Microfluidics and Nanofluidics最新文献_第9页

Exploring the stability of single emulsion created by microfluidics and its use in the production of core–shell microparticles 探索微流控技术产生的单一乳液的稳定性及其在核壳微颗粒生产中的应用

IF 2.3 4区工程技术

Microfluidics and Nanofluidics Pub Date : 2024-04-08 DOI: 10.1007/s10404-024-02723-1

Mehrnaz Oveysi, Vahid Bazargan, Amir Nejat, Marco Marengo

{"title":"Exploring the stability of single emulsion created by microfluidics and its use in the production of core–shell microparticles","authors":"Mehrnaz Oveysi, Vahid Bazargan, Amir Nejat, Marco Marengo","doi":"10.1007/s10404-024-02723-1","DOIUrl":"10.1007/s10404-024-02723-1","url":null,"abstract":"<div><p>This study introduces an innovative method aimed at achieving exceptional stability in emulsions. The primary focus is on re-emulsifying precisely controlled and uniform initial single emulsions, generated by microfluidic devices, to produce single-core double emulsions and core–shell microparticles. Departing from traditional approaches, our method employs a unique combination of advanced Two-level fractional factorial design and numerical simulation. These tools are utilized to discern and optimize critical parameters necessary for the formation of highly monodispersed stable single emulsions and their subsequent transformation into double emulsions. Correlations are established to estimate the size and stability of the primary single emulsion based on immiscible phase flow rate ratio and surfactant concentration. These correlations provide a comprehensive understanding that facilitates the intentional development of desired water-in-oil emulsions. The proposed microfluidic paradigm shows promise for the controlled and efficient production of single-core double emulsions, with broad applications in Pharmaceuticals, Food, and Cosmetics.</p></div>","PeriodicalId":706,"journal":{"name":"Microfluidics and Nanofluidics","volume":"28 5","pages":""},"PeriodicalIF":2.3,"publicationDate":"2024-04-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140571067","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Localized flow control by photothermal actuation of pNIPAAm hydrogel brushes in a macroporous silicon membrane 通过光热驱动大孔硅膜中的 pNIPAAm 水凝胶刷实现局部流量控制

IF 2.3 4区工程技术

Microfluidics and Nanofluidics Pub Date : 2024-04-04 DOI: 10.1007/s10404-024-02726-y

Youngsik Song, Nafis Mustakim, Mayank Pandey, Sang-Woo Seo

{"title":"Localized flow control by photothermal actuation of pNIPAAm hydrogel brushes in a macroporous silicon membrane","authors":"Youngsik Song, Nafis Mustakim, Mayank Pandey, Sang-Woo Seo","doi":"10.1007/s10404-024-02726-y","DOIUrl":"10.1007/s10404-024-02726-y","url":null,"abstract":"<div><p>We present the control of liquid flow through arrayed micron-sized pores in a macroporous silicon membrane. The pores are coated with about 150 nm polymer N-isopropylacrylamide (pNIPAAm) hydrogel brushes and 200 nm polypyrrole layer, which works as photothermal actuator. The size of pore openings is controlled by utilizing the swelling and de-swelling behavior of temperature-sensitive pNIPAAm brushes, and the temperature on pNIPAAm brushes is changed by 815 nm near infra-red (NIR) illumination to polypyrrole photothermal element layer. The dimension change of the pore openings is investigated by observing the transmitted light and fluorescence signal intensity through the pores in the membrane while changing the ambient temperature. It has shown that the intensity of transmitted light can be controlled by adjusting the ambient temperature across the low critical solution temperature (LCST) of the hydrogel brushes. The localized control of liquid flow through the pores is demonstrated by the diffusion of fluorescein dye from the bottom of the membrane to the surface of the membrane using pulsed NIR light illumination. Fast dynamic response of fluorescein dye diffusion upon the illumination of NIR light suggests that the presented photothermal actuation approach could be applied to diverse biomedical applications such as a localized drug release system.</p></div>","PeriodicalId":706,"journal":{"name":"Microfluidics and Nanofluidics","volume":"28 5","pages":""},"PeriodicalIF":2.3,"publicationDate":"2024-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140570912","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Microfluidic chip for synergic drugs assay in 3D breast cancer cell 用于三维乳腺癌细胞协同药物检测的微流控芯片

IF 2.3 4区工程技术

Microfluidics and Nanofluidics Pub Date : 2024-04-02 DOI: 10.1007/s10404-024-02724-0

Franciele Flores Vit, Yu Tzu Wu, Eric Fujiwara, Hernandes F. Carvalho, Lucimara Gaziola de la Torre

{"title":"Microfluidic chip for synergic drugs assay in 3D breast cancer cell","authors":"Franciele Flores Vit, Yu Tzu Wu, Eric Fujiwara, Hernandes F. Carvalho, Lucimara Gaziola de la Torre","doi":"10.1007/s10404-024-02724-0","DOIUrl":"10.1007/s10404-024-02724-0","url":null,"abstract":"<div><p>Some anticancer treatments may cause Multidrug Resistance (MDR). In these cases, cells pump the drug out of the intracellular environment, thereby preventing drug effects. Several strategies have been used to avoid MDR, including using two or more drugs at low concentrations to increase the sensitivity of cells to treatment. We present an effective, cheap, fast microfluidic alternative to test two drugs simultaneously using a reversible sealing and reusable device to determine the optimal concentration. We used the rugs doxorubicin (DOX) and paclitaxel (PXT) as proof of concept. The microdevice allows the testing of two drugs in real time. Furthermore, running two experiments in sextuplicates and control in the same microchip is possible. We used two combinations of drugs, varying the drug concentration (C<sub>1</sub> = 0.010 mg.mL<sup>− 1</sup> DOX and 0.002.mL<sup>− 1</sup> mg PXT, C<sub>2</sub> = 0.010 mg.mL<sup>− 1</sup> DOX and 0.004 mg.mL<sup>− 1</sup> PXT), and evaluated cell death over time. The intermediate drug concentrations were more efficient, reducing the time required to decrease the viability of breast tumor cells, MCF-7 (C<sub>1</sub> = 180 and C<sub>2</sub> = 120). In further analysis, the microdevice also allowed characterization of the effects of the drugs (antagonist, synergic, or additive). This microdevice is a reliable tool for estimating the different combinations of two drug concentrations in a single assay simply and quickly.</p></div>","PeriodicalId":706,"journal":{"name":"Microfluidics and Nanofluidics","volume":"28 5","pages":""},"PeriodicalIF":2.3,"publicationDate":"2024-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140571004","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Quantifying the performances of SU-8 microfluidic devices: high liquid water tightness, long-term stability, and vacuum compatibility 量化 SU-8 微流体设备的性能：高液体水密性、长期稳定性和真空兼容性

IF 2.3 4区工程技术

Microfluidics and Nanofluidics Pub Date : 2024-03-29 DOI: 10.1007/s10404-024-02720-4

Said Pashayev, Romain Lhermerout, Christophe Roblin, Eric Alibert, Jerome Barbat, Rudy Desgarceaux, Remi Jelinek, Edouard Chauveau, Saïd Tahir, Vincent Jourdain, Rasim Jabbarov, Francois Henn, Adrien Noury

{"title":"Quantifying the performances of SU-8 microfluidic devices: high liquid water tightness, long-term stability, and vacuum compatibility","authors":"Said Pashayev, Romain Lhermerout, Christophe Roblin, Eric Alibert, Jerome Barbat, Rudy Desgarceaux, Remi Jelinek, Edouard Chauveau, Saïd Tahir, Vincent Jourdain, Rasim Jabbarov, Francois Henn, Adrien Noury","doi":"10.1007/s10404-024-02720-4","DOIUrl":"10.1007/s10404-024-02720-4","url":null,"abstract":"<div><p>Despite several decades of development, microfluidics lacks a sealing material that can be readily fabricated, leak-tight under high liquid water pressure, stable over a long time, and vacuum compatible. In this paper, we report the performances of a micro-scale processable sealing material for nanofluidic/microfluidics chip fabrication, which enables us to achieve all these requirements. We observed that micrometric walls made of SU-8 photoresist, whose thickness range from 35 to 135 µm, are at least leak-tight to 1.5 bars and up to 5.5 bars, exhibit no water porosity even after 2 months of aging, and are able to sustain under <span>(10^{-5})</span> mbar vacuum. This sealing material is therefore reliable and versatile for building microchips, part of which must be isolated from liquid water under pressure or vacuum. Moreover, the fabrication process we propose does not require the use of either aggressive chemicals or high-temperature or high-energy plasma treatment. It thus opens a new perspective to seal microchips with sensitive surfaces containing nanomaterials.</p></div>","PeriodicalId":706,"journal":{"name":"Microfluidics and Nanofluidics","volume":"28 5","pages":""},"PeriodicalIF":2.3,"publicationDate":"2024-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140325418","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Behaviors of non-wetting phase snap-off events in two-phase flow: microscopic phenomena and macroscopic effects 两相流中非润湿相卡断事件的行为：微观现象和宏观效应

IF 2.3 4区工程技术

Microfluidics and Nanofluidics Pub Date : 2024-03-26 DOI: 10.1007/s10404-024-02718-y

Ran Li, Zhaolin Gu, Zhang Li, Weizhen Lu, Guozhu Zhao, Junwei Su

引用次数: 0

Modified capillary number to standardize droplet generation in suction-driven microfluidics 修改毛细管数量，使抽吸驱动微流控技术中的液滴生成标准化

IF 2.3 4区工程技术

Microfluidics and Nanofluidics Pub Date : 2024-03-22 DOI: 10.1007/s10404-024-02714-2

Jatin Panwar, Rahul Roy

{"title":"Modified capillary number to standardize droplet generation in suction-driven microfluidics","authors":"Jatin Panwar, Rahul Roy","doi":"10.1007/s10404-024-02714-2","DOIUrl":"10.1007/s10404-024-02714-2","url":null,"abstract":"<div><p>In droplet microfluidic devices with suction-based flow control, the microchannel geometry and suction pressure at the outlet govern the dynamic properties of the two phases that influence the droplet generation. Therefore, it is critical to understand the role of geometry along with suction pressure in the dynamics of droplet generation to develop a predictive model. We conducted a comprehensive characterization of droplet generation in a flow focusing device with varying control parameters. We used these results to formulate a scaling argument and propose a governing parameter, called as modified capillary number (Ca<sub>L</sub>), that combines normalized droplet volume with geometrical parameters (length of dispersed and continuous phase channels) and flow parameters (interfacial tension, phase viscosity and velocity) in a power law relationship. Ca<sub>L</sub> effectively captures the transition from squeezing to dripping regimes of droplet generation, providing essential insights into the design requirements for suction-driven droplet generation. These findings are key to standardize microfluidic flow-focusing devices that can achieve the desired droplet generation behavior with optimal pressure consumption.</p></div>","PeriodicalId":706,"journal":{"name":"Microfluidics and Nanofluidics","volume":"28 4","pages":""},"PeriodicalIF":2.3,"publicationDate":"2024-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140204062","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

A hybrid Gaussian mixture/DSMC approach to study the Fourier thermal problem 研究傅立叶热问题的混合高斯混合物/DSMC 方法

IF 2.3 4区工程技术

Microfluidics and Nanofluidics Pub Date : 2024-03-20 DOI: 10.1007/s10404-024-02719-x

Shahin Mohammad Nejad, Frank A. Peters, Silvia V. Nedea, Arjan J. H. Frijns, David M. J. Smeulders

{"title":"A hybrid Gaussian mixture/DSMC approach to study the Fourier thermal problem","authors":"Shahin Mohammad Nejad, Frank A. Peters, Silvia V. Nedea, Arjan J. H. Frijns, David M. J. Smeulders","doi":"10.1007/s10404-024-02719-x","DOIUrl":"10.1007/s10404-024-02719-x","url":null,"abstract":"<div><p>In rarefied gas dynamics scattering kernels deserve special attention since they contain all the essential information about the effects of physical and chemical properties of the gas–solid surface interface on the gas scattering process. However, to study the impact of the gas–surface interactions on the large-scale behavior of fluid flows, these scattering kernels need to be integrated in larger-scale models like Direct Simulation Monte Carlo (DSMC). In this work, the Gaussian mixture (GM) model, an unsupervised machine learning approach, is utilized to establish a scattering kernel for monoatomic (Ar) and diatomic (<span>(hbox {H}_{2})</span>) gases directly from Molecular Dynamics (MD) simulations data. The GM scattering kernel is coupled to a pure DSMC solver to study isothermal and non-isothermal rarefied gas flows in a system with two parallel walls. To fully examine the coupling mechanism between the GM scattering kernel and the DSMC approach, a one-to-one correspondence between MD and DSMC particles is considered here. Benchmarked by MD results, the performance of the GM-DSMC is assessed against the Cercignani–Lampis–Lord (CLL) kernel incorporated into DSMC simulation (CLL-DSMC). The comparison of various physical and stochastic parameters shows the better performance of the GM-DSMC approach. Especially for the diatomic system, the GM-DSMC outperforms the CLL-DSMC approach. The fundamental superiority of the GM-DSMC approach confirms its potential as a multi-scale simulation approach for accurately measuring flow field properties in systems with highly nonequilibrium conditions.</p></div>","PeriodicalId":706,"journal":{"name":"Microfluidics and Nanofluidics","volume":"28 4","pages":""},"PeriodicalIF":2.3,"publicationDate":"2024-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10404-024-02719-x.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140204105","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Simulation of avascular tumor growth and drug response in a microfluidic device with a cellular automaton model 利用细胞自动机模型模拟微流控装置中血管瘤的生长和药物反应

IF 2.3 4区工程技术

Microfluidics and Nanofluidics Pub Date : 2024-03-16 DOI: 10.1007/s10404-024-02717-z

Sijia Liu, Yuewu Li, Chunxiao Chen, Zhiyu Qian, Hongjun Wang, Yamin Yang

{"title":"Simulation of avascular tumor growth and drug response in a microfluidic device with a cellular automaton model","authors":"Sijia Liu, Yuewu Li, Chunxiao Chen, Zhiyu Qian, Hongjun Wang, Yamin Yang","doi":"10.1007/s10404-024-02717-z","DOIUrl":"10.1007/s10404-024-02717-z","url":null,"abstract":"<div><p>The microfluidic system is capable of recapitulating key attributes of in vivo circumstances and, therefore, becomes a valuable platform for better understanding tumor growth dynamics and evaluating drug efficiency. While numerical simulations have been envisioned as powerful tools for validating versatile performance of advanced microfluidic platforms, cell growth within these microchannels has not yet been theoretically modeled. In this paper, we developed an experimental data-driven cellular automaton model, which was adopted for simulating cell behaviors and drug responses in a microfluidic system. The boundaries of the cellular automata lattices and prohibited zones for simulation were directly converted from microscopic images of cell morphology and the microchamber configuration. The dynamic progression of tumor growth at the avascular stage was predicted by incorporating the biophysical and molecular characteristics of cells and their interactions with surrounding environment. The simulated proliferation rate of tumor cells over time demonstrated its dependency on nutrient delivery, aligning well with experimental observations in the microfluidic culture. The spatiotemporal efficacy of the chemotherapeutic compound doxorubicin (DOX) on the microfluidic culture was also simulated. The similarity between in silico simulations and in vitro tumor response upon drug interaction highlighted the potential of the computational models as complementary tools for predicting the drug treatment efficacy with acceptable accuracy before practical applications.</p></div>","PeriodicalId":706,"journal":{"name":"Microfluidics and Nanofluidics","volume":"28 4","pages":""},"PeriodicalIF":2.3,"publicationDate":"2024-03-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140155819","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Curved microchannels with inner wall expansion–contraction array for particle focusing 用于粒子聚焦的带内壁膨胀-收缩阵列的弯曲微通道

IF 2.3 4区工程技术

Microfluidics and Nanofluidics Pub Date : 2024-03-15 DOI: 10.1007/s10404-024-02715-1

Ruihan Zhuang, Kaixin Song, Zhibin Wang, Gang Chen, Ying Chen, Lisi Jia

{"title":"Curved microchannels with inner wall expansion–contraction array for particle focusing","authors":"Ruihan Zhuang, Kaixin Song, Zhibin Wang, Gang Chen, Ying Chen, Lisi Jia","doi":"10.1007/s10404-024-02715-1","DOIUrl":"10.1007/s10404-024-02715-1","url":null,"abstract":"<div><p>To enhance focusing performance, we proposed an integrated microchannel with expansion–contraction arrays (ECA) on the inner wall of the curved microchannel (CIECA) and compared it with a straight microchannel with ECA (SECA) as well as the traditional integrated microchannel of ECA on the outer wall of the curved channel (COECA). We investigated the particle-focusing mechanisms in these microchannels through a combination of experiments and numerical simulations. The proposed integrated microchannel demonstrates significant improvements in focusing performance compared to SECA and COECA, which is attributed to its consistent Dean flow. In contrast, COECA shows the poorest performance because of inconsistent Dean flow. The focusing width in the proposed integrated microchannel is reduced to 1/3 of that in COECA and 1/2 of that in SECA. Furthermore, the focusing performance of CIECA improves as the Reynolds number increases, eventually forming a single trajectory when the Reynolds number (at contraction) reaches 83.33. Finally, the impact of particle size on focusing performance was investigated through numerical simulations. The focusing performance of the CIECA is the best in these three microchannels. In CIECA, as the particle size increases, the focusing width initially decreases and then increases. Among them, 8 and 10 μm particles can achieve complete focusing. This study serves as a crucial reference for comprehending and enhancing particle focusing through the synergy of multi-Dean flow.</p></div>","PeriodicalId":706,"journal":{"name":"Microfluidics and Nanofluidics","volume":"28 4","pages":""},"PeriodicalIF":2.3,"publicationDate":"2024-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140155683","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

A thermally actuated biocompatible flexible micropump for surface adaptable mounting 用于表面适应性安装的热致动生物兼容柔性微型泵

IF 2.3 4区工程技术

Microfluidics and Nanofluidics Pub Date : 2024-03-09 DOI: 10.1007/s10404-024-02708-0

Victor Bradley Bednar, Kenichi Takahata

{"title":"A thermally actuated biocompatible flexible micropump for surface adaptable mounting","authors":"Victor Bradley Bednar, Kenichi Takahata","doi":"10.1007/s10404-024-02708-0","DOIUrl":"10.1007/s10404-024-02708-0","url":null,"abstract":"<div><p>Pulsed thermal energy causes piecewise actuation of a nitinol cantilever providing the mechanical force required to evacuate a chamber constructed of parylene C. This proof-of-principle micropump demonstrates an alternative to typical evacuation and rectification methods utilized in most micropumps. The chamber and normally closed channels that serve as valves are all of parylene C construction, leading to the flexibility of the device. The nitinol cantilever functions as an actuator capable of yielding successive partial chamber evacuations until achieving complete evacuation. Piecewise shape recovery of the actuator was made viable by implementing a Peltier device, providing the means for supplying responsive and controlled thermal energy. Experiments delivered measurements of consecutive advancement of shape recovery using a laser displacement sensor while monitoring the temperature with fiber-optic sensors. The release of a saturated lithium chloride solution from the pump was monitored by observing conductivity changes in the experimental area. Theoretically predicting a release amount used calculations for the expected recovery of the actuator based on displacement characterization via a logistic curve fit against actuator temperature data. The measured release amounts correlated well with the theoretically predicted values made using the temperature values obtained near the device during the release. These works provide novel approaches to micropump fabrication and implementation and new strategies for predicting the recovery of shape memory alloys. The micropump concepts are viable in many fields, such as biomedical applications: in vivo drug delivery, organ-on-chip, and lab-on-chip devices, to name a few. Likewise, a simple prediction for nitinol recovery has vast potential.</p></div>","PeriodicalId":706,"journal":{"name":"Microfluidics and Nanofluidics","volume":"28 4","pages":""},"PeriodicalIF":2.3,"publicationDate":"2024-03-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140097288","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0