Liquid Flow Research Articles

Thermal performance analysis of supporting column ultra-thin vapor chamber with graded microgroove

To analyze the thermal behavior of a graded microgroove ultra-thin vapor chamber with supporting column, a three-dimensional steady-state numerical model coupled with graded capillary force network, which involves hydraulic and heat transfer on hydraulic and heat transfer performance on ultra-thin vapor chamber with different supporting column sizes. This model considers the influence of supporting column with varying diameters and intervals on liquid flow and temperature distribution, as well as the effects of a graded capillary force network on heat transfer limit of ultra-thin vapor chamber. The numerical results show that the additional heat transfer provided by the central support column causes an outward shift in the saturation temperature of vapor, creating a new liquid reflux path at the condensation surface. The accuracy of the model is verified by the preparation of ultra-thin vapor chamber with a graded microgroove a graded microgroove. Compared with the experimental results on conventional microgrooves, graded microgrooves can improve the heat transfer limit by 29.3%. According to the theoretical analysis model, the graded capillary force network can effectively resist incremental increases in vapor pressure drop, enhancing the efficiency of gas–liquid circulation of ultra-thin vapor chamber.

Analysis of droplet motion in cavity zone of rotating packed bed

Droplet motion in outer cavity zone of rotating packed bed is a complex phenomenon that requires analysis of liquid and gas flow to clarify influences of factors such as rotation speed, liquid flow rate, or gas flow rate. In this study, hydrodynamics is described using laser Doppler velocimetry and high-resolution visualization for droplet motion characterization. The results reveal that droplet motion initially depends on the peripheral velocity of the packing, while further from the packing, it loses kinetic energy mainly due to the drag force caused by the surrounding gas. Two-way coupling is investigated as both phases interact with each other. Rankine vortex theory is applied to simulate gas flow in the outer cavity zone. A model, based on Newton’s second law, is developed to predict droplet dynamics, including impingement velocity, trajectory length, and total residence time. Validation of the model shows that it can predict the liquid velocity in the outer cavity zone accurately. Upon impingement of droplets on the casing, part of the liquid rebounds as secondary droplets into the cavity, where they circulate with the gas flow. Overall, this study provides insights into droplet dynamics in the rotating packed bed and offers a basis for optimizing process efficiency and design in various applications, including chemical processing and environmental engineering.

Mixing efficacy and residence time distribution measurement in heavy water upgradation plant using radiotracer

To evaluate the efficiency of catalyst packing and to characterize the liquid phase flow dynamics in a heavy water distillation column, a series of residence time distribution (RTD) measurements were carried out using radiotracer. For a RTD measurement, about 1 mCi (37 MBq) of 82Br as ammonium bromide was injected as an impulse and its movement was monitored by thirty NaI(Tl) detectors at the inlet and outlet of the five catalyst cages present in the distillation column. The tracer measurements were carried out at varying liquid phase flow rate from 80 to 180 LPH. From the radiotracer data, it was concluded that radial distribution of the liquid phase at the top and bottom of the five cages was uniform. However, a slight non uniformity was observed in the middle cages. The residence time of the heavy water in the five cages varying the liquid flowrate was found to be varying from 4.2 min to 36.7 Min. To characterize the liquid mixing in each section of the distillation column, axial dispersion model was used using convolution method. The model parameter peclet number (Pe) was used to characterize the mixing. The Pe values for the five sections were found to be varying from 7 to 35. The Pe value suggests that flow of the liquid phase in the column was close to the plug flow in bottom three sections as desired.

Enhancing pipe chilldown with axial grooves filled with silicone sealant

This study proposes a method to accelerate the chilldown process in pipes using liquid nitrogen flow. Axial grooves were machined along the inner surface of the pipe and then filled with silicone sealant. This approach achieves a shorter chilldown time compared to previously proposed methods. Initial experiments involving pool boiling in liquid nitrogen were conducted to determine the optimal groove width and the ratio of groove-to-sealant area. The shortest chilldown time in pool boiling was achieved when the groove pitch was close to the capillary length. The effect of the copper-to-silicone sealant area ratio on the chilldown process was minimal. The shortest chilldown time was achieved with a surface that had a 2 mm pitch and a copper-to-silicone sealant area ratio of 0.25. The chilldown time was 1/4.4 of that of the bare surface. Pipes with different pitch and groove widths were tested in a flow chilldown experiment. Using the surface texture, the chilldown time of a stainless-steel pipe with an outer diameter of 1/2″ and a length of 120 mm from room temperature to the saturation temperature was reduced to a maximum of 1/3.6. The shortest cooling time is obtained at a groove pitch of 2 mm. In addition to the shorter cooling time, the amount of liquid nitrogen required for chilldown was also reduced.

Novel energy efficient integration of chimney ventilation, liquid desiccant dehumidification, and evaporative cooling for humid climates

The chimney effect for driving passively building ventilation is effective in dry and moderate climates to introduce cool fresh air into the space. However, its application in hot humid climates is limited due to the high energy demands associated with dehumidifying and cooling outdoor air. Thus, a novel energy-efficient assistive system is proposed integrating a chimney-driven ventilation with liquid desiccant dehumidification membrane loop and indirect evaporative cooling. This system leverages natural buoyancy to supply ventilation airflow and uses potassium formate loops through semi-permeable membranes for effective dehumidification. The objective is to dehumidify and cool the induced outdoor air to the room conditions of 24°C and relative humidity between 40% and 60% at minimal energy consumption. Mathematical models were developed to simulate the heat and mass transfer processes in the air and liquid desiccant flows within the system components. The system was sized, and its operation was optimized using an advanced machine learning-genetic algorithm model for a typical office space in Beirut. During the summer, the chimney air flowrate ranged from 45L/s to 48L/s, and it was delivered at the target room conditions. The system saved around 350kWh of electrical energy during the summer months due to elimination of the need to treat ventilation air by room cooling system. This was equivalent to the total energy required to handle the ventilation load during the summer season and resulted in a saving of $50/month in the case study.

Numerical simulation on gas-liquid two phase flow in the U-type pipe

Abstract An effective way to improve the formation of gas hydrate is to increase the gas-liquid contact area, which can also improve the gas-liquid heat and mass transfer efficiency. Designed a natural gas hydrate formation flow experimental device, and a set of folding pipes are the gas hydrate formation units. The folding pipe hydrate formation units are composed of many U-type pipes, which are the main carrier of hydrate formation. The gas-liquid flow law in the U-type pipe has the great significance on gas hydrate formation. The gas-liquid two phase flow in a single U-type pipe has been simulated by Fluent, gas distribution rule and flow characteristics in the U-type pipe has been investigated. The range of the entrance gas volume fraction is 0.1～0.6. Calculation results show that there is a certain degree of mixture between gas and liquid in the former straight section. The gas and liquid began to layer in the front of bend, the gas and liquid stratified obviously in the process of bend. The gas and liquid began to mix in the later straight section, but the degree of mixture is lower than the former. The liquid and gas flow phenomenon is different with disparate gas volume fraction. The gas and liquid stratified more obviously in the bend with the higher gas volume fraction. The law that the gas and liquid have a better mixture when gas volume fraction change range is 0.2～0.4 has been found, which is beneficial to hydrate formation.

Non-negligible buoyancy effect on bubbles travelling in horizontal microchannels of comparable size at small Bond numbers

When a gas bubble is transported by a liquid flow confined within a horizontal channel of comparable size, buoyancy effects are usually assumed to be negligible if the Bond number of the flow is less than unity. However, recent experimental studies showed that buoyancy may still significantly impact the bubble dynamics even when Bo≪1, provided that the flow speed is sufficiently small, such that the viscous and inertial forces are weak. To derive a new criterion to assess the significance of buoyancy on the flow of small bubbles in horizontal microchannels, we have performed systematic numerical simulations using the free software Basilisk, covering a wide range of Bond, capillary and Reynolds numbers, Bo=0.004−0.4, Ca=10−4−0.5 and Re=0−100, and exploring the bubble-to-channel diameter ratios db/D=0.2−0.9. We demonstrate that the nondimensional group Bo(db/D)2/Ca is effective in assessing the importance of buoyancy in flows with negligible inertial effects. When Bo(db/D)2/Ca<0.1, buoyancy effects are negligible and the bubble travels along the channel axis. When Bo(db/D)2/Ca>10, buoyancy effects dominate and the bubble travels in the vicinity of the upper wall. For intermediate values, bubbles take equilibrium positions between the channel centre and the wall, and the threshold Bo(db/D)2/Ca=1 is effective in predicting whether bubbles will travel closer to the channel centre or to the wall. The capillary number at the denominator describes the lift force generated by the deformation of the bubble due to viscous shear, which acts towards the channel centre thus opposing buoyancy. Inertial forces significantly alter the shape and equilibrium position of the bubble when the Weber number of the flow exceeds unity and Bo/We<1. Under the action of inertia, bubbles of size comparable to the channel diameter become elongated but remain centred. Smaller bubbles migrate towards the channel wall and do not exhibit a preferential near-wall circumferential position.

Power production characteristics of binary particles pulsed anaerobic fluidized bed microbial fuel cell

A novel binary particulate pulsating anaerobic fluidized bed microbial fuel cell (BPFB-MFC) was designed and constructed in order to improve the efficiency of low-grade energy conversion in sewage. The effects of pulsed liquid flow rate and bed filling rate on the electricity production performance and effluent treatment characteristics of the BPFB-MFC were investigated experimentally. The results showed that when the pulsed liquid flow was u=1.95sin(π/3)t cm·s-1 and when the bed materials in the anode chamber consisted of 10% bed height activated carbon particles and 10% bed height ceramic particles, the highest voltage produced was 519.7mV, the highest power density was 587.5mW·m-2, and the lowest internal resistance was 171.2Ω, which was the optimal experimental working condition. It was found that the electricity production performance and effluent treatment efficiency of the mixed particles system were better than those of a system with single particles. This work held promise of promoting the industrialization of MFC.

Numerical investigation into the transition of electrohydrodynamic spraying modes and behaviors

Electrohydrodynamic (EHD) spraying is an interesting phenomenon where the liquid subjected to an electrical stress deforms into an electrified liquid drop, a thin liquid jet, or the so-called Taylor cone, which is also highly complicated owing to its various spraying modes and behaviors. Due to the lack of critical information such as the electric charge density and internal velocity profile, the underlying physics behind the transition of different EHD spraying modes are still not adequately understood. In light of this, we conducted a numerical investigation into the transition of EHD spraying modes and behaviors under the three most important operating parameters including electric voltage, nozzle height, and liquid flow rate. Four typical spraying modes, namely, dripping, cone-jet, multi-jet, and jetting, are observed. From the numerical results, we obtained the voltage distribution in the environment, electric charge density at the liquid–air interface, and velocity profile inside the liquid, which help us to comprehensively analyze and explicate the influences of these three parameters on the transition of spraying modes and behaviors. This eventually leads us to a spraying mode map showing the correlation between the spraying modes and the electric Bond number. To the best of our knowledge, this is the first numerical work focusing on the transition of EHD spraying mode, from which we intend to expand the knowledge of this interesting phenomenon.

Research on The Accumulation Law and Treatment Measures of Low-pressure Wet Gas Pipeline Network in A Certain Gas Field

Abstract With the increasing development and utilization of natural gas resources, the operational problems of low-pressure wet gas pipelines are gradually becoming prominent, especially in low-pressure wet gas pipelines where changes in gas pressure and temperature are often accompanied by the precipitation of free water and the formation of accumulated liquid. Liquid accumulation not only increases pipeline friction and reduces transportation efficiency, but may also cause a series of safety issues such as corrosion and hydrate freezing, seriously threatening the stable operation of the pipeline network and the efficient supply of natural gas. Therefore, in-depth research and exploration of the accumulation law of low-pressure wet gas pipeline network and corresponding treatment measures have important practical significance and application value for ensuring the safety production of gas fields, improving transportation efficiency, and extending pipeline life. This article selects a low-pressure wet gas pipeline network in a certain gas field as the research object. Through a detailed analysis of its structural characteristics, wet gas transportation process, and the mechanism of liquid accumulation, the impact of liquid accumulation on the pipeline network system is deeply explored. The study analyzed the structural characteristics of the pipeline network, moisture transportation technology, and the mechanism of liquid accumulation. A numerical simulation model was established using advanced OLGA software, and detailed simulation analysis was conducted on the phenomenon of liquid accumulation under different production conditions. The research results show that changes in pipeline throughput and shutdowns and restarts can have an impact on liquid accumulation, especially an increase in start-up throughput can effectively shorten the equilibrium time of liquid accumulation and increase the liquid flow rate at the pipeline outlet. On this basis, this study further explores the best practices for pipeline cleaning operations, proposes a series of suggestions, and explores reasonable cleaning cycles. The optimization of cleaning operations can not only reduce the accumulation of liquid, but also help improve the operational efficiency and safety of the pipeline network. This study not only provides theoretical guidance for the safe and stable operation of low-pressure wet gas pipelines, but also provides strong technical support for related engineering practices. By deeply understanding the law of liquid accumulation and taking corresponding treatment measures, the frictional resistance along the pipeline can be effectively reduced, and accidents such as corrosion and hydrate freezing can be reduced, thereby ensuring the long-term, efficient, and safe production of the gas field.

Numerical analysis of oil liquid sloshing in fuel tanks of plug-in hybrid electric vehicles under different structure baffles

Abstract To solve a large amount of oil liquid sloshing in the fuel tank and a series of problems caused by oil liquid sloshing in the plug-in hybrid electric vehicle (PHEV) under the condition of electric drive only, this paper analyzes the oil liquid sloshing in fuel tank under different liquid filling rates under complex situations. After determining the representative liquid filling rates, the optimal scheme is finally determined. We conduct the specific analysis of different types, structures, and installation modes of fuel tank baffles under the same working conditions and liquid filling amount. The results show that the less liquid is filled in the fuel tank, the larger the sloshing amplitude is, and the more complicated the sloshing situation is. When the oil liquid sloshes, the non-porous baffle has an obvious zoning effect on the oil liquid and suppresses the oil liquid fluctuations effect, but the oil liquid fluidity is poor. The angle between the linear baffle and the oil liquid flow direction is larger, which has a better attenuation effect on the impact force of oil liquid. In conditions of significant oil liquid sloshing, a high baffle enhances the contact area of the oil liquid, resulting in improved inhibition effects. After considering various advantages and disadvantages, the analysis of the cruciform baffle found that the cruciform baffle limited the multi-directional movement of oil liquid, caused substantial vortex inside the oil liquid, and attenuated the kinetic energy generated by oil liquid sloshing. This greatly reduced the impact of the oil liquid on the fuel tank wall and improved the effect of suppressing oil liquid fluctuations.

Bubble generation in a 3-D flow-focusing microchannel: From squeezing to jetting

Fine bubbles have been applied in many fields; however, the controllable preparation of monodispersed fine bubbles remains a challenge. In this study, a three-dimensional (3-D) flow-focusing microfluidic device was designed. Compared with bubble formation in one-dimensional (1-D) and two-dimensional (2-D) flow-focusing, the 3-D flow-focusing microchannel owns the features of making bubbles with much smaller sizes and wider operation range. Four different gas–liquid flow regimes (squeezing, squeezing-dripping transition, dripping, and jetting) and three different gas–liquid dispersion states (mono-dispersion, bi-dispersion, and poly-dispersion) were observed in the 3-D flow-focusing microchannels. Importantly, the bi-dispersion in the squeezing-dripping transition regime experimentally verified that the squeezing and viscous shearing mechanisms separately control bubble formation in the transition region based on the time sequence. The intrinsic reason for poly-dispersion in the squeezing-dripping transition and jetting regimes was revealed. Finally, a mathematical model is proposed to predict the bubble size in the flow-focusing microchannels.

Brownian motion in a magneto Thermo-diffusion fluid flow over a semi-circular stretching surface

The current study explores the mass and heat transport analysis of a Casson liquid stream past a curved surface. The current model considers the effect of magnetic strength brought on by the strength of the applied uniform magnetic field. The significance of thermophoresis and Brownian motion are also taken into account using the Buongiorno nano-liquid model. The study of liquid flow over stretching sheets frequently addresses practical issues that have garnered significant attention from researchers due to their importance in various domains, including microfluidics, fibreglass production, manufacturing, transportation, metal extrusion, thermal insulation, glass production, paper manufacturing, and acoustic blasting. The governing partial differential equations (PDEs) are converted into ordinary differential equations (ODEs) using the similarity variables. These equations are numerically solved using the finite difference method (FDM). The concentration, temperature, and velocity graphs were produced by varying the different physical parameters. The upsurge in the magnetic parameter reduces the velocity profile. As the magnetic parameter increases, thermal and concentration profiles upsurge. The decrease in velocity profile can be seen as the Casson parameter rises. The intensification in values of thermophoretic parameter enhances the thermal and concentration profiles. The concentration and thermal profiles reduce as the curvature parameter upsurges.

The evolution of the bubble collapse morphology between two cylinders within a confined space

This work investigates the dynamic bubble behaviors between two cylinders within a confined space using high-speed photographic experiments and Kelvin impulse theory. First, the evolution of the collapse morphologies of bubbles located at the origin and along the y axis between two cylinders is qualitatively investigated. The effects of the cylinder spacing and bubble ordinate on the characteristics of the bubble deformation and the liquid velocity are then explored. The variations of the bubble interface velocities, the roundness of the bubble cross section, and the bubble radius are quantitatively analyzed. The conclusions can be summarized as follows: (1) The experimental bubble collapse phenomena at the origin can be divided into three cases: hourglass-shaped collapse, “8”-shaped collapse, and capsule-shaped collapse. Bubble collapse at the y axis can also be divided into three scenarios: awl-shaped collapse, spindle-shaped collapse, and inverted triangle-shaped collapse. (2) The cylinder spacing and the bubble ordinate significantly affect the experimental bubble collapse behaviors and the theoretical liquid flow field. (3) High-velocity liquid regions are generated around the bubble when it oscillates freely, and the nearby cylinders always lead to low-velocity regions between them and the bubble. The closer the bubble is to the cylinder, the smaller the low-velocity regions and the larger the high-velocity regions.

Струйный эффект при возникновении присоединенной каверны от системы импульсивных давлений

We consider the plane problem of the emergence of an attached cavity caused by the sudden action of impulsive pressures at some initial time. It is assumed that these pressures are distributed on the upper part of the boundary of a stationary circular cylinder immersed in liquid. A problem with unilateral constraints is formulated, on the basis of which the flow of liquid at the initial moment of time and the initial zone of separation of liquid particles are determined. At the next moments of time, an attached cavity is formed, the shape of which is determined based on the solution of the dynamic initial-boundary value problem of the theory of potential flows of an ideal incompressible fluid with free boundaries. The main unknowns in it are the velocity potential, the shape of the cavity, the dynamics of the separation points, and the perturbation of the external free boundary of the liquid. It is required to study the posed problem at short times, focusing on the behavior of the internal free boundary of the liquid near the separation points. When studying this problem, pressure in the cavern, which is created artificially, plays an important role. At low pressures, the internal free boundary of the liquid near the separation point is located on opposite sides of this point. In this case, the end part of the cavity resembles a stream of gas directed along the boundary of the cylinder towards the liquid.

Study of the Flow Characteristics of Pumped Media in the Confined Morphology of a Ferrofluid Pump With Annular Microscale Constraints

Abstract The driving mechanism of ferrofluid micropumps under the constraints of an annular microscale morphology is not fully understood. The gap between microfabrication technology and the fundamental theory of microfluidics has become a substantial obstacle to the development and application of ferrofluid micropumps. In this study, we first theoretically analyzed the Knudsen numbers of millimeter-scale microfluids using Jacobson's molecular hard sphere model, obtaining the initial conclusion that liquid flow conforms to the continuum hypothesis in geometric morphologies with characteristic dimensions greater than 7 × 10−8 m. Subsequently, using a microscopic lens combined with the particle image velocimetry optical measurement method, the flow patterns in millimeter-scale annular flow channels were captured and we observed wall slip phenomena in which the slip length of the millimeter-scale channel approached the micron level. The slip velocity and flowrate through the cross section of the microscale channel followed a logarithmic function relationship and could be divided into rapid growth, slow growth, and stable stages. As the characteristic scale of the channel was further reduced, the linear relationship between the slip velocity and cross-sectional flowrate in the rapid growth stage was broken, and the nonlinear relationship approximated an exponential function. Finally, a theoretical model for the flow behavior of the driving fluid in a ferrofluid micropump was established using slip boundary conditions. The flow patterns in microscale ring flow under slip conditions conformed to a quadratic function.

Enhanced rheology and firefighting performance of fluorine-free soft foams through the assembly of cellulose nanofibres and cellulose nanocrystals at the air–liquid interface

In this work, we developed soft and highly stable perfluorocarbon-free foams based on cellulose nanofibres (CNFs), cellulose nanocrystals (CNCs) and alkyl polyglycoside (APG). Neither the CNCs nor the CNFs can effectively stabilise the APG foam, which is reflected in the spontaneous degradation of the foam. Interestingly, blending these two nanocelluloses and foaming resulted in an ultrastable foam. The reflective optical interference technique was used to visualise liquid flow in the liquid film, and the results showed that the foam film with a thickness of only a few tens of nanometres gained excellent mechanical stability by tuning the assembly of CNCs and CNFs at the air–liquid interface. Moreover, the interfibril interactions at the Plateau borders reduce the bubble coarsening rate and drainage rate. In pool fire extinguishing tests, increasing the total concentration of CNCs and CNFs improved the foam stability, but increasing the viscosity led to a decrease in the foam spreading rate. Thus, a formulation with 0.4 % nanocellulose has poorer firefighting performance than a formulation with 0.15 % nanocellulose. When the ratios of CNCs and CNFs are properly controlled, the burnback performance of perfluorocarbon-free foam is better than that of state-of-the-art fluorinated AFFFs for n-heptane pool fires. The sustainability of the firefighting process is considerably improved by switching to the nonperfluorinated liquid foam developed in this work.

Numerical Investigation of Flow Characteristics in Internally Flowing Pipes with Varying Roughness and Helical Angles of Vortex Generators

In this study, the turbulent behavior inside a pipe containing an aluminum helical vortex generator plate was investigated using computational fluid dynamics (CFD) methods, considering different plate roughness and helical angle values. Accordingly, numerical analyses of velocity and pressure distributions for a liquid flow with a constant inlet velocity of 0.5 m/s and four different helical angles were performed and compared in a computer software. To observe the effects of the roughness values of the metal plate on flow behavior, analyses were conducted for three different roughness values for each helical angle and the results were compared and interpreted. As a result of the study, the combination of a roughness value of 0.04 and a helical angle of 0° led to the highest pressure and velocity values, while the same roughness value combined with a 270° helical angle resulted in the lowest pressure and velocity values. Detailed analysis showed that helical angles (90° and 180°) presented moderate pressure and velocity values, indicating a non-linear relationship between helical angle and flow characteristics. The results demonstrate that optimizing the helical angle and roughness is crucial for enhancing the efficiency of vortex generators. This way, a design will be developed to prevent performance degradation in industrial applications that require flow efficiency and pressure management.

Parametric Study on Venturi Pressure Drop for Two Phase Oil (D130)-Water Flow for Different Operating Conditions – An Experimental Investigation

The governing parameters which affect pressure drop of two-phase oil-water flow across the venturi meter are water cut and angle of inclination. The study investigates experimentally the effect of inclination and water cut on pressure drop measurements across different venturi meters with beta ratios (β) = 0.4, and 0.6 for oil–water two-phase flow experiments in a 3-inch pipe for different operating conditions. Two-phase inclinable flow loop has been employed for conducting the experiments for different fluid mixture flow rates and water cuts. The working fluids utilized are Exxsol mineral oil (D130) and potable water. The experiments were conducted for water cuts varying from 0 to 100% in steps of 20%, flow rates ranging from 2000 to 12000 barrels per day (BPD), and for horizontal and vertical flow loop inclinations (0◦ and 90◦). Liquid flow rates considered in the study match flow rates of real oil wells. The results indicate that the venturi pressure drop varies linearly with water cuts for both β ratios (0.4 and 0.6). The study indicates that the effect of inclination on venturi pressure drop is not appreciable for all water cuts and flow rates. Also, from the experimental results it can be concluded that venturi with β = 0.6 is favourable for multiphase flow metering (with flow rates ranging from 8000 to 12000 BPD). The tangible findings of the study will be helpful in combating multi-phase flow challenges in oil and petroleum industries.

Modeling and Optimization of Wet ALE Process

Wet ALE (atomic layer etch) processes are emerging as an important alternative to standard ALE processes in semiconductor manufacturing. Here we present a model for simulating an idealized wet ALE process that includes both chemical reactions and liquid flow in order to predict the amount of material etch, how much of the etching is true ALE vs continuous etch, and its uniformity across the wafer. This model is applied to both a simple test flow cell and flow across a spinning wafer in a typical wet single wafer process. Results show that etch amount and uniformity depends on timing of the dispense steps, flow parameters, and the kinetics of the specific chemical reactions.