Forces

Kusumaatmaja, Halim; Kuzmin, Alexandr; Shardt, Orest; Silva, Gonçalo; Viggen, Erlend Magnus

doi:10.1007/978-3-319-44649-3_6

Cited by 49 publications

(127 citation statements)

References 56 publications

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“…The Navier–Stokes equations are recovered in the limit of small Mach and Knudsen numbers by the lattice Boltzmann method (LBM), which is based on the discretisation of the Boltzmann–BGK (Bhatnagar, Gross & Krook 1954) equation in time and phase space (Benzi, Succi & Vergassola 1992; Succi 2001; Krüger et al. 2017). The LBM describes the evolution of the single-particle distribution function at a position and time with a microscopic velocity , where , on a regular -dimensional lattice in discrete time steps .…”

Section: Methodsmentioning

confidence: 99%

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Structure and rheology of suspensions of spherical strain-hardening capsules

2021

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Section: Methodsmentioning

confidence: 99%

“…For detailed reviews on the IBM and its accuracy, we refer the reader to Mittal & Iaccarino (2005) and Krüger et al. (2017) among other existing works on this topic. In what follows, we use a two-point linear interpolation function as discussed in Krüger (2012), which is given by where can denote , or .…”

Section: Methodsmentioning

confidence: 99%

Structure and rheology of suspensions of spherical strain-hardening capsules

2021

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“…Each component obeys the standard lattice Bhatnagar–Gross–Krook (LBGK) equation with a single relaxation time, which can be written as (Krüger et al. 2017) where is the distribution function of component along the discrete velocity direction . Here is the lattice relaxation time towards local equilibrium which relates to the macroscopic component viscosity where is the lattice speed of sound (the mixture viscosity is a more complex expression when the components have different ).…”

Section: Methodsmentioning

confidence: 99%

Droplet–turbulence interactions and quasi-equilibrium dynamics in turbulent emulsions

Mukherjee

Safdari²,

Shardt³

et al. 2019

J. Fluid Mech.

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We perform direct numerical simulations (DNSs) of emulsions in homogeneous, isotropic turbulence using a pseudopotential lattice-Boltzmann (PP-LB) method. Improving on previous literature by minimizing droplet dissolution and spurious currents, we show that the PP-LB technique is capable of long, stable simulations in certain parameter regions. Varying the dispersed phase volume fraction φ, we demonstrate that droplet breakup extracts kinetic energy from the larger scales while injecting energy into the smaller scales, increasingly with higher φ, with the Hinze scale dividing the two effects. Droplet size (d) distribution was found to follow the d −10/3 scaling (Deane & Stokes 2002). We show the need to maintain a separation of the turbulence forcing scale and domain size to prevent the formation of large connected regions of the dispersed phase. For the first time, we show that turbulent emulsions evolve into a quasi-equilibrium cycle of alternating coalescence and breakup dominated processes. Studying the system in its state-space comprising kinetic energy E k , enstrophy ω 2 and the droplet number density N d , we find that their dynamics resemble limit-cycles with a time delay. Extreme values in the evolution of E k manifest in the evolution of ω 2 and N d with a delay of ∼ 0.3T and ∼ 0.9T respectively (with T the large eddy timescale). Lastly, we also show that flow topology of turbulence in an emulsion is significantly more different than singlephase turbulence than previously thought. In particular, vortex compression and axial straining mechanisms become dominant in the droplet phase, a consequence of the elastic behaviour of droplet interfaces.

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“…For multicomponent flows, we consider a binary mixture of fluids and , characterised by an order parameter , such that corresponds to a bulk fluid and to a bulk fluid. The coexistence of these two bulk fluids can be realised by using a simple form for the Helmholtz free energy where the bulk and the gradient free energy densities are (Briant & Yeomans 2004; Krüger et al 2017) Here, and are free parameters, which are related to the interface width and surface tension through For simplicity, we consider the case when and have constant values throughout the fluid. The chemical potential can be derived by taking the functional derivative of the free energy with respect to the order parameter, giving …”

Section: Hydrodynamics On Curved Surfacesmentioning

confidence: 99%