Fluid Dispersion Research Articles

Flow and mixing characteristics of dual parallel plane jets subject to acoustic excitation

The effects of jet pulsation intensity and excitation Strouhal number on the flow and dispersion characteristics of dual parallel plane jets at a low Reynolds number of 200 were experimentally studied so that the transition from laminar to turbulence was focused. A hot-wire anemometer was used to record the jet velocities. The flow patterns were obtained using the laser-light sheet assisted smoke flow visualization technique. Jet spread widths were derived from the long-exposure images using the binary edge detection method. The jet fluid dispersion characteristics were examined using the tracer-gas concentration detection technique. Four characteristic flow modes (discrete coherent vortices, contiguous coherent vortices, early vortex breakup, and lateral dispersion) were identified in the domain of the jet pulsation intensity and excitation Strouhal number. At small jet pulsation intensities, discrete and contiguous coherent vortices appeared at low and high excitation Strouhal numbers, respectively. The vortices appearing in the jet shear layers broke up slowly and caused small jet expansions and turbulent intensities, thus inducing a low efficiency of jet fluid dispersion. The early vortex breakup mode was induced by the low-frequency back-and-forth flow motions in the near region at large jet pulsation intensities and low excitation Strouhal numbers. Large turbulence fluctuations caused by the early vortex breakup increased the jet dispersion significantly. At large jet pulsation intensities and excitation Strouhal numbers, high-frequency back-and-forth flow motions in the region near the jet exits significantly reduced the time-averaged axial momentum and induced large lateral jet expansion and jet fluid dispersions.

Surface modification of transversely twisted-turbulator using perforations and winglets: An extended study

Twisted-turbulators are effective passive techniques for enhancing the thermal performance of heat exchangers. Although numerous studies have been conducted on longitudinal forms, there are very scarce studies on transverse forms. In this study, particular attention is paid on the effects of perforation, winglet, and a combination of both, as modifications, on the performance of transversely twisted-turbulators (TTTs) through a rectangular channel. Firstly, experimental tests are performed on the TTTs with three different twist-angles of 0°, 90°, and 180° for the Reynolds number range from 1643 to 4929. Then, numerical simulations are carried out on these models. It is found that the effects of perforations and winglets depend on the twist-angle of TTTs. In the case of 0° TTTs, introducing both perforations and winglets leads to lower values of h and ∆p. The results show that the solid model is more effective in fluid dispersion towards the hot walls and generate stronger vortices inside the channel. Based on the experimental data, for the case of 0° TTTs, the average reduction of h and ∆p between the solid model and other models are as follows, 9.8% and 16.4% for the perforated model, 16.2% and 16.9% for the winged model, and 23.6% and 41.8% for the combined model. However, in the cases of 90° and 180° TTTs, creating winglets enhances these parameters, leading to better overall performance. The highest overall performance indexes of 1.55, 1.66, and 1.65 are recorded for the solid 0° TTT, winged 90° TTT, and winged 180° TTT models at the Reynolds number of 1643.

Effects of pulsation intensity on the flow and dispersion of pulsed dual plane jets

The effects of jet pulsation intensity on the flow and dispersion characteristics of dual parallel plane jets were experimentally studied. The jet pulsations were generated by acoustic excitations. The laser-light-sheet-assisted smoke flow visualization method was used to study the flow evolution processes. The lateral spreading characteristics of the jets were measured using the binary edge detection method. A hotwire anemometer was used to measure the velocity pulsations, mean velocities, turbulence intensities, and Lagrangian turbulent length and time scales. The dispersion characteristics of the jet fluids were measured by the tracer-gas concentration detection method. The jet Reynolds number and excitation Strouhal number were fixed at 600 and 0.106, respectively. The jet pulsation intensities were varied from 0 to 1.6. As the jets were pulsed, the turbulence intensity, lateral spread width, and jet fluid dispersion capability markedly increased compared with those of the non-pulsed jets. The larger the pulsation intensity was, the higher the turbulence intensity, lateral spread width, and jet fluid dispersion. The Lagrangian time and length scales of the turbulent eddies decreased as the jet pulsation intensity increased because the mushroom-shaped structures generated by the jet pulsations broke up into small turbulent eddies caused by the strong vortex-stretching effect.

On the genesis of the gold-silver deposit Kupol (North-East of Russia)

A new version of genesis of the epithermal gold-silver deposit Kupol (Chukotka), its mineral composition of ores and conditions of ore-localization based on the analysis of published geological materials on the geological structure had purposed in this article. The active thermal ore-forming role of completing the volcanic cycle of the multiphase subvolcanic complex’ the proximal bodies of the Upper Cretaceous rhyolites had been proved. The main factors of this deposit’ formation and the conditions that favored the appearance of large ore bodies and rich ores were considered. The magma chamber, unified faulty magmatic and fluid conductor, rock screen, flank clusters of subvolcanic rhyolite bodies and their integral thermal anomalies that initiated and sustained the deep fluid thermal convection under the screen, its mixing with fractured pore and meteoric waters and formation of gradient temperature zones, were considered among the main factors. The conjugation of these factors in space and time, the active tectonic regime and the long-term preservation of the deformation plan were the favorable conditions for ore formation. They maintained the high permeability of the fluid conductor, prevented a wide dispersion of fluids and provided a telescopic deposition of different mineral parageneses.

On the genesis of the gold-silver deposit Kupol (North-East of Russia)

A new version of genesis of the epithermal gold-silver deposit Kupol (Chukotka), its mineral composition of ores and conditions of ore-localization based on the analysis of published geological materials on the geological structure had purposed in this article. The active thermal ore-forming role of completing the volcanic cycle of the multiphase subvolcanic complex’ the proximal bodies of the Upper Cretaceous rhyolites had been proved. The main factors of this deposit’ formation and the conditions that favored the appearance of large ore bodies and rich ores were considered. The magma chamber, unified faulty magmatic and fluid conductor, rock screen, flank clusters of subvolcanic rhyolite bodies and their integral thermal anomalies that initiated and sustained the deep fluid thermal convection under the screen, its mixing with fractured pore and meteoric waters and formation of gradient temperature zones, were considered among the main factors. The conjugation of these factors in space and time, the active tectonic regime and the long-term preservation of the deformation plan were the favorable conditions for ore formation. They maintained the high permeability of the fluid conductor, prevented a wide dispersion of fluids and provided a telescopic deposition of different mineral parageneses.

Use of computed tomography to assess subcutaneous drug dispersion with recombinant human hyaluronidase PH20 in a swine model

IntroductionSubcutaneous (SC) formulations of therapeutics with recombinant human hyaluronidase PH20 (rHuPH20) are currently approved across various disease indications. The rHuPH20-mediated enzymatic degradation of SC hyaluronan (HA) facilitates bulk fluid flow and dispersion of co-administered therapeutics. However, current methods of quantifying dispersion in the SC space are limited. Here, a novel method is outlined to quantify and follow rapid SC volumetric dispersion of a representative therapeutic fluid in the presence of rHuPH20 using computed tomography (CT). MethodsTen Yucatan miniature swine were randomized to three groups. Animals received simultaneous infusions of contrast agent (CA) alone (left side of the animal) or in combination with rHuPH20 (right side) at infusion rates of 2.5, 5, or 10 mL/min. Spiral CT scans (1.5 mm thickness) were conducted before and after the infusion and at regular time intervals throughout. Scans were used to create three-dimensional (3D) reconstructions of the fluid pockets and analyze surface area, volume, and sphericity. Results3D reconstruction showed increased dispersion of CA with rHuPH20 compared with CA alone, with fenestration and increased dispersion in the craniocaudal and lateromedial directions. The CA with rHuPH20 fluid pockets showed an average increase of 46% in surface area (p = 0.001), a 35% increase in volume (p = 0.001) and a 17% decrease in sphericity post-infusion compared with CA alone at 30 min post-infusion. DiscussionThis exploratory study confirms the value of CT imaging as a non-invasive method of assessing real-time spatial and temporal behavior of SC-administered fluids. This technique could help to assess the dispersion pattern of novel rHuPH20 SC co-formulations.

Development of a rapid manufacturable microdroplet generator with pneumatic control

This paper presents a T-junction microdroplet generator equipped with a pneumatic actuation for controlling the droplet size. The multi-layer device is compatible with rapid manufacturing using a desktop-based laser cutter to fabricate the fluidic and pneumatic layers. A T-junction fluidic layer sits at the bottom and the control layer consists of a pneumatic chamber, as well as inlet and outlet channels are placed at the top. Our results with pneumatic control showed that the generated droplet size is inversely proportional to the pressure inside the pneumatic chamber. Pneumatic pressure of up to 0.4 MPa showed a 38% reduction in droplet size compared to without control. The droplet size can additionally be regulated by controlling the relative flow rates of the continuous and dispersed fluid. Pneumatic actuation is advantageous, as it does not require additional fluid usage and the flow rate does not need to be ramped up to decrease the droplet size. The device presented in this paper with pneumatic control and fabrication ease provides an attractive method for microdroplet manipulation.

Stimulus-responsive mechanism of salt-responsive polymer and its application in saturated saltwater drilling fluid

AM-AMPS-TAC polymers with different charge distribution are synthesized using acrylamide (AM), 2-acrylamido-2-methylpropanesulfonate (AMPS) and 3-acrylamidopropyl trimethylammonium (TAC) at different feed ratios by polymerization in solution. The salt-responsive behavior, reasons leading to salt-responsiveness, and effects of polymers molecular structure on salt-responsiveness are studied by laboratory experiments to find out the adaptability of the polymers. Rheology test under stepwise shear mode shows that the AM-AMPS-TAC polymers have salt responsiveness, and the closer the feeds of AMPS and ATC, the more significant the salt responsiveness will be. Conformation change of polymers molecular chain under salt stimulus is studied by turbidity test and micro-morphology analysis, and the responsive mechanism is further investigated by intrinsic viscosity test and copolymer composition analysis. Results indicate that the salt-responsive behavior of AM-AMPS-TAC polymers derives from the “curled to expanded” transition of chain conformation under salt stimulus, and this transition is led by the screening effect of salt which weakens polymers intramolecular ionic bond. Application in saturated saltwater drilling fluid shows that the AM90-AMPS5-TAC5 polymer has the best salt-tolerance and temperature-tolerance when used together with fluid loss controller PAC-Lv. The drilling fluid saturated with NaCl can maintain stable viscosity, good dispersion and low fluid loss for long time under 150 °C.

Flow behaviours and velocity fields of non-oscillating and transversely oscillating jets

The near-field flow characteristics and jet fluid dispersion properties of non-oscillating and transversely oscillating jets issued from a fluidic oscillator were studied experimentally. A V-shaped fluidic oscillator was designed to induce transverse jet oscillations by merging two bifurcated alternatively issuing side jets. The characteristic flow patterns, evolution processes, velocities, vorticities, turbulence intensities and jet fluid dispersion capabilities in the median plane of the jets were examined. The characteristic flow patterns were obtained using laser-light-sheet-assisted smoke flow visualization method. The flow velocities were measured using particle image velocimetry. The jet fluid dispersion properties were analysed using tracer gas detection method. The non-oscillating jet was axial momentum-dominated—the axial momentum of the jet was limited within a narrow region around the central axis and was significantly larger than the transverse momentum. Therefore, the transverse velocities and vorticities were small and the dispersion of the jet fluid was relatively low. The transversely oscillating jets meandered in the near-field so the flow patterns presented a violent breakup of vortical flow structures and large transverse widths. The streamlines expanded transversely outwards and caused a part of the axial momentum to transfer towards the transverse direction. The vorticities and transverse velocities were increased and the axial velocities were decreased, so the dispersion of jet fluid was augmented in the transversely oscillating jets.

Loading effects on the performance of needle-free jet injections in different skin models

Intradermal delivery of vaccines with jet injection is one of the alternatives to conventional delivery techniques with hypodermic needles via the Mantoux technique and multi-puncture devices etc. However, for a given fluid, the effects of various parameters related to injector design, as well as skin properties are still not well understood. While the key design parameters are orifice diameter, jet speed, cartridge volume, and standoff distance, we must also consider the applied load of the device on the skin and axial skin tension. These parameters are all studied herein using different ex vivo models (guinea pig, pig, and human skin) and different fluid viscosities. We find that the applied load can have a significant effect on the amount of drug delivered through the skin, as well as the fluid dispersion pattern in the intradermal tissues. Regardless of skin type or fluid viscosity, we show that minimal standoff and applied force loads of approximately 1 kg (9.81 N) should be used to maximize injection efficiency when targeting intradermal tissue with the spring-powered device used in this study.

Understanding the Specific Heat Enhancement in Metal-Containing Nanofluids for Thermal Energy Storage: Experimental and Ab Initio Evidence for a Strong Interfacial Layering Effect

Nanofluids have emerged as an addition for thermal management and energy conversion applications. The dispersion of a small amount of solid nanoparticles occasionally leads to an unexpected enhancement in the specific heat of the dispersant fluid. This effect has technical, economic, and social significance, and for that, it has received a lot of attention from applied research, but the associated physical and chemical phenomena explaining this phenomenon are yet to be described. We report here a combined experimental and theoretical investigation of nanofluids consisting of palladium nanoplates in a typical heat transfer oil used for concentrating solar power. Their specific heat per unit volume is found to be maximally enhanced at intermediate nanoparticle concentrations, at all temperatures. This is consistent with the phenomenological description provided by the mesolayer model. Density functional theory calculations of adsorption energies and diffusion/desorption activation barriers reveal a strong interaction between the base fluid molecules and palladium surfaces, leading to a nanofluid model where the metal particles are decorated by a static layer of organic molecules. Such layering is potentially responsible for the anomalous enhancement on the thermal properties of the nanofluid, such as the specific heat. Our contribution with this work is a first step toward a complete understanding on the structure and properties of nanofluids using ab initio molecular simulation techniques rather than phenomenological descriptions only.

Fluid dynamic simulations of EG-W (ethylene glycol–water)​ mixtures to predict nanofluid heat transfer coefficients

In previous scholarly studies, the water and ethylene glycol mixtures as base liquids have been considered in the ratio of 40:60 (60EGW), with specific investigations focusing on a nanofluid in the form of Silicon dioxide (SiO 2 ) in relation to its thermo-physical properties, besides its nature of the heat transfer coefficients (HTC). In this study, the main aim lies in SiO 2 heat transfer coefficient prediction. With the approach of computational fluid dynamics (CFD) considered, the experimental conditions constitute 40EGW. For SiO 2 nanoparticles, their viscosity and thermal conductivity are experimentally assessed, having been dispersed in 60EGW and 40EGW. Also, the existing literature and experimental values are used to conduct regression analysis. With thermal features on the focus, there is also the formulation of correlations. Furthermore, there is the invocation of correlations in heat transfer coefficients and CFD simulations that target Al 2 O 3 and SiO 2 nanoparticles, with predictions entailing their dispersion in 40EGW and 60EGW base fluids. The inlet temperature is set at 60 to 80 °C, and it is at this stage that there is CFD simulation implementation. For the volume concentration, the ranges include 0.0 percent to 1.5 percent. The existing literature is relied upon relative to the validation of the coefficients of heat transfer, besides previously predicted nanofluids. From the results, compared to the case of 40EGW base fluid, there is 51 percent and 53 percent enhancement when the experimental conditions are set at 1.0 percent volume concentration, with temperatures being 80 °C. From the computational outcomes, Al 2 O 3 /40EGW nanofluids tend to be associated with significant heat transfer coefficients. Specifically, the enhancement of heat transfer for these materials stands at 52.9%. On the other hand, the enhancement of heat transfer when the base fluid of SiO 2 /40EGW is considered stands at 51.0%. These values are obtained when the experimental conditions are considered at 80 °C, as well as a volume concentration of 1.0%. Therefore, when aspects of heat transfer coefficients and thermal conductivity are considered, the superiority of 40EGW is confirmed. As such, the study confirms the impact of the base nanofluids set at 40EGW relative to the coefficients of heat transfer and also the thermal properties of materials.

Исследование механизма повышения стабильности ствола скважины при бурении трещиноватых аргиллитов

The paper presents the relevance of enhancing wellbore stability by developing and applying efficient drilling fluid compositions for well constructions in fractured argillite. In the process of well constructions, there comes a range of complications associated with instability of rocks forming borehole walls, which sometimes results in lower penetration rates, higher construction costs and well abandonment. Often, drilling problems occur at drilling through mudrocks that account for up to 70 % of field sections. When using water-base drilling fluids, the mudrock swelling due to the contact with the fluid dispersion medium adversely affects the drilling process and can significantly increase well construction costs. The accumulation of wellbore cavings inhibits well circulation, causes landing of drilling tools and may result in tool sticking. An analysis of drilling problems in fractured argillite is presented; the mechanisms affecting open hole stability in the fractured argillite deposits are shown. The use of potassium chloride is recommended to enhance the stability of argillite-formed borehole walls. The results are supported by experimental studies using the Chenevert method, as well as fracture propping tests. When the argillite sample was placed in potassium chloride (KCl) solution, there was a minor fracture expansion and propagation over the entire sample length, which is a positive result. To enhance wellbore stability, further study approaches are proposed: upgrading mud by adding inhibiting compounds, such as salt solutions in combination with high-molecular polymer compositions.

Intensification of gas dispersion in pseudoplastic fluids with coaxial mixers

The present study investigates the intensification of gas dispersion in non-Newtonian fluids using a coaxial mixer comprised of two pitched blade impellers and an anchor. The gas holdup was assessed for this aerated coaxial mixing system via electrical resistance tomography and computational fluid dynamics (CFD). The investigation aimed to find the effects of the impellers’ speed, fluid rheology, impeller pumping direction, rotational mode, and gas flow rate on the aeration efficiency of the coaxial mixers. It was found that the downward pumping and co-rotating mode of the impellers resulted in having the highest gas holdup. Moreover, the anchor speed of 10 rpm generated the highest gas holdup in downward pumping mode at a constant specific power consumption under all the aeration rates. In upward pumping system, the CFD simulations confirmed the results of experiment showing that the anchor rotation deteriorated the gas circulation inside the tank resulting in a lower gas holdup compared to that achieved without anchor. The superiority of the downward pumping and co-rotating mode was demonstrated by comparing the efficiency of different configurations in terms of gas holdup per specific power consumption. Empirical correlations for the gas holdup were developed for the configuration with the highest efficiency.

Evidence of Vent-Adaptation in Sponges Living at the Periphery of Hydrothermal Vent Environments: Ecological and Evolutionary Implications.

The peripheral areas of deep-sea hydrothermal vents are often inhabited by an assemblage of animals distinct to those living close to vent chimneys. For many such taxa, it is considered that peak abundances in the vent periphery relate to the availability of hard substrate as well as the increased concentrations of organic matter generated at vents, compared to background areas. However, the peripheries of vents are less well-studied than the assemblages of vent-endemic taxa, and the mechanisms through which peripheral fauna may benefit from vent environments are generally unknown. Understanding this is crucial for evaluating the sphere of influence of hydrothermal vents and managing the impacts of future human activity within these environments, as well as offering insights into the processes of metazoan adaptation to vents. In this study, we explored the evolutionary histories, microbiomes and nutritional sources of two distantly-related sponge types living at the periphery of active hydrothermal vents in two different geological settings (Cladorhiza from the E2 vent site on the East Scotia Ridge, Southern Ocean, and Spinularia from the Endeavour vent site on the Juan de Fuca Ridge, North-East Pacific) to examine their relationship to nearby venting. Our results uncovered a close sister relationship between the majority of our E2 Cladorhiza specimens and the species Cladorhiza methanophila, known to harbor and obtain nutrition from methanotrophic symbionts at cold seeps. Our microbiome analyses demonstrated that both E2 Cladorhiza and Endeavour Spinularia sp. are associated with putative chemosynthetic Gammaproteobacteria, including Thioglobaceae (present in both sponge types) and Methylomonaceae (present in Spinularia sp.). These bacteria are closely related to chemoautotrophic symbionts of bathymodiolin mussels. Both vent-peripheral sponges demonstrate carbon and nitrogen isotopic signatures consistent with contributions to nutrition from chemosynthesis. This study expands the number of known associations between metazoans and potentially chemosynthetic Gammaproteobacteria, indicating that they can be incredibly widespread and also occur away from the immediate vicinity of chemosynthetic environments in the vent-periphery, where these sponges may be adapted to benefit from dispersed vent fluids.

Effects of transversely twisted-turbulators on heat transfer and pressure drop of a channel with uniform wall heat flux

Air flow and heat transfer through a rectangular channel equipped with transversely twisted-turbulators are studied experimentally. Three twist-angles and two pitch-ratios are considered to explore the effects of design factors. To create a better understanding of possible mechanisms, a numerical simulation is also carried. The experimental data show that decreasing twist-angle and pitch-ratio increases both h and Δp. Among the studied models, the 0° turbulators give the highest values, followed by the 90° and 180° turbulators come in the second and third, respectively. The use of 0° turbulators enhances h by about 141.2 % at pitch-ratio of 1.875 and 109.4 % at pitch-ratio of 3.75, but these enhancements for the models with 90° and 180° turbulators are 133.2 %–102.7 % and 54.6 %–42.1 %, respectively. The numerical results display that the 0° turbulators are more effective in fluid dispersion towards hot walls and generate stronger swirl flows. However, the best overall performance is seen for the 90° turbulators. It is also found that at min. Re, the models with lower pitch-ratio show a better overall performance, while at the max. Re, an inverse outcome is found. The highest performance index of 1.62 is recorded for the 90° turbulators at the Reynolds number of 1643.

Analysis of power consumption for gas dispersion in non-Newtonian fluids with a coaxial mixer: New correlations for Reynolds and power numbers

Coaxial mixers are efficient in mixing of highly viscous fluids. The main objective of this study was to assess the power consumption for the gas dispersion in carboxymethyl cellulose solution, a power-law non-Newtonian fluid, with a coaxial mixer consisting of an anchor impeller and two central impellers as a function of the speed ratio (central impeller speed/anchor speed), fluid rheology, pumping direction of the central impeller, and the rotation mode (co-rotating vs. counter-rotating). This goal was achieved using both experimental and numerical approaches. A computational fluid dynamic model (CFD) was developed and validated using the experimental data. Electrical resistance tomography (ERT) was employed to measure the gas holdup. New equivalent impeller speed and diameter were defined and two novel correlations for the Power number and Reynolds number were proposed and successfully validated at different operating conditions. Additionally, new dimensionless correlations for the ratio of the gassed to un-gassed power consumption and the aerated power number as a function of the flow number, Froude number, and Reynolds number were developed and successfully tested for different coaxial mixing configurations.

Evaluation of tribological characteristics of nano zirconia dispersed biodegradable canola oil methyl ester metalworking fluid

This paper focusses on the tribological characteristics of biodegradable Canola Oil Methyl Ester (COME) dispersed with various concentrations of nano-zirconium oxide i.e., ZrO2 - 0.5, 1, and 1.5 wt%. The nano particles are characterized using TEM and XRD analyses. The wear and friction properties were investigated using the four-ball tribometer and the wear and friction monitor. The worn surface and surface roughness analyses were examined using SEM/EDS and atomic force microscopes respectively. The Hastealloy pin material lubricated by COME with 0.5 wt% of ZrO2 shows significant lowering of the values of average frictional torque, mean wear scar diameter, frictional coefficient, wear, and average surface roughness in comparison with other metalworking fluids under study.

Thermal Conductivity of Multiwalled Carbon Nanotubes‐Kapok Seed Oil‐Based Nanofluid

AbstractThe synthesis of a nanofluid from multiwalled carbon nanotubes (MWCNTs) and Kapok seed oil by a one‐step method is reported. The nanofluid showed excellent stability of nanoparticle dispersion in the base fluid. Furthermore, this study deals with the prediction of the thermal conductivity of the MWCNTs‐kapok seed oil nanofluid. To improve the prediction of the thermal conductivity of the nanofluid, the artificial neural network (ANN) computing approach was used with different algorithms including the back‐propagation, Levenberg‐Marquardt, and genetic algorithm (GA). Finally, the ANN‐GA model is recommended for the prediction of thermal conductivity with higher accuracy.

The effect of negative ion population on dust acoustic wave propagation in a self gravitating Lorentzian dusty plasma

A theoretical investigation into the effect of negative ion population on dust acoustic wave propagation is presented in a self-gravitating dusty plasma consisting of electrons, negative ions, positive ions, and charged dust grains. The kappa distributed suprathermal electrons and Maxwellian ions are assumed. The inertial dust grain is assumed to have a variable charge which is negative or positive in the equilibrium condition depending on the population density of negative ion. A general fluid dispersion relation is derived by using continuity, momentum, and Poissons equations for electrostatic potential as well as gravitational potential. The analysis shows that the higher negative ion and suprathermal electron population favored the reduction of the decay rate when the equilibrium dust charge is negative. On the other hand, when the negative ion population increases, the equilibrium dust charge becomes positive. In this case, the negative ion and suprathermal electron population enhance the decay rate.