Dr. Uma Balakrishnan

Email: ubalakrishnan@engineering.ucsb.edu

Telephone: (805) 893 4942

CURRENT WORK

RESEARCH EXPERIENCE

TEACHING EXPERIENCE

Education

Indian Institute of TechnologyMadras, Chennai, India, Ph.D (2003)
Indian Institute of TechnologyMadras, Chennai, India, M.Sc Mathematics (1998)
University of Madras, Chennai, India, B.Sc Mathematics (1996)

Professional Appointments

University of California, Santa Barbara, California, USA, Research Fellow (2007-).
University of North Dakota, Grand Forks, USA, Research Assistant Professor, (Sep 2006 – Jan 2007)
College of Engineering Guindy, Anna University, India, Lecturer in Mathematics, (Feb 2005 – Aug 2006)
Indian Institute of Technology Madras, Department of Mathematics, India, Post Doctoral Researcher (Jan 2004 – Feb 2005)
Indian Institute of Technology Madras, Department of Chemical Engineering & Department of Physics, India, Research Associate (May 2003 – Aug 2003 & Sep 2003 – Dec 2003)
Indian Institute of Technology Madras, Department of Mathematics, India, Researcher (1999 – 2003)
Indian Institute of Technology Madras, Department of Mathematics, India, Project Associate (1998 – 1999)

Internships

Ecole Polytechnique Federale de Lausanne , Lausanne , Switzerland (Sep 2000 – Oct 2000)

Fellowships

Post Doctoral Fellowship, National Board of Higher Mathematics (NBHM) (2004)
Young Scientist Fellow, Department of Science and Technology (DST) (2004)
Young Scientist Fellow, Council of Scientific and Industrial Research (CSIR) (2002)
Research Fellow, Indian Institute of Technology Madras (IITM) (1999-2003)

Research Interests

Dynamics and stability of thin films down an inclined plane/vertical wall and on rotating disk;

Stagnation point flows; interfacial instabilities in parallel flows for viscoelastic fluids.

Current Work

Currently I am working on interfacial instability of pressure-driven, two-layer flows with one of the fluids being viscoelastic (like a polymeric solution or a polymer melt) by including finite extensibility in a complete way (as appropriate for the strong elongational flows), and by extending the parameter space considered in the literature. While from the complete model existing theory in literature find only a Yih mode, and while by matching viscosities find an elastic mode, we find the simultaneous existence of both modes. The parameter space for this occurrence is a subset of conditions from 1<De<5, 5<n<30, k>4.5, and viscoelastic layer thicknesses less than the Newtonian one (less viscous). In the above, n is the viscosity ratio (solution divided by the solvent) and k is the wave number. For Re>40, the elastic mode disappears, and the shear (T-S) becomes dominant mode. I have developed an executable source code AROS-VE (All Regime Orr-Sommerfeld for Viscoelastic Fluids) in FORTRAN with quadruple precision to discuss the stability of interface formed by two different viscoelastic fluids. This work has been collaborated with Prof.Theo.G.Theofanous and Dr.Svetlana Sushchikh. Also I am working on flow and stability characteristics of thin film systems down an inclined plane or vertical wall or on rotating disk. The studies include the investigation of stationary waves on effect of electric field and surfactant on the porous inclined plane, surface instabilities of heated falling films and dynamics of thin films on rotating disks. I have developed a MATLAB code for numerical schemes used to solve highly nonlinear partial differential equations which describe the evolution of waves on the free surface and to capture the bifurcation scenarios for nonlinear permanent waves.

Currently I am working on interfacial instability of pressure-driven, two-layer flows with one of the fluids being viscoelastic (like a polymeric solution or a polymer melt) by including finite extensibility in a complete way (as appropriate for the strong elongational flows), and by extending the parameter space considered in the literature. While from the complete model existing theory in literature find only a Yih mode, and while by matching viscosities find an elastic mode, we find the simultaneous existence of both modes. The parameter space for this occurrence is a subset of conditions from 1<De<5, 5<n<30, k>4.5, and viscoelastic layer thicknesses less than the Newtonian one (less viscous). In the above, n is the viscosity ratio (solution divided by the solvent) and k is the wave number. For Re>40, the elastic mode disappears, and the shear (T-S) becomes dominant mode. I have developed an executable source code AROS-VE (All Regime Orr-Sommerfeld for Viscoelastic Fluids) in FORTRAN with quadruple precision to discuss the stability of interface formed by two different viscoelastic fluids. This work has been collaborated with Prof.Theo.G.Theofanous and Dr.Svetlana Sushchikh.

Also I am working on flow and stability characteristics of thin film systems down an inclined plane or vertical wall or on rotating disk. The studies include the investigation of stationary waves on effect of electric field and surfactant on the porous inclined plane, surface instabilities of heated falling films and dynamics of thin films on rotating disks. I have developed a MATLAB code for numerical schemes used to solve highly nonlinear partial differential equations which describe the evolution of waves on the free surface and to capture the bifurcation scenarios for nonlinear permanent waves.

Selected Recent Publications

1. B.Uma and R.Usha, A Thin Conducting Liquid Film on a Spinning Disk in the Presence of a
Magnetic Field: Dynamics and Stability, (2008) Trans. ASME Journal of Applied Mechanics, (in press).

2. B.Uma and R.Usha, A Thin Conducting Viscous Film on an Inclined Plane in the Presence
of a Uniform Normal Electric Field: Bifurcation Scenarios, (2008) Physics Fluids, 20, 032102.

3. B.Uma and R.Usha, Weakly Nonlinear Stability Analysis of Counter-current Gas-Liquid Film
Down an Inclined Plane, (2008) Nonlinear Dynamics, 52, 115-128.

4. B.Uma and R.Usha, Dynamics of a Thin Viscoelastic Film on an Inclined Plane, (2006)
Int. J. Engg. Sci., 44, 1449-1481.

5. R.Usha, R.Ravindran and B.Uma, Dynamics and stability of a thin liquid film on a heated
rotating disk film with variable viscosity, (2005) Physics of Fluids, 17, 102103.

6. R.Usha, R.Ravindran and B.Uma, Dynamics of thin film with temperature-dependent
viscosity on a rotating disk, (2005) Acta Mechanica, 179, 25-39.

7. R.Usha, R.Ravindran and B.Uma, Numerical study of a thin liquid film on a disk under
nonuniform rotation-Thermocapillary effects, (2005) Fluid Dynamics Research, 37, 154-172.

8. R.Usha and B.Uma, Modeling of Stationary Waves on a Thin Viscous Film Down an Inclined
Plane at High Reynolds Numbers and Moderate Weber Numbers Using Energy Integral
Approach, (2004) Physics of Fluids, 16, 2679-2696.

9. B.Uma and R.Usha, Interfacial Phase Change Effects on the Stability Characteristics of
Thin Viscoelastic Liquid Film Down a Vertical Wall, (2004) Int. J. Engg. Sci., 42, 1381 - 1406.

10. R.Usha and B.Uma, Long Waves on a Viscoelastic Film Flow down a Wavy Incline, (2004)
Int. J. Non-linear Mech., 39, 1589-1602.

11. R.Usha and B.Uma, Weakly Nonlinear Stability Analysis of Condensate / Evaporating
Power-law Liquid Film Down an Inclined Plane, (2003) Trans. ASME Journal of Applied
Mechanics, 70, 915-923.

12. R.Usha and B.Uma, The Role of Induced Air Shear on the Development of a Conducting
Fluid Film Over a Rough Spinning Disk in the Presence of a Transverse Magnetic Field,
(2002) ZAMM, 82, 211-216.

13. R.Usha and B.Uma, Flow of a Thin Liquid Film over a Rough Rotating Disk in the Presence of
Transverse Magnetic Field, (2001) ZAMP, 52, 793-809.