Purpose

The purpose of this study is two-fold. First, it aims to differentiate the response of a stretching jet encountering a quadratic air resistance from the classical jet shape formed in a frictionless medium. Second, it investigates how the resulting jet forms with and without air resistance, seeking evidence that supports the similarity flows frequently studied for stretching/moving thin bodies under the boundary layer approximation.

Design/methodology/approach

This study extends the established electrohydrodynamic stretching jet theory, used to model electrospinning or jet printing in the absence of air resistance, to encompass the impact of the retarding force on the jet stretching in both the cone and final regimes before it impinges on a substrate.

Findings

A close examination of the nonlinear governing equations reveals that the jet rapidly thins near the nozzle because of the combined action of viscous and electrical forces. In this region, the exponentially decaying jet receives further support from the air resistance, resulting in a closer alignment with the observed experimental jet. This exponential decay, accelerated by the inversely quadratic speed of the liquid particles, serves as clear evidence for the existence of a similarity flow over an exponentially stretching sheet. Furthermore, in the final regime, the jet stretching exhibits an algebraic decay in the absence of air friction, while with air resistance, it decays exponentially to reach a limiting speed. In the former case, a square root dependence of the stretching jet speed leads to the emergence of a similarity flow over a thin stretching jet, while in the latter case, a Sakiadis’ similarity flow appears over a continuously moving flat surface.

Practical implications

The analysis goes beyond jet hydrodynamics, delving into the interplay of electrostatic forces (including Coulomb’s law) and quadratic air drag, drawing upon experimental data on glycerol liquid presented in earlier publications.

Originality/value

Finally, the asymptotic behavior of the stretching jet under the combined influence of electrostatic pull and its electric currents because of bulk conduction and surface convection is validated through a comprehensive numerical simulation of the nonlinear system.

中文翻译：

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拉伸/移动片材触发非线性相似流的证据：有/没有空气阻力的雾化和静电纺丝

 目的

这项研究的目的有两个。首先，它的目的是将遇到二次空气阻力的拉伸射流的响应与在无摩擦介质中形成的经典射流形状区分开来。其次，它研究了在有和没有空气阻力的情况下所产生的射流如何形成，寻找支持边界层近似下拉伸/移动薄体经常研究的相似流的证据。

设计/方法论/途径

这项研究扩展了已建立的电流体动力学拉伸喷射理论，用于在没有空气阻力的情况下模拟静电纺丝或喷射打印，以涵盖在喷射撞击基材之前在锥体和最终状态中减速力对喷射拉伸的影响。

 发现

对非线性控制方程的仔细检查表明，由于粘性力和电力的共同作用，喷嘴附近的射流迅速变细。在该区域中，呈指数衰减的射流受到空气阻力的进一步支持，从而与观察到的实验射流更接近。这种由液体粒子的二次方倒数速度加速的指数衰减是指数拉伸片材上存在相似流的明确证据。此外，在最终状态中，在没有空气摩擦的情况下，射流拉伸表现出代数衰减，而在有空气阻力的情况下，它会呈指数衰减以达到极限速度。在前一种情况下，拉伸射流速度的平方根依赖性导致在薄拉伸射流上出现相似流，而在后一种情况下，Sakiadis 相似流出现在连续移动的平坦表面上。

 实际意义

该分析超越了喷射流体动力学，利用早期出版物中提供的甘油液体的实验数据，深入研究了静电力（包括库仑定律）和二次空气阻力的相互作用。

 原创性/价值

最后，通过对非线性系统的全面数值模拟，验证了拉伸射流在静电拉力及其电流（由于体传导和表面对流）的综合影响下的渐近行为。