scholarly journals Energy dispersion in turbulent jets. Part 1. Direct simulation of steady and unsteady jets

2014 ◽  
Vol 763 ◽  
pp. 500-537 ◽  
Author(s):  
John Craske ◽  
Maarten van Reeuwijk
Keyword(s):  
Steady State ◽  
Momentum Flux ◽  
Propagation Speed ◽  
Turbulent Jets ◽  
Type I ◽  
Type Ii ◽  
Governing Equations ◽  
Unsteady Jets ◽  
Longitudinal Mixing ◽  
Self Similar

AbstractWe study the physics of unsteady turbulent jets using direct numerical simulation (DNS) by introducing an instantaneous step change (both up and down) in the source momentum flux. Our focus is on the propagation speed and rate of spread of the resulting front. We show that accurate prediction of the propagation speed requires information about the energy flux in addition to the momentum flux in the jet. Our observations suggest that the evolution of a front in a jet is a self-similar process that accords with the classical dispersive scaling$z\sim \sqrt{t}$. In the analysis of the problem we demonstrate that the use of a momentum–energy framework of the kind used by Priestley & Ball (Q. J. R. Meteorol. Soc., vol. 81, 1955, pp. 144–157) has several advantages over the classical mass–momentum formulation. In this regard we generalise the approach of Kaminskiet al. (J. Fluid Mech., vol. 526, 2005, pp. 361–376) to unsteady problems, neglecting only viscous effects and relatively small boundary terms in the governing equations. Our results show that dispersion originating from the radial dependence of longitudinal velocity plays a fundamental role in longitudinal transport. Indeed, one is able to find dispersion in the steady state, although it has received little attention because its effects can then be absorbed into the entrainment coefficient. Specifically, we identify two types of dispersion. Type I dispersion exists in a steady state and determines the rate at which energy is transported relative to the rate at which momentum is transported. In unsteady jets type I dispersion is responsible for the separation of characteristic curves and thus the hyperbolic, rather than parabolic, nature of the governing equations, in the absence of longitudinal mixing. Type II dispersion is equivalent to Taylor dispersion and results in the longitudinal mixing of the front. This mixing is achieved by a deformation of the self-similar profiles that one finds in steady jets. Using a comparison with the local eddy viscosity, and by examining dimensionless fluxes in the vicinity of the front, we show that type II dispersion provides a dominant source of longitudinal mixing.

scholarly journals Energy dispersion in turbulent jets. Part 2. A robust model for unsteady jets

2014 ◽  
Vol 763 ◽  
pp. 538-566 ◽  
Author(s):  
John Craske ◽  
Maarten van Reeuwijk
Keyword(s):  
Momentum Flux ◽  
Longitudinal Velocity ◽  
Sudden Change ◽  
Turbulent Jets ◽  
Local Deformation ◽  
Integral Model ◽  
Type I ◽  
Gaussian Form ◽  
Gaussian Profile ◽  
Unsteady Jets

AbstractIn this paper we develop an integral model for an unsteady turbulent jet that incorporates longitudinal dispersion of two distinct types. The model accounts for the difference in the rate at which momentum and energy are advected (type I dispersion) and for the local deformation of velocity profiles that occurs in the vicinity of a sudden change in the momentum flux (type II dispersion). We adapt the description of dispersion in pipe flow by Taylor (Proc. R. Soc. Lond. A, vol. 219, 1953, pp. 186–203) to develop a dispersion closure for the longitudinal transportation of energy in unsteady jets. We compare our model’s predictions to results from direct numerical simulation and find a good agreement. The model described in this paper is robust and can be solved numerically using a simple central differencing scheme. Using the assumption that the longitudinal velocity profile in a jet has an approximately Gaussian form, we show that unsteady jets remain approximately straight-sided when their source area is fixed. Straight-sidedness provides an algebraic means of reducing the order of the governing equations and leads to a simple advection–dispersion relation. The physical process responsible for straight-sidedness is type I dispersion, which, in addition to determining the local response of the area of the jet, determines the growth rate of source perturbations. In this regard the Gaussian profile has the special feature of ensuring straight-sidedness and being insensitive to source perturbations. Profiles that are more peaked than the Gaussian profile attenuate perturbations and, following an increase (decrease) in the source momentum flux, lead to a local decrease (increase) in the area of the jet. Conversely, profiles that are flatter than the Gaussian amplify perturbations and lead to a local increase (decrease) in the area of the jet.

Effects of KCNQ channel blockers on K+ currents in vestibular hair cells

2001 ◽  
Vol 280 (3) ◽  
pp. C473-C480 ◽  
Author(s):  
Katherine J. Rennie ◽  
Tianxiang Weng ◽  
Manning J. Correia
Keyword(s):  
Steady State ◽  
Hair Cells ◽  
Low Voltage ◽  
Dissociation Constants ◽  
Channel Blockers ◽  
Type I ◽  
Type Ii ◽  
Kcnq Channels ◽  
Vestibular Hair Cells ◽  
Inward Currents

Linopirdine and XE991, selective blockers of K+ channels belonging to the KCNQ family, were applied to hair cells isolated from gerbil vestibular system and to hair cells in slices of pigeon crista. In type II hair cells, both compounds inhibited a slowly activating, slowly inactivating component of the macroscopic current recruited at potentials above −60 mV. The dissociation constants for linopirdine and XE991 block were <5 μM. A similar component of the current was also blocked by 50 μM capsaicin in gerbil type II hair cells. All three drugs blocked a current component that showed steady-state inactivation and a biexponential inactivation with time constants of ∼300 ms and 4 s. Linopirdine (10 μM) reduced inward currents through the low-voltage-activated K+ current in type I hair cells, but concentrations up to 200 μM had little effect on steady-state outward K+ current in these cells. These results suggest that KCNQ channels may be present in amniote vestibular hair cells.

scholarly journals Modeling the Dynamic Concentration Profiles and Efficacy of Type-I and Type-II Photopolymerization

2018 ◽  
Author(s):  
Jui-Teng Lin ◽  
Da-Chuan Cheng ◽  
Kuo-Ti Chen ◽  
Hsia-Wei Liu
Keyword(s):  
Steady State ◽  
Light Intensity ◽  
Light Exposure ◽  
Light Dose ◽  
Type I ◽  
Concentration Profiles ◽  
Type Ii ◽  
Photoinitiated Polymerization ◽  
Lower Light ◽  
Dynamic Concentration

The kinetics and efficacy profiles of photoinitiated polymerization are theoretically presented. For the same dose, lower light intensity achieves a higher steady-state-efficacy (SSE) in type-I; in contrast, type-II has an equal SSE. Higher light intensity has a faster rising efficacy, due to faster depletion of photoinitiator (PS) concentration. However, type-II process is also affected by the available oxygen. Higher light intensity produces more efficient singlet oxygen, resulting a higher transient efficacy, in which all intensities reach the same SSE when oxygen is completely depleted. With external oxygen, type-II efficacy increases with time, otherwise, it is governed only by the light dose, i.e., same dose achieves same efficacy. Moreover, type-II has an efficacy follows Bunsen Roscoe law (BRL), whereas type-I follows non-BRL. The measured type-I efficacy and gelation profile are analyzed by our analytic formulas. Schematics of the photocrosslinking stage defined by the availability of oxygen is developed, where both type-I and &ndash;II coexist until the oxygen is depleted. The overall efficacy may be enhanced by resupply of PS or oxygen during the light exposure. The roles of light dose and PS concentration on the efficacy of photoinitiated polymerization should be are governed a new concept of a volume efficacy (Ve), defined by the product of the crosslink (or gelation) depth (CD) and local [efficacy].

Extracellular matrix synthesis and turnover by type II pulmonary epithelial cells

1992 ◽  
Vol 262 (5) ◽  
pp. L582-L589 ◽  
Author(s):  
D. E. Rannels ◽  
S. E. Dunsmore ◽  
R. N. Grove
Keyword(s):  
Extracellular Matrix ◽  
Steady State ◽  
Epithelial Cells ◽  
Primary Cultures ◽  
Calf Serum ◽  
Type I ◽  
Type Ii Cells ◽  
Type Ii ◽  
Pulmonary Epithelial Cells ◽  
Type Ii Cell

Both type I and type II pulmonary epithelial cells contact the extracellular matrix (ECM). Type II cell-ECM interactions are bidirectional; they involve matrix-mediated modulation of type II cell differentiation, as well as cellular synthesis and deposition of ECM components. The present experiments examine the kinetics of accumulation of newly synthesized proteins in cell and matrix fractions from primary cultures of type II pneumocytes. Cycloheximide-sensitive incorporation of [3H]leucine into total protein of both the cell and ECM fractions was linear for 24–30 h, when steady-state labeling was reached and maintained to at least day 8. Over this interval, the cells enlarged but did not divide. Newly synthesized proteins recovered in the matrix fraction averaged 1–2% of those in the cells. Relative rates of radiolabeling of matrix proteins peaked at culture day 2 and increased in the absence of serum. In short-pulse studies, initial rates of protein synthesis were equal on culture days 1 and 3; this suggested that the steady-state labeling kinetics above reflected protein turnover. This was supported by rapid loss of radioactivity from the ECM after fresh type II cells were seeded on a prelabeled, cell-free matrix surface. Fresh or conditioned Dulbecco's modified Eagle's medium containing 10% fetal calf serum had little effect on matrix stability. These results demonstrate regulated deposition and turnover of a complex ECM by type II cells and provide a basis for further investigations of factors that control these processes.

scholarly journals Excitability and Threshold Mechanism for Enhanced Neuronal Response Induced by Inhibition Preceding Excitation

2021 ◽  
Vol 2021 ◽  
pp. 1-18
Author(s):  
Hanqing Ma ◽  
Bing Jia ◽  
Yuye Li ◽  
Huaguang Gu
Keyword(s):  
Steady State ◽  
Neuronal Response ◽  
Inhibitory Effect ◽  
Type I ◽  
Type Ii ◽  
Neural Firing ◽  
Firing Activity ◽  
Subthreshold Oscillations ◽  
Auditory Nervous System ◽  
Threshold Mechanism

Postinhibitory facilitation (PIF) of neural firing presents a paradoxical phenomenon that the inhibitory effect induces enhancement instead of reduction of the firing activity, which plays important roles in sound location of the auditory nervous system, awaited theoretical explanations. In the present paper, excitability and threshold mechanism for the PIF phenomenon is presented in the Morris-Lecar model with type I, II, and III excitabilities. Firstly, compared with the purely excitatory stimulations applied to the steady state, the inhibitory preceding excitatory stimulation to form pairs induces the firing rate increased for type II and III excitabilities instead of type I excitability, when the interval between the inhibitory and excitatory stimulation within each pair is suitable. Secondly, the threshold mechanism for the PIF phenomenon is acquired. For type II and III excitabilities, the inhibitory stimulation induces subthreshold oscillations around the steady state. During the middle and ending phase of the ascending part and the beginning phase of the descending part within a period of the subthreshold oscillations, the threshold to evoke an action potential by an excitatory stimulation becomes weaker, which is the cause for the PIF phenomenon. Last, a theoretical estimation for the range of the interval between the inhibitory and excitatory stimulation for the PIF phenomenon is acquired, which approximates half of the intrinsic period of the subthreshold oscillations for the relatively strong stimulations and becomes narrower for the relatively weak stimulations. The interval for the PIF phenomenon is much shorter for type III excitability, which is closer to the experiment observation, due to the shorter period of the subthreshold oscillations. The results present the excitability and threshold mechanism for the PIF phenomenon, which provide comprehensive and deep explanations to the PIF phenomenon.

scholarly journals Up-Dated the Critical Issues of Corneal Cross-Linking (Type-I and II): Safety Dose for Ultra-Thin Cornea, Role of Oxygen and Initiator Regeneration

2021 ◽  
Author(s):  
Jui-Teng Lin
Keyword(s):  
Steady State ◽  
Light Intensity ◽  
Transient State ◽  
Threshold Dose ◽  
Type I ◽  
Type Ii ◽  
Minimum Thickness ◽  
Increasing Function ◽  
Thin Cornea

Aims:To update analytic formulas for the overall efficacy of corneal collagen crosslinking (CXL) including both type-I and oxygen-mediated type-II mechanisms, the role of oxygen and the initiator regeneration. Study Design:modeling the kinetics of CXL in UV light and using riboflavin as the photosensitizer.Place and Duration of Study:New Taipei City, Taiwan, between June, 2021 and July, 2021.Methodology:Coupled kinetic equations are derived under the quasi-steady state condition for the 2-pathway mechanisms of CXL. For type-I CXL, the riboflavin (RF) triplet state [T] may interact directly with the stroma collagen substrate [A] to form radical (R) and regenerate initiator. For type-II process, [T] interacts with oxygen to form a singlet oxygen [1O2]. Both reactive radical (R) and [1O2], can relax to their ground state, or interact with the substrate [A]) for crosslinking. Based on a safety dose, the minimum corneal thickness formula is derived. Results:Our updated theory/modeling showed that oxygen plays a limited and transient role in the process, in consistent with that of Kamave [2]. In contrary, Kling et al [3] believed that type-II is the predominant mechanism, which however conflicting with the epi-on CXL results. For both type-I and type-II, a transient state conversion (crosslink) efficacy in an increasing function of light intensity (or dose), whereas, its steady state efficacy is a deceasing function of light intensity. RF depletion in type-I is compensated by the RF regeneration term (RGE) which is a decreasing function of oxygen. For the case of perfect regeneration case (or when oxygen=0), RF is a constant due to the catalytic cycle. Unlike the conventional Dresden rule of 400 um thickness, thin cornea CXL is still safe as far as the dose is under a threshold dose (E*), based on our minimum thickness formula (Z*). Our formula for thin cornea is also clinically shown by Hafez et al forultra thin (214 nm) CXL. Conclusion: For both type-I and type-II, a transient state conversion (crosslink) efficacy in an increasing function of light intensity (or dose), whereas, its steady state efficacy is a deceasing function of light intensity. Ultra thin cornea is still safe as far as it is under a threshold dose (E*), based on our minimum thickness formula.

scholarly journals Behavior of oxygen saturation and blood filling in the venous capillary system of the biceps brachii muscle during a fatiguing isometric action

2020 ◽  
Vol 30 (1) ◽  
pp. 79-87 ◽  
Author(s):  
Silas Dech ◽  
Frank Bittmann ◽  
Laura Schaefer
Keyword(s):  
Steady State ◽  
Oxygen Saturation ◽  
Biceps Brachii ◽  
Rank Correlation ◽  
Type I ◽  
Type Ii ◽  
Venous Oxygen Saturation ◽  
Capillary Circulation ◽  
Muscle Actions ◽  
Isometric Muscle

The objective of the study is to develop a better understanding of the capillary circulation in contracting muscles. Ten subjects were measured during a submaximal fatiguing isometric muscle action by use of the O2C spectrophotometer. In all measurements the capillary-venous oxygen saturation of hemoglobin (SvO2) decreases immediately after the start of loading and levels off into a steady state. However, two different patterns (type I and type II) emerged. They differ in the extent of deoxygenation (–10.37 ±2.59 percent points (pp) vs. –33.86 ±17.35 pp, P = .008) and the behavior of the relative hemoglobin amount (rHb). Type I reveals a positive rank correlation of SvO2 and rHb (ρ = 0.735, P <.001), whereas a negative rank correlation (ρ = –0.522, P <.001) occurred in type II, since rHb decreases until a reversal point, then increases averagely 13% above the baseline value and levels off into a steady state. The results reveal that a homeostasis of oxygen delivery and consumption during isometric muscle actions is possible. A rough distinction in two types of regulation is suggested.

scholarly journals Analysis of Dynamic Efficacy Profile of Corneal Cross-Linking: Role of Oxygen and Rate Constants

2021 ◽  
Author(s):  
Jui-Teng Lin ◽  
Yi-Ze Lee
Keyword(s):  
Steady State ◽  
Singlet Oxygen ◽  
Uv Light ◽  
Scaling Law ◽  
Kinetic Equations ◽  
Type I ◽  
Type Ii ◽  
Steady State Condition ◽  
Time Profiles

Purpose:To explore (theoretically) the key parameters and their influence on the time profiles of photosensitizer (riboflavin), free radicals, singlet oxygen, oxygen and the efficacy of corneal collagen crosslinking (CXL)in both type-I and oxygen-mediated type-II mechanisms, specially the role of oxygen and the initiator regeneration. Methodology:Coupled kinetic equations are derived and numerically solved under the quasi-steady state condition for the 2-pathway mechanisms of CXL. The key parameters explored include (bI, V, Q', K, K',Q,P) and their influence on the time profiles of photosensitizer (riboflavin, C), radicals (R), singlet oxygen(S), oxygen (X) and efficacy (E), parameters of (K,K',Q) define the relative strength of type-I and type-II process. The oxygen depletion profile, X(t), and the associated singlet oxygen, S(t), depend on the parameters of V, Q' and the initial value of oxygen. The coupling strength given by (bI) governs almost all profiles, where b is an effective absorption parameter and I is the UV light intensity.Results:Our numerical method for CXL dynamic profiles demonstrated the following important features: (i) Type-I and type-II coexit in CXL, in the presence of oxygen. However, there is no type-II when oxygen is depleted or in a condition without oxygen. (ii) Type-I with bimolecular termination, the radical R(t) is a function of [K'(bIgC)]0.5, leading to the steady-state efficacy given by a scaling law of 1/(bI)0.5, in contract to that of type-II which is almost independent to the light intensity. (iii) The depletion rate (2 to 5 minutes) of X(t) is much faster than that of C(t) (10 to 20 minutes), (iv) Thepure type-II profile, has a transition point from straight line to saturating curve and matches the depletion point of singlet oxygen S(t). (v) Improved CXL efficacy of type-I and type-II may be achieved by external supply of photoinitiator (riboflavin) and oxygen, respectively.

Self-similar gravity currents with variable inflow revisited: plane currents

1994 ◽  
Vol 258 ◽  
pp. 77-104 ◽  
Author(s):  
Julio Gratton ◽  
Claudio Vigo
Keyword(s):  
Density Ratio ◽  
Gravity Currents ◽  
Type I ◽  
Type Ii ◽  
Ambient Fluid ◽  
Discontinuous Solutions ◽  
Continuous Solutions ◽  
Self Similar ◽  
Similar Solutions ◽  
Transition Type

We use shallow-water theory to study the self-similar gravity currents that describe the intrusion of a heavy fluid below a lighter ambient fluid. We consider in detail the case of currents with planar symmetry produced by a source with variable inflow, such that the volume of the intruding fluid varies in time according to a power law of the type tα. The resistance of the ambient fluid is taken into account by a boundary condition of the von Kármán type, that depends on a parameter β that is a function of the density ratio of the fluids. The flow is characterized by β, α, and the Froude number [Fscr ]0 near the source. We find four kinds of self-similar solutions: subcritical continuous solutions (Type I), continuous solutions with a supercritical-subcritical transition (Type II), discontinuous solutions (Type III) that have a hydraulic jump, and discontinuous solutions having hydraulic jumps and a subcritical-supercritical transition (Type IV). The current is always subcritical near the front, but near the source it is subcritical ([Fscr ]0 < 1) for Type I currents, and supercritical ([Fscr ]0 > 1) for Types II, III, and IV. Type I solutions have already been found by other authors, but Type II, III, and IV currents are novel. We find the intervals of parameters for which these solutions exist, and discuss their properties. For constant-volume currents one obtains Type I solutions for any β that, when β > 2, have a ‘dry’ region near the origin. For steady inflow one finds Type I currents for O < β < ∞ and Type II and III Currents for and β, if [Fscr ]0 is sufficiently large.

scholarly journals Critical Analysis of Corneal Cross-linking (Part-I): Formulas for Efficacy, Safety Dose, Minimum Thickness, Demarcation Line Depth and the Role of Oxygen

2021 ◽  
pp. 29-41
Author(s):  
Sheng-Fu Cheng ◽  
Jui-Teng Lin
Keyword(s):  
Steady State ◽  
Light Intensity ◽  
Corneal Thickness ◽  
Transient State ◽  
Threshold Dose ◽  
Type I ◽  
Type Ii ◽  
Minimum Thickness ◽  
Demarcation Line ◽  
Line Depth

Purpose: To update and derive formulas for the efficacy and kinetics of corneal collagen crosslinking (CXL) including both type-I and oxygen-mediated type-II mechanisms, the role of oxygen, the initiator regeneration, safety dose, minimum corneal thickness and demarcation line depth. Study Design: Modeling the kinetics of CXL in UV light and using riboflavin as the photosensitizer. Place and Duration of Study: Taipei, Taiwan, between June, 2021 and July, 2021. Methodology: Coupled kinetic equations are derived under the quasi-steady state condition for the 2-pathway mechanisms of CXL. For type-I CXL, the riboflavin (RF) triplet state [T] may interact directly with the stroma collagen substrate [A] to form radical (R) and regenerate initiator. For type-II process, [T] interacts with oxygen to form a singlet oxygen [1O2]. Both reactive radical (R) and [1O2], can interact with the substrate [A]) for crosslinking. Based on a safety dose and a threshold dose, formulas for the minimum corneal thickness and demarcation line depth (DLD) are derived. Results: Our updated theory/modeling showed that oxygen plays a limited and transient role in the process, in consistent with that of Kamave. In contrary, Kling et al believed that type-II is the predominant mechanism, which however conflicting with the epi-on CXL results. For both type-I and type-II, a transient state conversion (crosslink) efficacy in an increasing function of light intensity (or dose), whereas, its steady state efficacy is a deceasing function of light intensity. RF depletion in type-I is compensated by the RF regeneration term (RGE) which is a decreasing function of oxygen. For the case of perfect regeneration case (or when oxygen=0), RF is a constant due to the catalytic cycle. Unlike the conventional Dresden rule of 400 um thickness, thin cornea CXL is still safe as far as the dose is under a threshold dose (E*), based on our minimum thickness formula (Z*). Our formula for thin cornea is also clinically shown by Hafez et al for ultra thin (214 nm) CXL. Conclusion: For both type-I and type-II, the transient state conversion (crosslink) efficacy in an increasing function of light intensity (or dose), whereas, its steady state efficacy is a deceasing function of light intensity. CXL for ultra thin corneas are still safe, as far as it is under a threshold dose (E*), based on our minimum thickness (Z*) formula, which has a similar tend as that of demarcation line depth (Z').

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