Steady laminar flow of fractal fluids

[1]  Frank H. Stillinger,et al.  Axiomatic basis for spaces with noninteger dimension , 1977 .

[2]  Kenneth Falconer,et al.  Fractal Geometry: Mathematical Foundations and Applications , 1990 .

[3]  R. Skalak,et al.  THE HISTORY OF POISEUILLE'S LAW , 1993 .

[4]  C. Tricot Curves and Fractal Dimension , 1994 .

[5]  A. Shiyan Viscosity for fractal suspensions: dependence on fractal dimensionality , 1996 .

[6]  A. Balankin Physics of fracture and mechanics of self-affine cracks , 1997 .

[7]  Umberto Mosco INVARIANT FIELD METRICS AND DYNAMICAL SCALINGS ON FRACTALS , 1997 .

[8]  B. Hills,et al.  NMR Q-space microscopy of concentrated oil-in-water emulsions. , 2000, Magnetic resonance imaging.

[9]  H. Shui,et al.  Viscosity and fractal dimension of coal soluble constituents in solution , 2004 .

[10]  Paul N. Stavrinou,et al.  Equations of motion in a non-integer-dimensional space , 2004 .

[11]  P. Snabre,et al.  Rheology and ultrasound scattering from aggregated red cell suspensions in shear flow. , 2004, Biophysical journal.

[12]  D. Montgomery Worlds of Flow: A history of hydrodynamics from the Bernoullis to Prandtl , 2005 .

[13]  V. E. Tarasov Fractional hydrodynamic equations for fractal media , 2005, physics/0602096.

[14]  W. Chen Time-space fabric underlying anomalous diffusion , 2005, math-ph/0505023.

[15]  O. Agrawal,et al.  A scaling method and its applications to problems in fractional dimensional space , 2009 .

[16]  M. Ostoja-Starzewski Continuum mechanics models of fractal porous media: Integral relations and extremum principles , 2009 .

[17]  Yu. A. Koksharov,et al.  Viscosity of liquid suspensions with fractal aggregates: Magnetic nanoparticles in petroleum colloidal structures , 2011 .

[18]  C. L. Martínez-González,et al.  Random walk in chemical space of Cantor dust as a paradigm of superdiffusion. , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

[19]  A. Balankin,et al.  Map of fluid flow in fractal porous medium into fractal continuum flow. , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

[20]  Q. Naqvi,et al.  Electromagnetic Fields and Waves in Fractional Dimensional Space , 2012 .

[21]  A. Balankin,et al.  Hydrodynamics of fractal continuum flow. , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

[22]  Alexander S. Balankin,et al.  Physics in space–time with scale-dependent metrics , 2013 .

[23]  H. Srivastava,et al.  Cantor-type cylindrical-coordinate method for differential equations with local fractional derivatives , 2013 .

[24]  A. Balankin,et al.  Electromagnetic fields in fractal continua , 2013 .

[25]  S. Arabia,et al.  Systems of Navier-Stokes equations on Cantor sets , 2013 .

[26]  Alexander S. Balankin,et al.  Stresses and strains in a deformable fractal medium and in its fractal continuum model , 2013 .

[27]  Xiangyun Hu,et al.  Generalized modeling of spontaneous imbibition based on Hagen-Poiseuille flow in tortuous capillaries with variably shaped apertures. , 2014, Langmuir : the ACS journal of surfaces and colloids.

[28]  Vasily E. Tarasov,et al.  Flow of fractal fluid in pipes: Non-integer dimensional space approach , 2014, 1503.02842.

[29]  A. Balankin Toward the mechanics of fractal materials: mechanics of continuum with fractal metric , 2014, 1409.5829.

[30]  H. Löwen,et al.  Classical Liquids in Fractal Dimension. , 2015, Physical review letters.

[31]  A. Balankin,et al.  Effective degrees of freedom of a random walk on a fractal. , 2015, Physical review. E, Statistical, nonlinear, and soft matter physics.

[32]  Xiao‐Jun Yang,et al.  Observing diffusion problems defined on cantor sets in different coordinate systems , 2015 .

[33]  Alexander S. Balankin,et al.  A continuum framework for mechanics of fractal materials I: from fractional space to continuum with fractal metric , 2015 .

[34]  M. J. Lazo,et al.  On a connection between a class of q-deformed algebras and the Hausdorff derivative in a medium with fractal metric , 2015, 1502.07606.

[35]  Xiangyun Hu,et al.  RECENT ADVANCES ON FRACTAL MODELING OF PERMEABILITY FOR FIBROUS POROUS MEDIA , 2015 .

[36]  Alexander S. Balankin,et al.  A continuum framework for mechanics of fractal materials II: elastic stress fields ahead of cracks in a fractal medium , 2015 .

[37]  M. Bazant Exact solutions and physical analogies for unidirectional flows , 2016, 1601.03203.

[38]  Spatiotemporal accessible solitons in fractional dimensions. , 2016, Physical review. E.

[39]  Jianchao Cai,et al.  Fractal analysis of the effect of particle aggregation distribution on thermal conductivity of nanofluids , 2016 .

[40]  Muhammad Sahimi,et al.  Flow and Transport in Porous Media and Fractured Rock - Toc , 2016 .

[41]  V. E. Tarasov Poiseuille equation for steady flow of fractal fluid , 2016 .

[42]  M. Shapiro,et al.  Towards a physics on fractals: Differential vector calculus in three-dimensional continuum with fractal metric , 2016 .

[43]  Jos'e Weberszpil,et al.  Variational approach and deformed derivatives , 2015, 1511.02835.

[44]  Lay Kee Ang,et al.  Coordinate System Invariant Formulation of Fractional‐Dimensional Child‐Langmuir Law for a Rough Cathode , 2016, Advanced Physics Research.

[45]  Alexander S. Balankin,et al.  Anomalous diffusion of fluid momentum and Darcy-like law for laminar flow in media with fractal porosity , 2016 .

[46]  Jianchao Cai,et al.  Recent developments on fractal-based approaches to nanofluids and nanoparticle aggregation , 2017 .