Equation of state for hard-sphere fluids offering accurate virial coefficients

Tian, Jianxiang; Jiang, Hua; Gui, Yuanxing; Mulero, A.

doi:10.1039/b915002a

Cited by 28 publications

(48 citation statements)

References 31 publications

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“…The first of (8) is the jump in the electric field amplitude |u| and there also exists a corresponding jump in the packing fraction, as in the second of (8). The correlation between these two jumps is linked by the state equation, a m 2 = g(η m )−g 0 .…”

Section: Uniform Soliton Theory and The Dispersive Shock Wavementioning

confidence: 99%

Dispersive shock waves in colloids with temperature dependent compressibility

Azmi

Marchant

2014

J. Nonlinear Optic. Phys. Mat.

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The formation of a dispersive shock wave in a colloidal medium, due to an initial jump in the light intensity, is studied. The compressibility of the colloidal particles is modeled using a series in the particle density, or packing fraction, where the virial coefficients depend on the particle interaction model. Both the theoretical hard disk and sphere repulsive models, and a model with temperature dependent compressibility, are considered. Experimental results for the second virial coefficient show that it is temperature dependent and that the particle interactions can be either repulsive or attractive. These effects are modeled using a power-law relationship. The governing equation is a focusing nonlinear Schrödinger-type equation with an implicit nonlinearity. The initial jump is resolved via a dispersive shock wave which forms before the onset of modulational instability. A semi-analytical solution is developed for the one-dimensional line bore case which predicts the amplitude of the solitary waves which form in the dispersive shock wave. The solitary wave amplitude versus jump height diagrams can exhibit three different kinds of behaviors. A unique solution, an Sshaped solution curve and multiple solution branches where the upper branch has separated from the lower branches. A bifurcation from the low to the high power branch can occur for many parameter choices as the amplitude of the initial jump increases. The effect of temperature on the evolution of the bore, the amplitude of the solitary waves and the bifurcation patterns are all discussed and the semi-analytical solutions are found to be very accurate. AbstractThe formation of a dispersive shock wave in a colloidal medium, due to an initial jump in the light intensity, is studied. The compressibility of the colloidal particles is modelled using a series in the particle density, or packing fraction, where the virial coefficients depend on the particle interaction model. Both the theoretical hard disk and sphere repulsive models, and a model with temperature dependent compressibility, are considered. Experimental results for the second virial coefficient show that it is temperature dependent and that the particle interactions can be either repulsive or attractive; these effects are modelled using a power law relationship. The governing equation is a focusing nonlinear Schrödinger-type equation with an implicit nonlinearity. The initial jump is resolved via a dispersive shock wave which forms before the onset of modulational instability. A semi-analytical solution is developed for the one dimensional line bore case which predicts the amplitude of the solitary waves which form in the dispersive shock wave. The solitary wave amplitude versus jump height diagrams can exhibit three different kinds of behaviours; an unique solution, an S-shaped solution curve and multiple solution branches where the upper branch has separated from the lower branches. A bifurcation from the low to the high power branch, can occur for many parameter choices, as the ...

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Section: Uniform Soliton Theory and The Dispersive Shock Wavementioning

confidence: 99%

Dispersive shock waves in colloids with temperature dependent compressibility

Azmi

Marchant

2014

J. Nonlinear Optic. Phys. Mat.

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“…(2). Thus, the models yielding the correct value of the packed density such as [16][17][18] might be also generalized by Eq. (5).…”

Section: Theorymentioning

confidence: 99%

About the physical validity of attaching the repulsive terms of analytical EOS models by temperature dependencies

Kalikhman

Kost

Polishuk

2010

Fluid Phase Equilibria

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“…For a fixed z value, the maximum amplitude can be significantly different to the long z average, hence the wide differences from the long term averages in table 4. Table 4 shows the z-weighted numerical average amplitudes, using (14) and the uniform soliton theory (12) and (13). We see that as temperature increases, the average maximum amplitude decreases.…”

Section: Semi-analytical Solutionsmentioning

confidence: 99%

“…For the stationary circular DSW, with r 0 = 600 and z 1 = 1200, the average maximum amplitudes are a = 2.56 and α = 0.273, which represent variations of only 1% and 8% for a and α. However, for the expanding circular DSW, the predictions of uniform soliton theory must be combined with (14). For the case where k = 1, by using z 1 = 1200 and other related information from figure 1, the predictions are a = 1.77 and α = 0.13 while the numerical averages are found to be a = 1.64 and α = 0.092.…”

Section: Semi-analytical Solutionsmentioning

confidence: 99%

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Circular dispersive shock waves in colloidal media

Azmi

Marchant

2016

J. Nonlinear Optic. Phys. Mat.

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A dispersive shock wave (DSW), with a circular geometry, is studied in a colloidal medium. The colloidal particle interaction is based on the repulsive theoretical hard sphere model, where a series in the particle density, or packing fraction is used for the compressibility. Experimental results show that the particle interactions are temperature dependent and can be either repulsive or attractive, so the second term in the compressibility series is modified to allow for temperature dependent effects, using a power-law relationship. The governing equation is a focusing nonlinear Schrödinger-type equation with an implicit nonlinearity. The initial jump in electric field amplitude is resolved via a DSW, which forms before the onset of modulational instability. A semi-analytical solution for the amplitude of the solitary waves in a DSW of large radius, is derived based on a combination of conservation laws and geometrical considerations. The effect of temperature and background packing fraction on the evolution of the DSW and the amplitude of the solitary waves is discussed and the semi-analytical solutions are found to be very accurate, when compared with numerical solutions. Abstract. A dispersive shock wave (DSW), with a circular geometry, is studied in a colloidal medium. The colloidal particle interaction is based on the repulsive theoretical hard sphere model, where a series in the particle density, or packing fraction is used for the compressibility. Experimental results show that the particle interactions are temperature dependent and can be either repulsive or attractive, so the second term in the compressibility series is modified to allow for temperature dependent effects, using a power law relationship. The governing equation is a focusing nonlinear Schrödinger-type equation with an implicit nonlinearity. The initial jump in electric field amplitude is resolved via a DSW, which forms before the onset of modulational instability. A semianalytical solution for the amplitude of the solitary waves in a DSW of large radius, is derived based on a combination of conservation laws and geometrical considerations. The effect of temperature and background packing fraction on the evolution of the DSW and the amplitude of the solitary waves is discussed and the semi-analytical solutions are found to be very accurate, when compared with numerical solutions.

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Equation of state for hard-sphere fluids offering accurate virial coefficients

Cited by 28 publications

References 31 publications

Dispersive shock waves in colloids with temperature dependent compressibility

Dispersive shock waves in colloids with temperature dependent compressibility

About the physical validity of attaching the repulsive terms of analytical EOS models by temperature dependencies

Circular dispersive shock waves in colloidal media

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