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An overview on collision dynamics of deformable particles

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Abstract

Interaction dynamics of rigid/deformable particles are included in a wide range of industrial and scientific approaches. The description of the binary collision of particles is required to predict the flow of a concentrated emulsion. The present review introduces the numerical approaches employed to simulate the interaction of two particles and evaluates the impact of deformability, configuration, and flow type on collision dynamics. Two closely interacting drops/bubbles can collide in in-line and side-by-side configurations in Newtonian and non-Newtonian surrounding fluids. Based on the previous investigations, the future trends for the binary collision of deformable particles are provided.

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Abbreviations

Ar:

Archimedes number

Bo:

Bond number

Ca:

Capillary number

\(d\) :

Particle diameter, m

Eo:

Eötvös number

\(g\) :

Gravity acceleration, m/s2

Ga:

Galileo number

\(F\) :

The force due to surface tension, N

\({F}_{b}\) :

Body force, N

\({\mathrm{F}}_{\mathrm{MP}}\) :

Added mass force, N

\({\mathrm{F}}_{\mathrm{D}}\) :

Drag force, N

\({\mathrm{F}}_{\mathrm{B}}\) :

Buoyancy force, N

\({\mathrm{F}}_{\mathrm{L}}\) :

Shear-induced lift force, N

K:

Solid-fluid viscosity ratio

M:

Mobility potential

Mo:

Morton number

n:

Power-law index

\(n\) :

Unit vector normal to the drop surface, m

S:

Second-order tensor

\(U\) :

Fluid velocity, m/s

\({U}_{p}\) :

Particle velocity, m/s

\(x\) :

Position in an Eulerian coordinate, m

\(X\) :

Position of the front in Lagrangian coordinate, m

\({\delta }^{\beta }\) :

Two- or three-dimensional delta function

\(\epsilon\) :

Dissipation rate

\(\eta\) :

Viscosity ratio

\({\eta }_{K}\) :

Kolmogorov length scale, m

\(\kappa\) :

Twice the mean curvature for three-dimensional flows

\({\kappa }^{^{\prime}}\) :

Consistency index

\(\uplambda\) :

Elastic relaxation time, s

\({\lambda }_{1}\) :

Relaxation time, s

\({\lambda }_{2}\) :

Retardation time, s

\({\mu }_{o}\) :

Zero shear rate

\({\mu }_{\infty }\) :

Infinite shear rate

\({\mu }_{d}\) :

Drop dynamic viscosity, Pa.s

\({\mu }_{f}\) :

Fluid dynamic viscosity, Pa.s

\({\rho }_{d}\) :

Drop density, kg/m3

\({\rho }_{f}\) :

Fluid density, kg/m3

\({\rho }_{l}\) :

Liquid density, kg/m3

\(\sigma\) :

Surface tension, N/m

\(\varphi\) :

Chemical potential

\(\Phi\) :

Volume fraction

\(\Omega\) :

Vorticity tensor

\(\tau\) :

Stress tensor, Pa

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  1. Department of Mechanical Engineering, Shahrekord University, Shahrekord, 8818634141, Iran

    Zohre Alinejad, Morteza Bayareh, Behzad Ghasemi & Afshin Ahmadi Nadooshan

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  1. Zohre Alinejad
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Alinejad, Z., Bayareh, M., Ghasemi, B. et al. An overview on collision dynamics of deformable particles. Chem. Pap. 76, 6017–6031 (2022). https://doi.org/10.1007/s11696-022-02317-7

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