Since 2000, I have been working on an outstanding issue in hydrodynamics --- the moving contact line in two-phase immiscible flows. This is one of these interesting physical problems whereby what happens at the molecular scale vicinity of the contact line (where the fluid-fluid interface intersects the wall) controls the macroscopic flow. Decades ago it was already known that the moving contact line is incompatible with the no-slip 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 fluid-wall 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 no-slip boundary condition with the moving contact line, but none was able to give a quantitative account of the MD slip velocity profile in the molecular-scale 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 convective-diffusive 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.
  1. Tiezheng Qian, Xiao-Ping Wang, and Ping Sheng, Molecular scale contact line hydrodynamics of immiscible flows, Phys. Rev. E 68, 016306 (2003). PDF

  2. Tiezheng Qian, Xiao-Ping Wang, and Ping Sheng, Power-Law Slip Profile of the Moving Contact Line in Two-Phase 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.

  3. Tiezheng Qian, Xiao-Ping 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)
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colloquium at Physics-CUHK
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


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 electric-field---induced 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).
  1. Tiezheng Qian and P. L. Taylor, Field-induced phase transitions in antiferroelectric liquid crystals, Phys. Rev. E 60, 2978 (1999).
    (cited for 13 times) download pdf


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 Ericksen-Leslie 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 Ericksen-Leslie theory, based on the Frank-Oseen 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 "Qian-Sheng Formalism"). Our generalized dynamical Landau-de Gennes theory has also been used to study the surface modes at the nematic-isotropic interface (see Phys. Rev. E 68, 061707 (2003) for the "Qian and Sheng generalized dynamical Landau-de Gennes theory"). For a review of the Qian-Sheng formalism, see Rep. Prog. Phys. 68, 2665 (2005).
  1. Tie-Zheng Qian, Zhi-Liang Xie, Hoi-Sing 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

  2. Tiezheng Qian and Ping Sheng, Generalized hydrodynamic equations for nematic liquid crystals, Phys. Rev. E 58, 7475 (1998).
    (cited for 15 times) download pdf


Since 1995, I have been interested in the area of liquid crystals (LC's). My first LC project is the LC-substrate interaction and surface-induced phase transition in nematics. Using Landau-de Gennes free energy functional, we studied the novel orientational states and phase transitions induced by micro-textured substrates, i.e., spatially mixed alignment potentials. Mean-field stable and metastable states were obtained by numerically minimizing the Landau-de Gennes free energy functional in a finite-difference scheme. We found that micro-texturing offers a systematic technique for varying the effective anchoring strength. Our theoretical calculation has been confirmed by a recent experimental report (A1-O8, Plenary session, 17th International Liquid Crystal Conference, Strasbourg 1998). These results have potential application in the manufacture of the twisted nematic (TN) and super-TN LC displays.
  1. Tie-Zheng Qian and Ping Sheng, Liquid Crystal Phase Transitions Induced by Microtextured Substrates, Phys. Rev. Lett. 77, 4564 (1996).
    (cited for 20 times) download pdf

  2. Tie-Zheng 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


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 one-dimensional systems), especially on the role of the spin degree of freedom. Simply put, we discussed the following problem. In the presence of spin-orbit 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 well-known Aharonov-Casher interference effect (Y. Aharonov and A. Casher, Phys. Rev. Lett. 53, 319 (1984)) and the Aharonov-Anandan phase in a spin cyclic evolution description. This work provides a spin geometric phase interpretation of the Aharonov-Casher 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 GPP-1: Geometric phases in physics, Am. J. Phys. 65, 180 (1997)). The effects of the spin-induced Zeeman coupling and spin-orbit interaction were also discussed in the contexts of persistent current and quantum transport.
  1. Tie-Zheng Qian and Zhao-Bin Su, Spin-Orbit Interaction and Aharonov-Anandan Phase in Mesoscopic Rings, Phys. Rev. Lett. 72, 2311 (1994).
    (cited for 35 times) download pdf

  2. Ya-Sha Yi, Tie-Zheng Qian, and Zhao-Bin Su, Spin precession and time-reversal symmetry breaking in quantum transport of electrons through mesoscopic rings, Phys. Rev. B 55, 10631 (1997).
    (cited for 16 times) download pdf


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 Aharonov-Anandan (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 time-dependent, 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 Lewis-Riesenfeld invariant formulation by introducing the basic invariants, which have proved useful in the study of quantum optical coherent states and squeezed states.
  1. Xiao-Chun Gao, Jing-Bo Xu, and Tie-Zheng Qian, The Exact Solution for the Generalized Time-Dependent Harmonic Oscillator and its Adiabatic Limit, Ann. Phys. (N.Y.) 204, 235 (1990).
    (cited for 38 times)

  2. Xiao-Chun Gao, Jing-Bo Xu, and Tie-Zheng Qian, Formally exact solution and geometric phase for the spin-j system, Phys. Lett. A 152, 449 (1991).
    (cited for 29 times)

  3. Xiao-Chun Gao, Jing-Bo Xu, and Tie-Zheng Qian, Geometric phase and the generalized invariant formulation, Phys. Rev. A 44, 7016 (1991).
    (cited for 41 times) download pdf