Dynamics Of Bubble Growth Research Articles

Modeling the chaotic dynamics of bubble growth under hydrodynamic interactions in pool boiling

This study seeks to understand the origins of intermittency in quantities of interest in pool boiling, such as bubble departure diameter and growth time. The intermittency of nucleation site activity due to hydrodynamic and thermal interactions with nearby nucleation sites is well-established; however, few mechanistic models have been developed that predict such intermittency. Here we assume a fluctuating pressure field at a nucleation site due to an adjacent bubble which alters bubble growth depending on the phase of the pressure oscillation with respect to the instant of bubble nucleation. The results suggest that even when a single departure frequency is assumed for nearby bubbles, its effect on the nucleation site being considered causes aperiodicity and intermittency in bubble departure quantities. The effects of pressure field phase angle, degree of superheat, and choice of force balance model on the bubble departure quantities are examined. The phase angle is shown to play a major role in determining bubble departure diameter and growth time. The departure diameter is observed to have a broad distribution, belying the assumption of a unique value. Period doubling of the ebullition cycle is observed for some conditions, a phenomenon documented by other investigators. A multifractal analysis of the time series of departure events indicates the presence of long term temporal correlations, which become weaker with increasing superheat. The second order Hurst exponent of the structure functions of departure events appears to have a universal behavior with Jakob number, independent of the choice of liquid. The Hurst exponent rises from zero to a value close to 0.5 at large superheats, suggesting a continuous transition from an ordered state to a disordered state along the boiling curve.

Bridging scales in multiscale bubble growth dynamics with correlated fluctuations using neural operator learning

The intricate process of bubble growth dynamics involves a broad spectrum of physical phenomena from microscale mechanics of bubble formation to macroscale interplay between bubbles and surrounding thermo-hydrodynamics. Traditional bubble dynamics models including atomistic approaches and continuum-based methods segment the bubble dynamics into distinct scale-specific models. To bridge the gap between microscale stochastic fluid models and continuum-based fluid models for bubble dynamics, we develop a composite neural operator model to unify the analysis of nonlinear bubble dynamics across microscale and macroscale regimes by integrating a many-body dissipative particle dynamics (mDPD) model with a continuum-based Rayleigh–Plesset (RP) model through a novel neural network architecture, which consists of a deep operator network for learning the mean behavior of bubble growth subject to pressure variations and a long short-term memory network for learning the statistical features of correlated fluctuations in microscale bubble dynamics. Training and testing data are generated by conducting mDPD and RP simulations for nonlinear bubble dynamics with initial bubble radii ranging from 0.1 to 1.5 micrometers. The results show that the trained composite neural operator model can accurately predict bubble dynamics across scales, with a 99% predictive accuracy for the time evolution of the bubble radius under varying external pressure while containing correct size-dependent stochastic fluctuations in microscale bubble growth dynamics. The composite neural operator is the first deep learning surrogate for multiscale bubble growth dynamics that can capture correct stochastic fluctuations in microscopic fluid phenomena, which sets a new direction for future research in multiscale fluid dynamics modeling.

Comprehensive experimental thermal analysis of single bubble nucleation in vertical flow boiling: Whole field temperature and microlayer dynamics

Nucleate boiling, an important heat transfer phenomenon, holds significance in the thermal management of numerous engineering applications. Understanding and predicting its heat transfer characteristics are vital for system optimization. The formation of a microlayer, resulting from rapid bubble growth on a heater substrate, subsequently facilitates further bubble growth through evaporation playing a critical role in overall bubble dynamics. This study examines the intricate relationship between bubble and microlayer dynamics and their impact on heat transfer rates. Experimental work is conducted for varying heat fluxes using rainbow schlieren deflectometry (RSD) and thin-film interferometry (TFI) in tandem for simultaneous mapping of key parameters: bubble dynamics, microlayer dynamics, and two-dimensional temperature field in vertical flow boiling. The analysis of these parameters has provided significant insights into some fundamental aspects of boiling. Firstly, this study emphasizes that the bubble growth rate models need to take into initial microlayer thickness in accurately predicting bubble growth dynamics. The iteratively obtained constant Ceff (describing the initial microlayer thickness) for bubble growth models matches well the value of Ceff obtained experimentally from thin film interferograms. Additionally, this study also validates the applicability of the kinetic theory-based model in predicting the evaporative heat transfer coefficient during the initial stage of flow boiling, while demonstrating that the accommodation coefficient is ∼0.04 for the investigated range of heat fluxes. Subsequently, using the experimentally obtained evaporative heat transfer coefficient, further insights are provided into the dry patch dynamics. Experimental dry patch dynamics were in good agreement with theoretical predictions up to the rewetting phase. The results also indicate a substantial contribution of microlayer evaporation, constituting approximately 34 % of the total heat flux.

Aerophobic P-MoS2 on MOF-Derived Co,N-Codoped Carbon Nanosheets with Accelerated H2 Bubble Release Dynamics for Efficient Alkaline Water Splitting at 1000 mA cm-2.

Rapid bubble release at high current densities results in the detachment of catalysts and performance degradation, posing a persistent challenge in actual alkaline water electrolysis (AWE). Here, hierarchical nanosheet structures (CoNC@P-MoS2) are constructed, with P-doped MoS2 on the surface of Co,N-codoped carbon. It exhibits low hydrogen evolution reaction overpotentials of 30 and 354 mV at 10 and 1000 mA cm-2 in 1 M KOH, respectively, with a small Tafel slope of 36 mV dec-1. The constructed CoNC@P-MoS2||NiFe-DLH cell requires only 1.44 and 1.92 V to achieve overall water splitting at 10 and 1000 mA cm-2, which outperforms the traditional catalysts like Pt/C||IrO2. The introduction of P stabilizes surface hydroxyl (OH*) and increases the proton penetration depth, thereby greatly enhancing its intrinsic activity. It also makes the surface aerophobic by introducing more microfeatures, which greatly improves the geometric activity by increasing the bubble release rate (∼5.8 times). Low energy consumption of 3.92 kW h Nm-3 was achieved with an energy efficiency close to 80%. Bubble growth kinetics analysis reveals that the time and growth factors for CoNC@P-MoS2 are increased to 0.54 and 11.79 from 0.45 and 6.09 for CoNC, respectively, which highlights its fast bubble reaction dynamics. The results suggest the feasibility of CoNC@P-MoS2 as a potential high-performance catalyst in commercial AWE.

Temperature-dependent bubble growth under synergistic interactions of hydrogen and helium in tungsten

A novel theoretical model based on modified diffusion rate equations is proposed to simulate the retention of hydrogen isotopes and the dynamics of bubble growth in tungsten (W) when exposed to simultaneous hydrogen (H) and helium (He) plasma irradiations. Simulation is conducted to assess the influence of temperature as well as simultaneous H and He irradiation at an increasing fluence. Not only to develop a holistic understanding but also to substantiate simulation findings about synergy between H and He plasma irradiation, a W sample is exposed sequentially to H and He plasma at 873 K using the large-power material irradiation experimental system. The topographical changes in the W sample are investigated using atomic force microscopy (AFM) after each plasma irradiation exposure sequence. Simulation results reveal that the ability of a bubble containing both H and He to trap adjacent H/He atoms is primarily governed by their individual partial pressure within the bubble. Furthermore, at elevated temperatures, the synergy between H and He significantly enhances the retention of H isotopes in W. AFM micrographs of the W sample exposed to both H and He plasma irradiation show a severely damaged and locally delaminated layer, absent in the sample exposed only to either H or He, conclusively establishing evidence of synergy between H and He irradiation effects. The average bubble radius computed using the model aligns excellently with experimentally determined values obtained through SEM/AFM analysis. The robustness of the proposed model is also assessed by comparing bubble radius and H isotopes retention at various temperatures with experimental data reported in the literature.

Experimental study on generation and growth of bubbles in external flash-boiling spray regime

High-performance liquid propulsion systems, such as hypersonic scramjets and liquid rockets, utilize regenerative cooling by employing fuel as a coolant to shield components from thermal damage. The flash-boiling spray, resulting from superheated liquid injection and prevalent in regenerative cooling, has received considerable research interest for enhancing atomization and combustion efficiency. In this study, superheated water jets at various temperatures between 30 and 90 ℃ were injected into a vacuum chamber at different pressures above 5 kPa, and their spray patterns were acquired through diffusive backlight imaging. Images were analyzed to determine key parameters, such as bubble nucleation flux, bubble growth rate, and spray angle, in an external flash-boiling spray regime. The estimated nucleation flux agreed well with the predictions the model based on nucleation theory in the region of sufficiently high superheat. The dynamics of bubble growth was investigated and explained using a bubble growth model. The jet-expansion energy was computed by measuring the spray angle and compared with the available energy. By mapping the evolution of flash-boiling spray in relation to relevant nondimensional numbers, the study underscores the necessity of accounting for the pressure inside the injector to adequately model bubble generation inside the injector. Furthermore, this study substantiates the feasibility of visually recognizing and analyzing individual bubbles in the external flash-boiling regime, thereby enabling the generation of experimental data crucial for the validation of bubble nucleation and growth models.

Generating Stable Nitrogen Bubble Layers on Poly(methyl methacrylate) Films by Photolysis of 2-Azidoanthracene.

2-Azidoanthracene (2N3-AN) can act as a photochemical source of N2 gas when dissolved in an optically transparent polymer such as poly(methyl methacrylate) (PMMA). Irradiation at 365 or 405 nm of a 150 μm-thick polymer film submerged in water causes the rapid appearance of a surface layer of bubbles. The rapid appearance of surface bubbles cannot be explained by normal diffusion of N2 through the polymer and likely results from internal gas pressure buildup during the reaction. For an azide concentration of 0.1 M and a light intensity of 140 mW/cm2, the yield of gas bubbles is calculated to be approximately 40%. The dynamics of bubble growth depend on the surface morphology, light intensity, and 2N3-AN concentration. A combination of nanoscale surface roughness, high azide concentration, and high light intensity is required to attain the threshold N2 gas density necessary for rapid, high-yield bubble formation. The N2 bubbles adhered to the PMMA surface and survived for days under water. The ability to generate stable gas bubbles "on demand" using light permits the demonstration of photoinduced flotation and patterned bubble arrays.

Bubble nucleation and growth on microstructured surfaces under microgravity

Understanding the dynamics of surface bubble formation and growth on heated surfaces holds significant implications for diverse modern technologies. While such investigations are traditionally confined to terrestrial conditions, the expansion of space exploration and economy necessitates insights into thermal bubble phenomena in microgravity. In this work, we conduct experiments in the International Space Station to study surface bubble nucleation and growth in a microgravity environment and compare the results to those on Earth. Our findings reveal significantly accelerated bubble nucleation and growth rates, outpacing the terrestrial rates by up to ~30 times. Our thermofluidic simulations confirm the role of gravity-induced thermal convective flow, which dissipates heat from the substrate surface and thus influences bubble nucleation. In microgravity, the influence of thermal convective flow diminishes, resulting in localized heat at the substrate surface, which leads to faster temperature rise. This unique condition enables quicker bubble nucleation and growth. Moreover, we highlight the influence of surface microstructure geometries on bubble nucleation. Acting as heat-transfer fins, the geometries of the microstructures influence heat transfer from the substrate to the water. Finer microstructures, which have larger specific surface areas, enhance surface-to-liquid heat transfer and thus reduce the rate of surface temperature rise, leading to slower bubble nucleation. Our experimental and simulation results provide insights into thermal bubble dynamics in microgravity, which may help design thermal management solutions and develop bubble-based sensing technologies.

Effect of barodiffusion on the dynamics of gas bubble growth in the magmatic melt

Effect of barodiffusion on the dynamics of gas bubble growth in the magmatic melt

Colloidal bubble propulsion mediated through viscous flows.

Bubble-propelled catalytic colloids stand out as a uniquely efficient design for artificial controllable micromachines, but so far lack a general theoretical framework that explains the physics of their propulsion. Here we develop a combined diffusive and hydrodynamic theory of bubble growth near a spherical catalytic colloid, that allows us to explain the underlying mechanism and the influence of environmental and material parameters. We identify two dimensionless groups, related to colloidal activity and the background fluid, that govern a saddle-node bifurcation of the bubble growth dynamics, and calculate the generated flows analytically for both slip and no slip boundary conditions on the bubble. We finish with a discussion of the assumptions and predictions of our model in the context of existing experimental results, and conclude that some of the observed behaviour, notably the ratchet-like gait, may stem from peculiarities of the experimental setup rather than fundamental physics of the propulsive mechanism.

Bubble Engineering on Micro-/Nanostructured Electrodes for Water Splitting.

Bubble behaviors play crucial roles in mass transfer and energy efficiency in gas evolution reactions. Combining multiscale structures and surface chemical compositions, micro-/nanostructured electrodes have drawn increasing attention. With the aim to identify the exciting opportunities and rationalize the electrode designs, in this review, we present our current comprehension of bubble engineering on micro-/nanostructured electrodes, focusing on water splitting. We first provide a brief introduction of gas wettability on micro-/nanostructured electrodes. Then we discuss the advantages of micro-/nanostructured electrodes for mass transfer (detailing the lowered overpotential, promoted supply of electrolyte, and faster bubble growth kinetics), localized electric field intensity, and electrode stability. Following that, we outline strategies for promoting bubble detachment and directional transportation. Finally, we offer our perspectives on this emerging field for future research directions.

Numerical simulation of Marangoni flow around a growing hydrogen bubble on a microelectrode

In this work, a numerical model for Marangoni flow around a growing hydrogen bubble on a microelectrode is developed and validated. The growth of the bubble is implemented using a body-fitted moving mesh method that moves the bubble interface based on the production of hydrogen at the cathode. The dissolved hydrogen that is produced at the cathode diffuses into the bubble. The geometry of the bubble is a spherical cap with a pinned contact line and a decreasing contact angle as the bubble grows larger. There are two cases: (1) a case in which the bubble grows on a microbubble carpet that grows during the evolution of the bubble, and (2) a case in which the carpet thickness is negligible. The purpose of this model is to simulate and investigate thermocapillary Marangoni convection during almost the entire bubble lifetime (nucleation and detachment are not included).We validate the model with data from two experiments reported in literature (Massing et al. 2019; Bashkatov et al. 2022; Bashkatov, 2022). The evolution of the bubble radius, the temperature profile around the bubble, and the profile of the Marangoni velocity, which is tangential to the bubble surface at 5 μm from the bubble, near the lower half of the bubble are accurately predicted. For the case with a bubble carpet, we investigated models with a growing carpet and fixed carpet thickness. We found that for a given bubble size the Marangoni velocity reduces with increasing carpet thickness.Stagnant bubble models are less complicated and computationally cheaper than the growing bubble model. For the case without a carpet, we compare the growing bubble model with two stagnant bubble models: one using constant current and another one using a transient current. A stagnant bubble model is recommended if the growth rate drb/dt<0.05uM where drb/dt is the instantaneous bubble growth rate and uM the average Marangoni velocity at the bubble interface. This is the case at a relatively late stage of the bubble evolution. At the early stage of the bubble evolution, the absence of bubble growth dynamics in the stagnant bubble models appears to have an effect on the velocity profile and the pressure part of the hydrodynamic force.

Investigating mass transfer around spatially-decoupled electrolytic bubbles

Electrolytic bubbles have a profound impact on mass transport in the vicinity of electrodes and greatly influence the electrolyzer efficiency and cell overpotential. However, experimental measurements of concentration fields around electrolytic bubbles with high spatio-temporal resolution is challenging. In this study, a succession of spatially-decoupled electrolytic bubbles growing in an initially quiescent electrolyte is simulated. The bubbles grow and depart from a hydrophobic cavity at the center of a ring microelectrode. The gas-liquid interface is modeled using a moving mesh topology. A geometric cutting protocol is developed to handle topology changes during bubble departure. The simulated bubbles show good agreement with the bubble growth dynamics observed in experiments. The bubbles in this spatially-decoupled system outgrow the region of electrolyte that is saturated with dissolved hydrogen. This leaves the apex of the bubble interface exposed to an undersaturated region of the electrolyte which leads to an outward flux of hydrogen gas. This is shown to limit the gas evolution efficiency of bubbles even though that they grow at a constant volumetric rate. By analyzing the distribution of the flux of dissolved hydrogen along the bubble interface along with the development of dissolve hydrogen concentration profiles around the bubble, we show that the magnitude of the outward diffusive flux at the apex of the bubble decreases with increasing electrolysis current.

Comparison of bubble parameters in natural and chemical surfactant solutions: a force analysis

The authors have investigated the potential of a plant-based natural surfactant in the modification of various bubble parameters. Bubble dynamics at the orifice were studied in natural surfactant solutions extracted from the plant Sapindus mukorossi at concentrations below and above its critical micellar concentration (CMC). The results were compared to the ones obtained with Sodium Dodecyl Sulfate solutions. The CMC values of Sapindus mukorossi and Sodium Dodecyl Sulfate are 7.5 × 10−3 g/cc and 2.39 × 10−3 g/cc, respectively. A photographic method was employed to observe bubble formation at the orifice. The results show that biosurfactants, like chemical surfactants, have a comparable effect on bubble density, size, and rise velocity. Experimentally determined bubble radius, volume, and radial velocity were used to calculate various forces contributing to the bubble dynamics. The buoyancy, pressure, and surface tension forces were significantly stronger in magnitude in comparison to the gas momentum, viscous drag, and added mass forces. Our findings suggest that the significance of various dynamic forces involved in bubble growth dynamics varies according to the bubble generation frequency regimes. We report for the first time the potential of Sapindus mukorossi in altering bubble properties and surface forces at the orifice and its usage in various bubble-related industrial applications.

Understanding diffusion-controlled bubble growth in porous media using experiments and simulations.

Nucleation and subsequent expansion of gas bubbles in porous media is relevant to many applications, including oil recovery, carbon storage, and boiling. We have built an experimental setup using microfluidic chips to study the dynamics of bubble growth in porous media. Visualization experiments of the growth of carbon dioxide bubbles in a supersaturated dodecane solution were conducted. We show that bubbles grow as dissolved gas molecules inside the oversaturated liquid diffuse to the gas-liquid interface. Bubbles expanding inside a porous medium displace the liquid phase until the cluster of the gas-filled pores becomes connected to the outlet at the critical gas saturation, which is used as a measure for the total liquid displacement. Our experiments uniquely focus on the growth of a single bubble and show that larger pressure drops lead to faster bubble growth while resulting in lower critical gas saturations. A nonlinear pore-network model is implemented to simulate bubble growth. We compare model predictions for bubble growth dynamics to our experimental results and present the need for further theoretical development to capture deviations from invasion-percolation when a large pressure drop is applied.

Dynamics of gas bubble growth in a high-viscosity gas-saturated liquid during its decompression at a finite rate

Dynamics of gas bubble growth in a high-viscosity gas-saturated liquid during its decompression at a finite rate

Investigation of the Enhancement of Boiling Heat Transfer Performance Utilizing a Hybrid Wetting Surface with a Macroscopic Millimeter-Scale Pillar Array

The heat transfer process is an important part of energy utilization and conversion, and boiling heat transfer is one of the most significant and effective heat transfer modes in use. Enhancing boiling heat transfer can directly improve energy use efficiency and promote the sustainable development of the energy industry. Surfaces with mixed wetting topologies have been proven to possess the potential to enhance boiling heat transfer. However, the heat transfer promoting mechanism of these types of surfaces requires further clarification on actual heat exchanger surfaces with macroscale heat transfer enhancement structures, such as millimeter-scale pillars. In this study, the boiling heat transfer enhancement mechanism and the performance of the hybrid wetting surfaces with an array of macropillars were explored using both experimentation and numerical simulation. In the experiment, the single bubble growth dynamics at the onset sites of nucleation of these hybrid wetting surfaces in the initial boiling stage were recorded using a CCD camera with a top view. The boiling heat transfer coefficient was also measured at the stable boiling stage. Within the entire tested range of heat flux (3.75–18 W/cm2), the hybrid wetting surfaces significantly enhanced the boiling heat transfer, and the HPo(bottom)–HPi(top) surface (surf-2) exhibited the best heat transfer performance. At the representative heat flux 12.5 W/cm2, the boiling heat transfer coefficient of the HPo (bottom)–HPi (top) surface (surf-2) and the HPi (bottom)–HPo (top) surface (surf-3) were more than 33% and 18% higher than the pure copper flat surface, and more than 16% and 3% higher than the uniform HPi surface (surf-4), respectively. On the one hand, due to the view field of camera being blocked by the fiercely growing bubbles in the stable boiling stage, it was difficult to record bubble numbers and gather statistics at the onset sites of nucleation in order to correlate the bubble dynamics with the mechanism of boiling heat transfer enhancement. On the other hand, the single bubble growth dynamics recorded during the initial boiling stage lacked information about the hybrid wetting surfaces in the vertical cross-sectional plane. Therefore, a two-dimensional VOF-based numerical simulation was adopted to supplement the contribution of hybrid wetting surfaces in the vertical plane. The simulation results indicated that the hybrid wetting surfaces with macropillars can inhibit bubble overgrowth and accelerate bubble departure compared with spatially uniform hydrophobic surface. The bubble radius and departure time on surf-2 were smaller than those on surf-3. These are believed to be the reasons why the surf-2 surface exhibited the best heat transfer performance in the experiment. Both the experiment and numerical analysis proved that the hybrid wetting surfaces with macroscale pillars can promote the boiling heat transfer, thus demonstrating potential applications in actual horizontal or vertical tube boiling heat exchangers.

Dimensional analysis of vapor bubble growth considering bubble–bubble interactions in flash boiling microdroplets of highly volatile liquid electrofuels

Electrofuels (e-fuels) produced from renewable electricity and carbon sources have gained significant attention in recent years as promising alternatives to fossil fuels for the transportation sector. However, the highly volatile e-fuels, such as short-chain oxymethylene ethers (OMEx) are prone to flash vaporization phenomena, which is associated with the formation and growth of vapor bubbles, followed by explosive bursting of the liquid jet. This phenomenon is important in many practical applications, for example, superheated liquid sprays in gasoline direct injection engines as well as cryogenic engines. The simulation of a flash boiling spray of such highly volatile liquid fuels is numerically challenging due to several reasons, including (1) the complexity of the bubble growth process in the presence of multiple vapor bubbles and (2) the need to use an extremely small time step size to accurately capture the underlying physics associated with the flash boiling process. In this paper, we first present a bubble growth model in flash boiling microdroplets considering bubble–bubble interactions along with the finite droplet size effects. A dimensional analysis of the newly derived Rayleigh–Plesset equation (RPE) with bubble–bubble interactions is then performed for Reynolds numbers of different orders of magnitude to estimate the relative importance of different forces acting on the bubble surface. Based on this analysis, a simplified nondimensional semi-analytical solution for bubble growth, which also includes the bubble–bubble interactions, is derived to estimate the bubble growth behavior with reasonable accuracy using the larger time step sizes for a wide range of operating conditions. The derived semi-analytical solution is shown to be a good approximation for describing the bubble growth rate over the whole lifetime of the bubble, thus making it useful for simulations of superheated sprays with large numbers of droplets and even more bubbles. The bubble–bubble interactions are found to have a significant impact on the bubble growth dynamics and result in delaying the onset of droplet bursting due to the slower growth of the vapor bubble compared to the bubble growth without bubble–bubble interactions. Furthermore, in a comparison with DNS results, the proposed bubble growth model is shown to reasonably capture the impact of bubble interactions leading to smaller volumetric droplet expansion.

Mathematical modeling of puffing and microexplosion in emulsified fuel droplets containing several bubbles: A case study on n-dodecane/water droplet

This paper presents a theoretical model for microexplosion and puffing in a single isolated emulsion droplet at high ambient temperature and one atmospheric pressure. The model considered transient heating of the droplet, bubble growth dynamics, bubble motion, and bubble interactions (e.g., bubble coalescence). The bubble growth is determined by solving a modified Rayleigh equation which considered bubble interactions. The model considered multiple bubbles inside a fuel droplet which were not accounted for in the models proposed in previous studies. The model is applied to simulating the microexplosion of n-dodecane/water droplets. The simulated microexplosion delay times are compared with the experimental data from the literature, with good qualitative and quantitative agreements obtained. Results show that microexplosion delay time diminished by 40% and 50% for a 10-times increase in the initial bubble diameter and changing the bubble location from droplet center to 0.4 times the droplet radius, respectively. For multiple bubbles inside the droplet, the microexplosion delay time converges to a minimum threshold value without further changing the bubble number. The simplified model bears practical potential in enabling spray combustion modeling of water-emulsified fuels with considerably reduced computational costs.

CFD-PBM simulation of PET and supercritical CO2 microcellular foaming

By loading Cross model and Oldroyd-B model with User-defined Function (UDF) program, a method to simulate the extrusion flow of viscoelastic non-Newtonian fluid in Fluent software was proposed. In the homogeneous solution of Polyethylene terephthalate (PET) and supercritical CO2, the microscopic bubble growth kinetics model was coupled with the Population Balance Module (PBM), analysis effect of shear rate on bubble nucleation and growth, numerically simulated of the nucleation and growth of bubbles in the extrusion die of PET microcellular foam sheet. Through analysis, the bubble size distribution is more uniform under the condition of 60° template convergence angle. The larger the extrusion speed, the wider the uniform distribution range of bubble density at the outlet position. The initial concentration of CO2 has the greatest impact on the bubble density. Increasing the initial concentration of CO2 can improve the bubble density, but appropriately reducing the initial concentration of CO2 can improve the effective distribution range of bubble density of foam sheet.