This special issue is dedicated to Professor Jason M. Reese, who died suddenly at the early age of 51 on 8 March 2019. Professor Reese was an internationally renowned Engineering Scientist, respected academic, and a valued mentor to many. At the time of his death, he was Regius Professor of Engineering at the University of Edinburgh. His research has delivered a new understanding of unusual behavior of gases and liquids at ultra-small length-scales, which is helping engineers to develop a diverse range of technologies, including ultra-efficient water filtration systems using carbon nanotubes, nano-structured surface coatings for drag reduction in ships, spacecraft hypersonic reentry systems, and lab-on-a-chip devices. He also made contributions through a spin-off company, government advisory roles, and the support of the Learned Societies, for which he was a Fellow. Therefore, the University of Edinburgh created the Jason Reese Chair in honor of his academic leadership and scientific achievements.

Owing to emerging micro/nano-electromechanical systems (MEMS/NEMS) and lab-on-a-chip devices, the knowledge of fluid flow and heat transfer at ultra-small length-scales has significantly advanced during the last decade. Heat and flow at the micro- and nano-scales exhibit peculiarities different from the intuition of macroscopic continuum fluid dynamics. For example, micro/nano gas flows at the ambient pressure can be rarefied and experience velocity slip and temperature jump at the flow boundaries.

In this special issue, readers can find contributions made by leading researchers in the fields of micro- and nano-fluid mechanics, applied and theoretical mathematics, and rarefied gas dynamics, covering a broad range of topics, including theoretical, numerical, and experimental studies. Advancement in extending the applicability of continuum-based Navier–Stokes–Fourier equations toward a non-equilibrium state through improved boundary conditions and constitutive relations is reported in Ref. 1. Gas flows induced by temperature gradients along the walls2–4 or even by uniform but different temperatures on the opposite walls5 are other features of rarefied micro- and nano-scale flows that are also considered in this special issue. Nanofluids6 and flow in microchannels7 and nanotubes8 are reported together with investigation of discontinuities in rarefied gas flows such as shock waves and their affiliated phenomenon.9–11 Flow in the porous media exhibits unique features at the pore scale different from the macroscopic flow domain, which should be treated with the tools appropriate for micro/nano scale flows.12–15 Classical problems of viscous fluid flow such as Couette flow exhibit peculiarities at the micro/nano scales.16,17 The experimental study of gas mixture and binary mixture separation in capillary tubes18 and the analytical study of fluid flow in the free molecular regime19,20 are also included.

In this special issue, researchers also report on the derivation of the transport coefficients of multicomponent mixtures of the noble gases,21,22 studies of the Mpemba effect,23 the rotational–translational relaxation process of diatomic molecules,24 the multi-temperature vibrational energy relaxation rates in CO2,25 the solid boundary's influence on the propagation of thermodynamic disturbances,26 flows through micro/nano-nozzles,27 the derivation of thermal slip coefficients,28 and the plume expansion.29 The other topics are analysis of breakdown criteria for the hybrid solvers,30 non-equilibrium effects with the membrane boundaries,31 development of the unified gas-kinetic wave-particle solver,32 study of the planar gas expansion under pulsed evaporation,33 the molecular dynamics study on energy accommodation coefficient,34 use of the moment method to model the Boltzmann equation,35 development of the rotational relaxation model for nitrogen,36 Langmuir evaporation of polyatomic liquids,37 and extension of the discrete unified gas kinetic scheme for incompressible flow.38 

The editors would like to take this opportunity to thank all the authors who have contributed to this specific issue.

1.
R.
Groll
,
S.
Kunze
, and
B.
Besser
, “
Correction of second-order slip condition for higher Knudsen numbers by approximation of free-molecular diffusion
,”
Phys. Fluids
32
(
9
),
092008
(
2020
).
2.
P.
Wang
,
W.
Su
, and
L.
Wu
, “
Thermal transpiration in molecular gas
,”
Phys. Fluids
32
(
8
),
082005
(
2020
).
3.
H.
Yamaguchi
and
G.
Kikugawa
, “
Molecular dynamics study on flow structure inside a thermal transpiration flow field
,”
Phys. Fluids
33
(
1
),
012005
(
2021
).
4.
J.
Zhang
,
S.
Yao
,
F.
Fei
,
M.
Ghalambaz
, and
D.
Wen
, “
Competition of natural convection and thermal creep in a square enclosure
,”
Phys. Fluids
32
(
10
),
102001
(
2020
).
5.
S.
Rafieenasab
,
E.
Roohi
, and
A.
Teymourtash
, “
Numerical analysis of nonlinear thermal stress flow between concentric elliptical cylinders
,”
Phys. Fluids
32
(
10
),
102007
(
2020
).
6.
Z. H.
Khan
,
W. A.
Khan
,
M.
Hamid
, and
H.
Liu
, “
Finite element analysis of hybrid nanofluid flow and heat transfer in a split lid-driven square cavity with Y-shaped obstacle
,”
Phys. Fluids
32
(
9
),
093609
(
2020
).
7.
F. D.
Bosco
and
Y.
Zhang
, “
Variance-reduction kinetic simulation of low-speed rarefied gas flow through long microchannels of annular cross sections
,”
Phys. Fluids
32
(
8
),
082002
(
2020
).
8.
M.
Rezaee
,
M.
Namvarpour
,
A.
Yeganegi
, and
H.
Ghassemi
, “
Comprehensive study of monatomic fluid flow through elliptical carbon nanotubes
,”
Phys. Fluids
32
(
9
),
092006
(
2020
).
9.
A.
Frezzotti
and
P.
Barbante
, “
Simulation of shock induced vapor condensation flows in the Lennard-Jones fluid by microscopic and continuum models
,”
Phys. Fluids
32
(
12
),
122106
(
2020
).
10.
S.
Singh
, “
Role of Atwood number on flow morphology of a planar shock-accelerated square bubble: A numerical study
,”
Phys. Fluids
32
(
12
),
126112
(
2020
).
11.
A.
Shoja-Sani
,
E.
Roohi
, and
S.
Stefanov
, “
Homogeneous relaxation and shock wave problems: Assessment of the simplified and generalized Bernoulli trial collision schemes
,”
Phys. Fluids
33
(
3
),
032004
(
2021
).
12.
S.
Takata
,
K.
Hatakenaka
,
M.
Hattori
, and
F.
Kasahara
, “
Modeling of gas transport in porous medium: Stochastic simulation of the Knudsen gas and a kinetic model with homogeneous scatterer
,”
Phys. Fluids
32
(
10
),
102004
(
2020
).
13.
L.
Germanou
,
M. T.
Ho
,
Y.
Zhang
, and
L.
Wu
, “
Shale gas permeability upscaling from the pore-scale
,”
Phys. Fluids
32
(
10
),
102012
(
2020
).
14.
A.
Phan
,
D.
Fan
, and
A.
Striolo
, “
Fluid transport through heterogeneous pore matrices: Multiscale simulation approaches
,”
Phys. Fluids
32
(
10
),
101301
(
2020
).
15.
Q.
Sheng
,
L.
Gibelli
,
J.
Li
,
M. K.
Borg
, and
Y.
Zhang
, “
Dense gas flow simulations in ultra-tight confinement
,”
Phys. Fluids
32
(
9
),
092003
(
2020
).
16.
J.
Ou
and
J.
Chen
, “
Nonlinear transport of rarefied Couette flows from low speed to high speed
,”
Phys. Fluids
32
(
11
),
112021
(
2020
).
17.
R.
Gómez González
and
V.
Garzó
, “
Non-Newtonian rheology in inertial suspensions of inelastic rough hard spheres under simple shear flow
,”
Phys. Fluids
32
(
7
),
073315
(
2020
).
18.
R.
Gao
,
S.
O'Byrne
,
F.
Sharipov
, and
J. L.
Liow
, “
Experimental investigation of the separation of binary gaseous mixtures flowing through a capillary tube
,”
Phys. Fluids
32
(
11
),
112008
(
2020
).
19.
S.
Cai
,
C.
Cai
, and
J.
Li
, “
Highly dilute gas flows over an ellipse
,”
Phys. Fluids
32
(
9
),
097104
(
2020
).
20.
S.
Cai
,
C.
Cai
, and
J.
Li
, “
Highly dilute gas flows through a non-isothermal planar microchannel
,”
Phys. Fluids
32
(
7
),
072006
(
2020
).
21.
F.
Sharipov
and
V. J.
Benites
, “
Transport coefficients of multicomponent mixtures of noble gases based on ab initio potentials: Viscosity and thermal conductivity
,”
Phys. Fluids
32
(
7
),
077104
(
2020
).
22.
F.
Sharipov
and
V. J.
Benites
, “
Transport coefficients of multicomponent mixtures of noble gases based on ab initio potentials: Diffusion coefficients and thermal diffusion factors
,”
Phys. Fluids
32
(
9
),
097110
(
2020
).
23.
A.
Santos
and
A.
Prados
, “
Mpemba effect in molecular gases under nonlinear drag
,”
Phys. Fluids
32
(
7
),
072010
(
2020
).
24.
V.
Kosyanchuk
and
A.
Yakunchikov
, “
A detailed multiscale study of rotational–translational relaxation process of diatomic molecules
,”
Phys. Fluids
33
(
2
),
022003
(
2021
).
25.
E.
Kustova
and
M.
Mekhonoshina
, “
Multi-temperature vibrational energy relaxation rates in CO2
,”
Phys. Fluids
32
(
9
),
096101
(
2020
).
26.
Y.
Ben-Ami
and
A.
Manela
, “
The effect of a solid boundary on the propagation of thermodynamic disturbances in a rarefied gas
,”
Phys. Fluids
32
(
9
),
092002
(
2020
).
27.
M.
Pfeiffer
, “
A particle-based ellipsoidal statistical Bhatnagar–Gross–Krook solver with variable weights for the simulation of large density gradients in micro- and nano-nozzles
,”
Phys. Fluids
32
(
11
),
112009
(
2020
).
28.
N. N.
Nguyen
,
I.
Graur
,
P.
Perrier
, and
S.
Lorenzani
, “
Variational derivation of thermal slip coefficients on the basis of the Boltzmann equation for hard-sphere molecules and Cercignani–Lampis boundary conditions: Comparison with experimental results
,”
Phys. Fluids
32
(
10
),
102011
(
2020
).
29.
V. A.
Petrov
,
O. A.
Ranjbar
,
P. A.
Zhilyaev
, and
A. N.
Volkov
, “
Kinetic simulations of laser-induced plume expansion from a copper target into a vacuum or argon background gas based on ab initio calculation of Cu–Cu, Ar–Ar, and Ar–Cu interactions
,”
Phys. Fluids
32
(
10
),
102010
(
2020
).
30.
O.
Ilyin
, “
Relative entropy based breakdown criteria for hybrid discrete velocity Bhatnagar–Gross–Krook and lattice Boltzmann method
,”
Phys. Fluids
32
(
11
),
112006
(
2020
).
31.
V. V.
Aristov
,
I. V.
Voronich
, and
S. A.
Zabelok
, “
Non-equilibrium nonclassical phenomena in regions with membrane boundaries
,”
Phys. Fluids
33
(
1
),
012009
(
2021
).
32.
Y.
Chen
,
Y.
Zhu
, and
K.
Xu
, “
A three-dimensional unified gas-kinetic wave-particle solver for flow computation in all regimes
,”
Phys. Fluids
32
(
9
),
096108
(
2020
).
33.
A. A.
Morozov
,
A. A.
Frolova
, and
V. A.
Titarev
, “
On different kinetic approaches for computing planar gas expansion under pulsed evaporation into vacuum
,”
Phys. Fluids
32
(
11
),
112005
(
2020
).
34.
A.
Tokunaga
and
T.
Tsuruta
, “
Non-equilibrium molecular dynamics study on energy accommodation coefficient on condensing liquid surface—Molecular boundary conditions for heat and mass transfer
,”
Phys. Fluids
32
(
11
),
112011
(
2020
).
35.
J.
Koellermeier
and
U.
Scholz
, “
Spline moment models for the one-dimensional Boltzmann–Bhatnagar–Gross–Krook equation
,”
Phys. Fluids
32
(
10
),
102009
(
2020
).
36.
A.
Yakunchikov
,
V.
Kosyanchuk
, and
A.
Iuldasheva
, “
Rotational relaxation model for nitrogen and its application in free jet expansion problem
,”
Phys. Fluids
32
(
10
),
102006
(
2020
).
37.
S.
Busuioc
and
L.
Gibelli
, “
Mean-field kinetic theory approach to Langmuir evaporation of polyatomic liquids
,”
Phys. Fluids
32
(
9
),
093314
(
2020
).
38.
M.
Zhong
,
S.
Zou
,
D.
Pan
,
C.
Zhuo
, and
C.
Zhong
, “
A simplified discrete unified gas kinetic scheme for incompressible flow
,”
Phys. Fluids
32
(
9
),
093601
(
2020
).