In this review the theory and application of Smoothed particle hydrodynamics (SPH) since its inception in 1977 are discussed. Emphasis is placed on the strengths and weaknesses, the analogy with particle dynamics and the numerous areas where SPH has been successfully applied.

https://iopscience.iop.org/article/10.1088/0034-4885/68/8/R01/pdf

Smoothed particle hydrodynamics

Smoothed particle hydrodynamics (SPH) is a meshfree particle method based on Lagrangian formulation, and has been widely applied to different areas in engineering and science. This paper presents an overview on the SPH method and its recent developments, including (1) the need for meshfree particle methods, and advantages of SPH, (2) approximation schemes of the conventional SPH method and numerical techniques for deriving SPH formulations for partial differential equations such as the Navier-Stokes (N-S) equations, (3) the role of the smoothing kernel functions and a general approach to construct smoothing kernel functions, (4) kernel and particle consistency for the SPH method, and approaches for restoring particle consistency, (5) several important numerical aspects, and (6) some recent applications of SPH. The paper ends with some concluding remarks.

Smoothed Particle Hydrodynamics (SPH): an Overview and Recent Developments

Manufacturing processes that can create extremely small machines have been developed in recent years. Microelectromechanical systems (MEMS) refer to devices that have characteristic length of less than 1 mm but more than 1 micron, that combine electrical and mechanical components and that are fabricated using integrated circuit batch-processing techniques. Electrostatic, magnetic, pneumatic and thermal actuators, motors, valves, gears, and tweezers of less than 100-μm size have been fabricated. These have been used as sensors for pressure, temperature, mass flow, velocity and sound, as actuators for linear and angular motion and as simple components for complex systems such as micro-heat-engines and micro-heat-pumps The technology is progressing at a rate that fa r exceeds that of our understanding of the unconventional physics involved in the operation as well as the manufacturing of those minute devices. The primary objective of this article is to critically review the status of our understanding of fluid flow phenomena particular to microdevices. In terms of applications, the paper emphasizes the use of MEMS as sensors and actuators for flow diagnosis and control.

/pdf/the-fluid-mechanics-of-microdevices-the-freeman-scholar-4k4thaspga.pdf

The Fluid Mechanics of Microdevices—The Freeman Scholar Lecture

Modelling fluid flows past a surface is a general problem in science and engineering, and requires some assumption about the nature of the fluid motion (the boundary condition) at the solid interface. One of the simplest boundary conditions is the no-slip condition1,2, which dictates that a liquid element adjacent to the surface assumes the velocity of the surface. Although this condition has been remarkably successful in reproducing the characteristics of many types of flow, there exist situations in which it leads to singular or unrealistic behaviour—for example, the spreading of a liquid on a solid substrate3,4,5,6,7,8, corner flow9,10 and the extrusion of polymer melts from a capillary tube11,12,13. Numerous boundary conditions that allow for finite slip at the solid interface have been used to rectify these difficulties4,5,11,13,14. But these phenomenological models fail to provide a universal picture of the momentum transport that occurs at liquid/solid interfaces. Here we present results from molecular dynamics simulations of newtonian liquids under shear which indicate that there exists a general nonlinear relationship between the amount of slip and the local shear rate at a solid surface. The boundary condition is controlled by the extent to which the liquid ‘feels’ corrugations in the surface energy of the solid (owing in the present case to the atomic close-packing). Our generalized boundary condition allows us to relate the degree of slip to the underlying static properties and dynamic interactions of the walls and the fluid.

A general boundary condition for liquid flow at solid surfaces

For several centuries fluid dynamics studies have relied upon the assumption that when a liquid flows over a solid surface, the liquid molecules adjacent to the solid are stationary relative to the solid. This no-slip boundary condition (BC) has been applied successfully to model many macroscopic experiments, but has no microscopic justification. In recent years there has been an increased interest in determining the appropriate BCs for the flow of Newtonian liquids in confined geometries, partly due to exciting developments in the fields of microfluidic and microelectromechanical devices and partly because new and more sophisticated measurement techniques are now available. An increasing number of research groups now dedicate great attention to the study of the flow of liquids at solid interfaces, and as a result a large number of experimental, computational and theoretical studies have appeared in the literature. We provide here a review of experimental studies regarding the phenomenon of slip of Newtonian liquids at solid interfaces. We dedicate particular attention to the effects that factors such as surface roughness, wettability and the presence of gaseous layers might have on the measured interfacial slip. We also discuss how future studies might improve our understanding of hydrodynamic BCs and enable us to actively control liquid slip.

https://iopscience.iop.org/article/10.1088/0034-4885/68/12/R05/pdf

Boundary slip in Newtonian liquids: a review of experimental studies

Shear‐induced particle structures of rheologically well‐characterized concentrated polymer dispersions were investigated by small angle neutron scattering (SANS) in a wide range of shear rates. The dispersions consist of electrostatically stabilized styrene–ethylacrylate–copolymer spheres in glycol or water. Their viscosity functions show pronounced shear thinning and strong shear thickening versus shear rate as measured by various rotational rheometers and by capillary rheometry. A quartz slit die, which could be tilted with regard to the neutron beam, enabled us to achieve wall shear rates as low as 10−5 s−1 and wall shear stresses up to 104 Pa. Part of the measurements were repeated using a Couette shear cell. Spheres of 320 nm mean diameter at a volume concentration of 58.7% in glycol show an amorphous structure at rest. In the range of strong shear thinning the halo intensity becomes anisotropic, the intensity in flow direction being increased, but no long range particle structure shows up. This result shows that drastic viscosity transitions may occur, whereas the structural changes detectable by SANS may remain weak. Nearly monosized 165 nm particles at 52.3% solid in glycol exhibit in the shear thinning regime distinct hexagonal maxima superimposed on the halo and also in a second and third ring indicating the formation of a long range particle structure. With increasing shear rate these maxima disappear and an anisotropy of the halo intensity shows up. An intensity increase in flow direction at small angles is observed in the shear thickening regime. The particle structures observed after stop of flow depend on the preceding shear rate. Similar structural changes are found at 43.4% solid for the 165 nm particles. The results obtained in Couette flow are in qualitative agreement with the slit data but show much sharper intensity maxima. The underlying type of superstructure is compared with nonequilibrium molecular dynamics (NEMD) simulations for a soft sphere model fluid. The intensity patterns extracted from the simulation bear a remarkable similarity to the directly measured SANS data.

Rheological and small angle neutron scattering investigation of shear‐induced particle structures of concentrated polymer dispersions submitted to plane Poiseuille and Couette flowa)

Abstract A nonlinear inhomogeneous relaxation equation for the alignment tensor is derived from a Fokker-Planck-equation for the orientational distribution function where torques exerted by a molecular field and by the gradient of the flow velocity are taken into account. Phenomenological coefficients characterizing the flow alignment in the isotropic and in the nematic phases are related to molecular parameters.

Fokker-Planck-Equation Approach to Flow Alignment in Liquid Crystals

A certain "critical" molecular weight controls rheological properties of the multibead finitely extensible nonlinear elastic (FENE) chain model polymer melt. The rheological crossover manifests itself in a change of power law behavior for the viscous properties at a critical number of beads per chain N(c) = 100+/-10. This finding confirms a newly proposed relationship between dimensionless critical weight, characteristic length, and flexibility which we obtain as a side result. Results further suggest that the entanglement molecular weight N(e) for the flexible FENE chain model could be comparable in size or even larger than its critical molecular weight N(c).

Rheological Evidence for a Dynamical Crossover in Polymer Melts via Nonequilibrium Molecular Dynamics

Results of nonequilibrium molecular dynamics computer simulations of a planar Couette flow are presented for the multibead anharmonic‐spring model. The finitely extensible nonlinear elastic force law is used to connect the up to 100 beads of a chain molecule. Rheological data (shear viscosity, normal pressure differences) are discussed and compared with quantities describing the chain conformation (e.g., alignment tensor, static structure factor). This renders possible a test of the theoretical approaches which connect these quantities. In agreement with recent experiments, the static strucure factor exhibits characteristic elliptical distortions of the polymer coil whose magnitude depends on the distance from the gyration center. In our simulations the zero‐shear‐rate viscosity is found to scale linearly with the number of beads N up to chains with N=60. A weak upturn of the viscosity per bead for N=100 is found which may indicate the onset of the reptation regime.

Rheology and structural changes of polymer melts via nonequilibrium molecular dynamics

The core structure of nematic defects cannot be represented by the usual director field, but requires the description by the full orial calculus.

Siegfried Hess

Papers

Rheological and small angle neutron scattering investigation of shear‐induced particle structures of concentrated polymer dispersions submitted to plane Poiseuille and Couette flowa)

Fokker-Planck-Equation Approach to Flow Alignment in Liquid Crystals

Rheological Evidence for a Dynamical Crossover in Polymer Melts via Nonequilibrium Molecular Dynamics

Rheology and structural changes of polymer melts via nonequilibrium molecular dynamics

Alignment tensor versus director: Description of defects in nematic liquid crystals.