Taylor-Aris dispersion for N-zone and continuous systems with variable sorption strength – extending Aris’s approach

Nonadditivity and Nonlinearity of Mobile and Stationary Zone Mass Transfer Resistances in Chromatography

“…To model the H C m curves (Figure ), we initially assumed the dependencies on k ″ and ν are separated ( H C m / d = f ( k ″)· g (ν)) because all known analytical solutions for H C m (e.g., eqs and ) are of this form. Furthermore, since the dependency on k ″ of these solutions is always quadratic, − a good candidate expression appeared to be H C normalm / d = c 1 + c 2 k ″ + c 3 k false″ 2 ( 1 + k ″ ) 2 ν f ( ν ) where f (ν) is a slowly increasing function accounting for the downward curvature of H C m . To date, the latter was always attributed to the enhancing effect of the velocity field on the local mass transfer (cf.…”

“…Comparing the C m terms in eqs and readily reveals a crucial shortcoming of the former: the k ″ dependency of eq and all other known plate height expressions in chromatography contains a polynomial c 1 + c 2 k ″ + c 3 k ″ 2 , − whereas eq only contains the k ″ 2 term, although there is no physical reason for the absence of the other terms in particulate media.…”

Microfluidic Validation of the Diffusional Bridging Effect Suppressing Dispersion in Multicapillary Flow Systems

“…Using an extended version of the classic Taylor–Aris theory, − an analytical expression could be derived for the plate height H in a binary capillary system with DB H = H 1 + H σ H 1 = 2 D mol u 0 + 1 210 10.72 + 35.47 k ″ + 26.49 k false″ 2 false( 1 + k ″ false) 2 u 0 d normalm 2 D normalm + 1 6 k false″ 2 false( 1 + k false″ false) 2 u 0 d normals 2 D normals H σ = σ 2 1…”

“…Using an extended version of the classic Taylor–Aris theory, − an analytical expression could be derived for the plate height H in a binary capillary system with DB wherein H 1 represents the dispersion in a single capillary and H σ represents the excess plate height created by the polydispersity effect under DB conditions. k ″ is the so-called zone-retention factor (time spent in porous walls versus time spent in the flowing zone), d m is the characteristic size (=hydrodynamic diameter) of the flow-through channels (m), D m is the diffusion coefficient in the mobile phase (m 2 /s), d s is the thickness of the stationary phase separating the flow-through channels (m), D s is the diffusion coefficient in the stationary phase (m 2 /s), and σ is the relative standard deviation of the flow-through channels.…”

Exact analytical expressions for the band broadening in polydisperse 2-D multi-capillary columns with diffusional bridging

“…The present study on the other hand aims at rigorously deriving a complete analytical expression describing the MCCDB band broadening directly from the general multi-dimensional advection-diffusion equation, known to describe the MCCDB problem with 100% accuracy. This is done using a recently developed and validated extension to the Aris method [24]. To retain a maximal physical insight during our first excursions into this problem, as well as to keep the numerical computation times affordable, the study is limited to a simplified 2D geometry.…”