REPRESENTATIVE PUBLICATIONS
I. IMMISCIBLE TWOPHASE FLOW OF MOVING CONTACT LINES
Since 2000, I have been working on an outstanding issue in
hydrodynamics  the moving contact line in twophase
immiscible flows. This is one of these interesting physical
problems whereby what happens at the molecular scale vicinity
of the contact line (where the fluidfluid interface intersects
the wall) controls the macroscopic flow.
Decades ago it was already known that the moving contact line
is incompatible with the noslip boundary condition,
since the latter would imply infinite dissipation
(we would not be able to drink coffee if that were true!).
While subsequent molecular dynamics (MD) studies have clearly
demonstrated relative fluidwall slipping at the contact line,
the exact rule that governs this relative slip has eluded
numerous prior attempts. In fact, over the years there have
been numerous ad hoc models and proposals aiming to
resolve the incompatibility of the noslip boundary condition
with the moving contact line, but none was able to give
a quantitative account of the MD slip velocity profile
in the molecularscale vicinity of the contact line.
As a result, a breakdown of hydrodynamics in the vicinity of
the contact line was even suggested.
Perhaps the opening paragraph of a recent publication
(Phys. Rev. Lett. 87, 178302 (2001)) best summed up the situation:
``Hydrodynamic theories of flow past a solid surface need to
assume boundary conditions for the fluid velocities at the surface.
Such interfacial behavior is often very difficult to
access experimentally. Recent simulation studies of fluids have
revealed a range of boundary conditions for single component
fluids and related them to the microscopic interactions.
However, there are many problems where the appropriate
boundary conditions are still in doubt.
These include flow near a moving contact line,
the liquid crystal order parameter in the presence of flow,
and convectivediffusive flow of miscible fluids.''
After more than two years of detailed analysis and extensive
MD studies, we have for the first time uncovered
the boundary condition governing the moving contact line,
denoted the generalized Navier boundary condition
(GNBC). We have used this discovery to formulate a continuum
hydrodynamics whose predictions are in remarkable quantitative
agreement with the MD simulation results at the molecular level.
These results serve to affirm the validity of the GNBC,
as well as to open up the possibility of continuum hydrodynamic
calculations of immiscible flows that are physically meaningful
at the molecular level.

Tiezheng Qian, XiaoPing Wang, and Ping Sheng,
Molecular scale contact line hydrodynamics of immiscible flows,
Phys. Rev. E 68, 016306 (2003).
PDF

Tiezheng Qian, XiaoPing Wang, and Ping Sheng,
PowerLaw Slip Profile of the Moving Contact Line in TwoPhase
Immiscible Flows,
Phys. Rev. Lett. 93, 094501 (2004).
PDF
This article has been selected for the September 13, 2004 issue of
Virtual Journal of Nanoscale Science & Technology.

Tiezheng Qian, XiaoPing Wang, and Ping Sheng,
A variational approach to the moving contact line hydrodynamics,
J. Fluid Mech. 564, 333  360 (2006).
PDF
Distinguished Lecture presented at the 2004
Annual Conference of HKSTAM
(Hong Kong Society of Theoretical and Applied Mechanics) (March 2004)
An invited talk at the Workshop:
Effective Theories for Materials and Macromolecules,
Institute for Mathematics and its Applications, University of Minnesota
(June 2005)
download PPT file
download PPT file (short version)
colloquium at PhysicsCUHK
Talk at Princeton
PDF
PPT
Talk at SISSA (the International School for Advanced Studies, Trieste, Italy)
PDF
PPT
Talk at the Physics Department of Zhejiang University
PDF
PPT
II. FIELDINDUCED PHASE TRANSITIONS
IN ANTIFERROELECTRIC LIQUID CRYSTALS
In 1998, I joined the soft condensed matter group at
Case Western Reserve Univ. We worked on the smectic C*
antiferroelectric liquid crystals (AFLC's).
We predicted an electricfieldinduced Freedericksz transition
in surface stabilized AFLC. This phase transition
was then observed by an experimental group
(see
Phys. Rev. Lett. 84, 4140 (2000)),
and has been well accepted by the liquid crystal community
(see section IV.C "Frederiks transition" in
Phys. Rev. E 66, 061708 (2002)
by P. Rudquist, J. P. F. Lagerwall, J. G. Meier, et al.,
a famous liquid crystal research group at Chalmers Univ. of Technology, Sweden).

Tiezheng Qian and P. L. Taylor,
Fieldinduced phase transitions in antiferroelectric liquid crystals,
Phys. Rev. E 60, 2978 (1999).
(cited for 13 times)
download pdf
III. NEMATOHYDRODYNAMICS OF LIQUID CRYSTALS
From 1996 to 1997, in collaboration with an experimental group (Dept.
of EEE, HKUST), we investigated the switching bistability in
twisted nematic liquid crystal (TNLC) cells
based on the interaction between dynamic flow and director rotation.
This interaction arises from the coupling between the translational
and orientational degrees of freedom.
Numerical calculation predicted that there exists a general
type of bistable, twisted director configurations,
which was then verified experimentally.
The experimental data, however, showed a small but systematic
deviation from the numerical results obtained
from the classic EricksenLeslie hydrodynamic theory,
when the cell becomes sufficiently thin and
the applied electric field is very large.
This led to our generalization
of the nematohydrodynamic equations.
The generalized equations can be used to study the nematodynamics
where the intrinsic liquid crystal correlation length becomes
comparable to the externally controlled electric/magnetic
coherence length. The EricksenLeslie theory,
based on the FrankOseen elastic free energy, is no longer
applicable in that regime because the microscopic liquid crystal correlation
length becomes accessible by extreme spatial variations,
and therefore should be incorporated into a generalized continuum
description. Our generalized nematohydrodynamic equations
have been selected as the target macroscopic equations in a generalized
lattice Boltzmann algorithm for the flow of a nematic liquid crystal
with variable order parameter (see
Phys. Rev. E 67, 061703 (2003) for the "QianSheng Formalism").
Our generalized dynamical Landaude Gennes theory has also been used to study
the surface modes at the nematicisotropic interface (see
Phys. Rev. E 68, 061707 (2003) for the "Qian and Sheng
generalized dynamical Landaude Gennes theory"). For a review of the
QianSheng formalism, see
Rep. Prog. Phys. 68, 2665 (2005).

TieZheng Qian, ZhiLiang Xie, HoiSing Kwok, and Ping Sheng,
Dynamic flow and switching bistability in
twisted nematic liquid crystal cells,
Appl. Phys. Lett. 71, 596 (1997).
(cited for 18 times)
download pdf

Tiezheng Qian and Ping Sheng,
Generalized hydrodynamic equations for nematic liquid crystals,
Phys. Rev. E 58, 7475 (1998).
(cited for 15 times)
download pdf
IV. LIQUID CRYSTAL PHASE TRANSITIONS INDUCED BY
TEXTURED SUBSTRATES
Since 1995, I have been interested in the area of liquid crystals
(LC's). My first LC project is the LCsubstrate interaction
and surfaceinduced phase transition in nematics.
Using Landaude Gennes free energy functional, we studied the
novel orientational states and phase transitions induced
by microtextured substrates, i.e., spatially mixed alignment
potentials. Meanfield stable and metastable states were obtained
by numerically minimizing the Landaude Gennes free energy functional
in a finitedifference scheme.
We found that microtexturing offers a systematic technique
for varying the effective anchoring strength.
Our theoretical calculation has been confirmed
by a recent experimental report (A1O8, Plenary session,
17th International Liquid Crystal Conference, Strasbourg 1998).
These results have potential application in the manufacture of the
twisted nematic (TN) and superTN LC displays.

TieZheng Qian and Ping Sheng,
Liquid Crystal Phase Transitions Induced by Microtextured Substrates,
Phys. Rev. Lett. 77, 4564 (1996).
(cited for 20 times)
download pdf

TieZheng Qian and Ping Sheng,
Orientational states and phase transitions induced by
microtextured substrates,
Phys. Rev. E 55, 7111 (1997).
(cited for 15 times)
download pdf
V. SPINORBIT INTERACTION AND
QUANTUM INTERFERENCE EFFECTS IN MESOSCOPIC RINGS
From 1994 to 1997, with the help of the concept of geometric phase,
we published a series of papers on the quantum interference
phenomena in mesoscopic rings
(multiply connected onedimensional systems),
especially on the role of the spin degree of freedom.
Simply put, we discussed the following problem.
In the presence of spinorbit interaction,
if the spin degree of freedom is integrated out,
then what is the effect left on the orbital degree of freedom?
Using a geometric phase approach, we established
the connection between the wellknown AharonovCasher
interference effect (Y. Aharonov and A. Casher,
Phys. Rev. Lett. 53, 319 (1984)) and the AharonovAnandan phase
in a spin cyclic evolution description. This work provides
a spin geometric phase interpretation
of the AharonovCasher effect and has been generally
recognized in the mesoscopic physics circle.
In addition, because of its generality, this work has been cited in
a Resource Letter published in American Journal of Physics,
a journal for physics teaching
(J. Anandan, J. Christian, and K. Wanelik,
Resource letter GPP1: Geometric phases in physics,
Am. J. Phys. 65, 180 (1997)).
The effects of the spininduced Zeeman coupling and spinorbit
interaction were also discussed in the contexts of
persistent current and quantum transport.

TieZheng Qian and ZhaoBin Su,
SpinOrbit Interaction and AharonovAnandan Phase in Mesoscopic Rings,
Phys. Rev. Lett. 72, 2311 (1994).
(cited for 35 times)
download pdf

YaSha Yi, TieZheng Qian, and ZhaoBin Su,
Spin precession and timereversal symmetry breaking in quantum transport
of electrons through mesoscopic rings,
Phys. Rev. B 55, 10631 (1997).
(cited for 16 times)
download pdf
VI. QUANTUM GEOMETRIC PHASES
From 1989 to 1994, my research interest was focused on
the geometric phases in quantum evolutions,
including the Berry phase in adiabatic evolution and
the AharonovAnandan (AA) phase in nonadiabatic evolution.
Employing the quantum invariant theory
(H. R. Lewis and W. B. Riesenfeld,
J. Math. Phys. 10, 1458 (1969)),
we studied the geometric phases in several typical Hamiltonian
systems characterized by their dynamic Lie algebras
(the Hamiltonian is a timedependent, linear combination
of the generators of a particular Lie algebra).
We obtained the exact nonadiabatic geometric phases and derived
the corresponding Berry phases by taking the adiabatic limit.
We also generalized the LewisRiesenfeld invariant formulation by
introducing the basic invariants,
which have proved useful in the study of quantum optical coherent
states and squeezed states.

XiaoChun Gao, JingBo Xu, and TieZheng Qian,
The Exact Solution for the Generalized TimeDependent Harmonic
Oscillator and its Adiabatic Limit,
Ann. Phys. (N.Y.) 204, 235 (1990).
(cited for 38 times)

XiaoChun Gao, JingBo Xu, and TieZheng Qian,
Formally exact solution and geometric phase for the spinj system,
Phys. Lett. A 152, 449 (1991).
(cited for 29 times)

XiaoChun Gao, JingBo Xu, and TieZheng Qian,
Geometric phase and the generalized invariant formulation,
Phys. Rev. A 44, 7016 (1991).
(cited for 41 times)
download pdf