A mathematical model for fluid-glucose-albumin transport in peritoneal dialysis

A mathematical model for fluid and solute transport in peritoneal dialysis is constructed. The model is based on a three-component nonlinear system of two-dimensional partial differential equations for fluid, glucose and albumin transport with the relevant boundary and initial conditions. Its aim is to model ultrafiltration of water combined with inflow of glucose to the tissue and removal of albumin from the body during dialysis, and it does this by finding the spatial distributions of glucose and albumin concentrations and hydrostatic pressure. The model is developed in one spatial dimension approximation and a governing equation for each of the variables is derived from physical principles. Under certain assumptions the model are simplified with the aim of obtaining exact formulae for spatially non-uniform steady-state solutions. As the result, the exact formulae for the fluid fluxes from blood to tissue and across the tissue are constructed together with two linear autonomous ODEs for glucose and albumin concentrations in the tissue. The obtained analytical results are checked for their applicability for the description of fluid-glucose-albumin transport during peritoneal dialysis.Comment: 28 pages, 8 figures. arXiv admin note: text overlap with arXiv:1110.128

Void Fraction Measurment Beneath a Stationary Breaking Wave

Impedance based techniques have been used to quantify air entrainment by a stationary breaking wave at the bow of a ship. The present paper describes an impedance based void fraction meter which was developed to make measurements in this high speed, unsteady, multiphase flow, and details of its calibration are provided. In addition, air entrainment data from an experimental simulation of a bow wave are presented. The local, time averaged void fraction was mapped for flow cross sections beneath the plunging wave jet, revealing the location of the clouds of bubbles formed by that jet impacting the incoming water surface. Size distribution functions for the bubbles within the bubble clouds are also presented. The results are correlated with the wave structure described in Waniewski et al. (1997)

Bubble Measurements Downstream of Hydraulic Jumps

A phase Doppler anemometer (PDA) system was used to measure the velocity profiles and air bubble size distributions downstream of two-dimensional hydraulic jumps for different upstream flow conditions in a 1.92m long laboratory flume. The PDA detected bubbles from 1 to 500 [microns] in diameter, and more were found at the bottom of the downstream flow near the elevation of the upstream free surface. This distribution was more marked for smaller bubbles, those with diameters less that 100 [microns]. The migration of the bubbles is controlled by the effects of buoyancy and by turbulent mixing; the relative magnitude of their effects on bubble distribution depends strongly on bubble size, and also on the energy of the upstream flow

The Evolution of Cavitation Events with Speed and Scale of the Flow

This paper focuses on the different forms that individual cavitating events may take when the cavitation number is below the inception value (but not so low as to produce only attached cavities) and individual nuclei trigger individual cavitation events. It is a sequel to those of Kuhn de Chizelle et al. (1992a, 1992b, 1995) which described a set of cavitation scaling observations on simple Schiebe headforms conducted in the US Navy Large Cavitation Channel (LCC). The most common events observed in those experiments were traveling, hemi-spherical shaped bubbles which grew and collapsed as they were convected through the low pressure region on the headform. Several interesting variations were also observed, including the development of bubble tails and the triggering of patches, or local regions of attached cavitation. In the present paper, the frequency of occurrence of the various types of events is analyzed as well as how those probabilities changed with cavitation number, velocity and headform size. In general, the probabilities of tails and patches increased with decreasing cavitation number, but they also increased with increasing headform size and increasing velocity. A specific parametric dependence on these variables is suggested

Bow Wave Dynamics

Experimental studies of air entrainment by breaking waves are essential for advancing the understanding of these flows and creating valid models. The present study used experimental simulations of a ship bow wave to examine its dynamics and air entrainment processes. The simulated waves were created by a deflecting plate mounted at an angle in a supercritical free-surface flow in a flume. Measurements of the bow wave geometry at two scales and also for a bow wave created by a wedge in a towing tank are presented. Contact line and bow wave profile measurements from the different experiments are compared and demonstrate the similarity of the flume simulations to the towing tank experiments. The bow wave profile data from the towing tank experiments were used to investigate the scaling of the wave with the flow and the dependence on geometric parameters. In addition, surface disturbances observed on the plunging wave are documented herein because of the role they play in air entrainment. The air entrainment itself is explored in Waniewski et al (2001)

Flow patterns in nappe flow regime down low gradient stepped chutes

Although modern gravity dam spillways include often steep chutes operating in skimming flow regime, succession of free-falling nappes (i.e. nappe flow regime) are more common on low gradient chutes and cascades, and this flow situation received little attention to date. New experiments were conducted in nappe flows without hydraulic jump in two large-size facilities with flat slopes. The flow on the stepped cascade displayed complex, three-dimensional patterns. Detailed air-water flow measurements were performed in the jet, at nappe impact and in the downstream flow region. Key results demonstrated that the flow on each step was rapidly varied (RVF), highly three-dimensional and strongly aerated