Advection–diffusion in a porous medium with fractal geometry: fractional transport and crossovers on time scales

Surface Diffusion of C1–C3 Alcohols on Multiwall Carbon Nanotubes

“…Therefore, at small times, the driving force of the mass release may be associated with the advective flow: (4) ∂ C ∂ t = − v ∙ ∂ C ∂ x , where v is the drift velocity (m/s). The solution of this equation admits linear evolution of the diffusing substance mass versus time [57]: (5) M t M 0 = 1 − v L ∙ t . …”

“…where v is the drift velocity (m/s). The solution of this equation admits linear evolution of the diffusing substance mass versus time [57]:…”

New prospects in non-conventional modelling of solids and structures

“…Concerning fractional calculus, the second group of articles deals with fractional models of complex phenomena in materials [5][6][7][8]. Mashayekhi et al [5] investigate the relaxation behaviour of fractal polymers and propose a generalized Scott-Blair fractional model of viscoelasticity, where the excluded volume effect and the hydrodynamic interaction are explicitly taken into account to derive the microscopic stress within the molecular theory of Rouse and Zimm.…”

“…The derivation unveils that the order of the fractional derivative in the linear fractional model of viscoelasticity is strongly correlated with fractal structure and excluded volume effects. Zhokh and Strizhak [6] deal with anomalous transport dynamics in porous fractal media due to crossover between different transport regimes. Taking as example methanol and methane transport through a zeolite/alumina porous particle, the authors investigate the mass transfer of the diffusing agents using as an analytical tool a one-dimensional time-fractional advection-diffusion equation.…”

Initial‐boundary value and interface problems on the real half line for the fractional advection–diffusion‐type equation

“…On the other hand, the ADE has been widely used in the modeling of physical phenomena where particles and energy are transferred due to the combination of two processes: diffusion and advection [32,33]. Given the interest in modeling complex phenomena, the anomalous diffusion may arise, so it can be studied through the fractional advection-diffusion-type equation (FADE) [34,35].…”