, such as the bond number, the capillary number, and the Sherwood number for external mass transfer are investigated. When gravity acts to enhance drying, a 1D solution is still possible if an appropriately defined Rayleigh number is above a critical threshold. We derive a linear stability analysis of a model problem under this condition that verifies front stability. Further analysis of this problem, when the Rayleigh number is below critical, requires a pore-network simulator which will be the focus of future work.

Several studies have reported the beneficial effects of Lawsonia inermis on wound healing, but the mechanism of action is still unknown. This study aimed to investigate the effectiveness of a new ointment formulation of hydroethanolic extract leaves of L. inermis on wound healing by gene expression of glucose transporter‐1 (Glut‐1) and insulin‐like growth factor I (Igf‐1) in Wistar rats. The animals were topically treated with different doses of L. inermis. An experimentally induced circular excisional wound model of 314 mm2 surface area was surgically created. The percentage of wound contraction and histopathological changes was assessed at different time points following wound induction. The expression of Glut‐1 and Igf‐1 was evaluated by reverse‐transcription PCR. Topical administration of L. inermis, dose dependently, shortened inflammatory phase, accelerated cellular proliferation, and enhanced wound contraction ratio. It also improved revascularization, collagen deposition, and re‐epithelialization rate and promoted intracytoplasmic carbohydrate storage (P < 0.05). Moreover, the mRNA levels of Igf‐1 and Glut‐1 were significantly higher in the L. inermis‐treated groups than the control group (P < 0.05). Topical administration of L. inermis promoted the healing process by reducing tissue inflammation and increasing glucose uptake, which was mediated by up‐regulating the expression of Igf‐1 and Glut‐1.

This paper presents an analytical model for three-phase flow towards a horizontal well with multi-stage hydraulic fractures, producing from a low-permeability oil reservoir (e.g. shale oil) under primary depletion. The model accounts for time-dependent trilinear-flow model (Brown et al. 2011) and solution-gas drive model (Muskat 1981). While there are numerous analytical models proposed for inflow of horizontal wells with multistage fractures, they do not consider three-phase flow condition and/or time dependent behavior (i.e. they assume steady or pseudo-steady state conditions). These two conditions should be honored for low-permeability oil reservoirs with prolonged transient period which produce oil, water and dissolved gas. In this paper, we first present the mathematical framework for the transient three-phase trilinear flow towards a multi-fractured horizontal well in a bounded oil reservoir. Later, we combine the flow equations with the material balance equations to account for pressure depletion and solution-gas drive during primary production. We compare the predictions of our analytical model with a commercial numerical simulator. We demonstrate very good agreements of these two different approaches. Last, the advantages and limitations of this new method are discussed. Production forecast using the presented analytical model is significantly faster in comparison to the numerical simulator. This finds applications where multiple realizations are required, either during the optimal design of key factors (i.e. number of stages, spacing, optimal fracture conductivity) or during the characterization of hydraulic fractures by matching the production history.