1991

Chandra [1]

${\beta }_{\max }^2=\frac{We+4}{3\left(1-\cos {\theta }_e\right)}$

1995

Scheller; bousfield [2]

${\beta }_{\max }\propto 0.61{\left(R{e}^{2}Ob\right)}^{1/6}=0.61R{e}^{1/5}{\left(WeR{e}^{-2/5}\right)}^{1/6}$

1996

Pasandidch-Fard [3]

${\beta }_{\max }^2=\frac{We+12}{3\left(1-\cos {\theta }_{\alpha }\right)+4\left(We/\sqrt{Re}\right)}$

2003

Kwon [4]

${\beta }_{\max }^2=\frac{-\left(1-\cos {\theta }_e\right)+\sqrt{{\left(1-\cos {\theta }_e\right)}^2+\frac{6We}{Re}\left(\frac{We}{3}+4\right)}}{3We/Re}$

2004

Clanet [5]

${\beta }_{\max }\propto W{e}^{1/4}$

2005

Ukiwe; kwok [6]

$\left[3\left(1-\cos {\theta }_d\right)+\frac{4We}{\sqrt{Re}}\right]{\beta }_{\max }^3-\left(We+12\right){\beta }_{\max }+8=0$

2009

Roisman [7]

${\beta }_{\max }\propto 0.87R{e}^{1/5}-0.4R{e}^{2/5}W{e}^{-1/2}$

2010

Eggers [8]

${\beta }_{\max }=R{e}^{1/5}f\left(P\right)$

2013

陈石 [9]

${\beta }_{\max }={\beta }_{\infty }+\sqrt{1+\frac{{\left(Re+C_1\right)}^2}{3C_{2}R{e}^2/We-C_1^2}}$

2015

李大树 [10]

${\beta }_{\max }=\sqrt{\frac{We+12}{3\left(1-\cos {\theta }_e\right)+3We/\sqrt{Re}}}\approx \frac{1}{\sqrt{3}}R{e}^{0.25}$

2016

J.B.Lee [11]

${\beta }_{\max }^2=R{e}^{2/5}\frac{We}{{\left(7.6+W{e}^{1/2}\right)}^2}+{\beta }_{V_i\to 0}^2$

2018

黄海梦 [12]

$\{\begin{array}{l}\frac{3}{4}\left(\frac{We}{\sqrt{Re}}+\frac{W{e}^{\ast }}{\sqrt{R{e}^{*}}}\right){\beta }_{\max }^4+3\left(1-\cos {\theta }_{\alpha }\right){\beta }_{\max }^3-\left(We+12\right){\beta }_{\max }+8=0,V_0<V^{\ast }\\ \frac{3}{4}\left(\frac{We}{\sqrt{Re}}+\frac{W{e}^{\ast }}{\sqrt{R{e}^{*}}}\frac{R{e}^{*}}{Re}\right){\beta }_{\max }^4+3\left(1-\cos {\theta }_{\alpha }\right){\beta }_{\max }^3-\left(We+12\right){\beta }_{\max }+8=0,V_0>V^{\ast }\end{array}$