Effect of core hydrophobicity on the electrophoresis of pH-regulated soft particles

Soft Matter ◽  
2021 ◽  
Vol 17 (11) ◽  
pp. 3074-3084
Author(s):  
Bharti ◽  
Partha P. Gopmandal ◽  
R. K. Sinha ◽  
H. Ohshima
Keyword(s):  
Inner Core ◽  
Theoretical Study ◽  
Slip Length ◽  
Hydrodynamic Slip ◽  
Soft Particles

We propose a theoretical study on the electrophoresis of pH-regualted soft particles considering the effect of hydrodynamic slip length of the hydrophobic inner core.

Electrophoresis of soft particles with hydrophobic inner core grafted with pH‐regulated and highly charged polyelectrolyte layer

2021 ◽  
Author(s):  
Saurabh Kumar Maurya ◽  
Sankar Sarkar ◽  
Hemanta Kumar Mondal ◽  
H. Ohshima ◽  
Partha P. Gopmandal
Keyword(s):  
Inner Core ◽  
Polyelectrolyte Layer ◽  
Soft Particles

scholarly journals Nusselt numbers for Poiseuille flow over isoflux parallel ridges accounting for meniscus curvature

2016 ◽  
Vol 811 ◽  
pp. 315-349 ◽  
Author(s):  
Toby L. Kirk ◽  
Marc Hodes ◽  
Demetrios T. Papageorgiou
Keyword(s):  
Nusselt Number ◽  
Poiseuille Flow ◽  
Numerical Solutions ◽  
Surface Deformation ◽  
Slip Length ◽  
Constant Heat Flux ◽  
Flux Boundary Condition ◽  
Nusselt Numbers ◽  
Dual Series Equations ◽  
Hydrodynamic Slip

We investigate forced convection in a parallel-plate-geometry microchannel with superhydrophobic walls consisting of a periodic array of ridges aligned parallel to the direction of a Poiseuille flow. In the dewetted (Cassie) state, the liquid contacts the channel walls only at the tips of the ridges, where we apply a constant-heat-flux boundary condition. The subsequent hydrodynamic and thermal problems within the liquid are then analysed accounting for curvature of the liquid–gas interface (meniscus) using boundary perturbation, assuming a small deflection from flat. The effects of this surface deformation on both the effective hydrodynamic slip length and the Nusselt number are computed analytically in the form of eigenfunction expansions, reducing the problem to a set of dual series equations for the expansion coefficients which must, in general, be solved numerically. The Nusselt number quantifies the convective heat transfer, the results for which are completely captured in a single figure, presented as a function of channel geometry at each order in the perturbation. Asymptotic solutions for channel heights large compared with the ridge period are compared with numerical solutions of the dual series equations. The asymptotic slip length expressions are shown to consist of only two terms, with all other terms exponentially small. As a result, these expressions are accurate even for heights as low as half the ridge period, and hence are useful for engineering applications.

Electroosmotic Flow Through a Circular Tube With Slip-Stick Striped Wall

2012 ◽  
Vol 134 (11) ◽  
Author(s):  
Henry C. W. Chu ◽  
Chiu-On Ng
Keyword(s):  
Electroosmotic Flow ◽  
Circular Tube ◽  
Plane Surface ◽  
Slip Length ◽  
Point Collocation ◽  
Hydrodynamic Slip ◽  
Poisson Boltzmann ◽  
Flow Enhancement ◽  
Circular Surface ◽  
Poisson Boltzmann Equation

This is an analytical study on electrohydrodynamic flows through a circular tube, of which the wall is micropatterned with a periodic array of longitudinal or transverse slip-stick stripes. One unit of the wall pattern comprises two stripes, one slipping and the other nonslipping, and each with a distinct ζ potential. Using the methods of eigenfunction expansion and point collocation, the electric potential and velocity fields are determined by solving the linearized Poisson–Boltzmann equation and the Stokes equation subject to the mixed electrohydrodynamic boundary conditions. The effective equations for the fluid and current fluxes are deduced as functions of the slipping area fraction of the wall, the intrinsic hydrodynamic slip length, the Debye parameter, and the ζ potentials. The theoretical limits for some particular wall patterns, which are available in the literature only for plane channels, are extended in this paper to the case of a circular channel. We confirm that some remarks made earlier for electroosmotic flow over a plane surface are also applicable to the present problem involving patterns on a circular surface. We pay particular attention to the effects of the pattern pitch on the flow in both the longitudinal and transverse configurations. When the wall is uniformly charged, the adverse effect on the electroosmotic flow enhancement due to a small fraction of area being covered by no-slip slots can be amplified if the pitch decreases. Reducing the pitch will also lead to a greater deviation from the Helmholtz–Smoluchowski limit when the slipping regions are uncharged. With oppositely charged slipping regions, local recirculation or a net reversed flow is possible, even when the wall is on the average electropositive or neutral. The flow morphology is found to be subject to the combined influence of the geometry of the tube and the electrohydrodynamic properties of the wall.

Analytic Expression for Electrophoretic Mobility of Soft Particles with a Hydrophobic Inner Core at Different Electrostatic Conditions

Langmuir ◽  
2020 ◽  
Vol 36 (12) ◽  
pp. 3201-3211 ◽  
Author(s):  
Bharti ◽  
Partha P. Gopmandal ◽  
Somnath Bhattacharyya ◽  
Hiroyuki Ohshima
Keyword(s):  
Electrophoretic Mobility ◽  
Inner Core ◽  
Soft Particles ◽  
Analytic Expression

Effective Temperature Jump Length and Influence of Axial Conduction for Thermal Transport Through Channels With Superhydrophobic Walls

2013 ◽  
Author(s):  
A. Cowley ◽  
D. Maynes ◽  
J. Crockett ◽  
B. W. Webb
Keyword(s):  
Thermal Transport ◽  
Peclet Number ◽  
Temperature Jump ◽  
Slip Length ◽  
Relative Size ◽  
Axial Conduction ◽  
Péclet Number ◽  
Jump Length ◽  
Wide Range ◽  
Hydrodynamic Slip

This paper presents a numerical investigation of thermal transport in a parallel-plate channel comprised of superhydrophobic walls. The scenario analyzed in this paper is laminar, fully developed, steady flow with constant properties. The superhydrophobic walls considered here have alternating micro-ribs and cavities aligned perpendicular to the flow direction. The cavities are assumed to be non-wetting and contain air. The thermal transport through the ribs is considered to have a constant heat flux while the thermal transport through the air/fluid interface over the cavity is considered to be negligible. Numerical results have been obtained over a range a Peclet numbers, cavity fractions, and relative rib/cavity widths. Results were also obtained where axial conduction was neglected and these results are compared to previous analytical work with excellent agreement. When the influence of axial conduction is not neglected, however, the results for local wall temperatures and Nusselt numbers show departure from the previous analytical results. The departure is more pronounced at low Peclet numbers and at large relative channel diameters. This paper provides a comparison over a wide range of parameters that characterize the overall influence of axial conduction. In general, the results show that the relative size of the cavity compared to the total rib/cavity module width (cavity fraction) and the flow Peclet number have a significant impact on the total thermal transport properties. Also, the rib/cavity module width compared to the hydraulic diameter affects the overall thermal transport behavior. Lastly, this paper explores the concept of a temperature jump length which is analogous to the hydrodynamic slip length. The ratio of temperature jump length to hydrodynamic slip length is presented in terms of cavity fraction, Peclet number, and relative size of the rib cavity module.

Isoflux Nusselt Number and Slip Length Formulae for Superhydrophobic Microchannels

2013 ◽  
Vol 136 (1) ◽  
Author(s):  
Ryan Enright ◽  
Marc Hodes ◽  
Todd Salamon ◽  
Yuri Muzychka
Keyword(s):  
Nusselt Number ◽  
Thermal Transport ◽  
Stokes Equations ◽  
Slip Length ◽  
Thermal Slip ◽  
Structured Surfaces ◽  
Transport Behavior ◽  
Hydrodynamic Slip ◽  
Flow Through ◽  
Plate Channel

We analytically and numerically consider the hydrodynamic and thermal transport behavior of fully developed laminar flow through a superhydrophobic (SH) parallel-plate channel. Hydrodynamic slip length, thermal slip length and heat flux are prescribed at each surface. We first develop a general expression for the Nusselt number valid for asymmetric velocity profiles. Next, we demonstrate that, in the limit of Stokes flow near the surface and an adiabatic and shear-free liquid–gas interface, both thermal and hydrodynamic slip lengths can be found by redefining existing solutions for conduction spreading resistances. Expressions for the thermal slip length for pillar and ridge surface topographies are determined. Comparison of fundamental half-space solutions for the Laplace and Stokes equations facilitate the development of expressions for hydrodynamic slip length over pillar-structured surfaces based on existing solutions for the conduction spreading resistance from an isothermal source. Numerical validation is performed and an analysis of the idealized thermal transport behavior suggests conditions under which superhydrophobic microchannels may enhance heat transfer.

Fully-Developed Thermal Transport in Microchannels With Streamwise Grooved Superhydrophobic Walls at Constant Heat Flux

2012 ◽  
Author(s):  
D. Maynes ◽  
J. Vanderhoff ◽  
G. Rosengarten
Keyword(s):  
Heat Flux ◽  
Nusselt Number ◽  
Thermal Transport ◽  
Average Nusselt Number ◽  
Temperature Jump ◽  
Slip Length ◽  
Relative Size ◽  
Constant Heat Flux ◽  
Constant Heat ◽  
Hydrodynamic Slip

This paper presents an analytical investigation of constant property, steady, fully-developed, laminar thermal transport in a parallel-plate channel comprised of metal superhydrophobic walls. The superhydrophobic walls considered here exhibit micro-ribs and cavities aligned in the streamwise direction. The cavities are assumed to be non-wetting and contain air, such that the Cassie-Baxter state is the interfacial state considered. The scenario considered is that of constant heat flux through the rib surfaces with negligible thermal transport through the air cavity interface. Closed form solutions for the local Nusselt number and local wall temperature are presented and are in the form of infinite series expansions. The analysis show the relative size of the cavity regions compared to the total rib and cavity width (cavity fraction) exercises significant influence on the aggregate thermal transport behavior. Further, the relative size of the rib and cavity module width compared to the channel hydraulic diameter (relative module width) also influences the Nusselt number. The spatially varying Nusselt number and wall temperature are presented as a function of the cavity fraction and the relative module width over the ranges 0–0.99 and 0.01–1.0, respectively. From these results the rib/cavity module averaged Nusselt number was determined as a function of the governing parameters. The results reveal that increases in either the cavity fraction or relative module width lead to decreases in the average Nusselt number and results are presented over a wide range of conditions from which the average Nusselt number can be determined for heat transfer analysis. Further, analogous to the hydrodynamic slip length, a temperature jump length describing the apparent temperature jump at the wall is determined in terms of the cavity fraction. Remarkably, it is nearly identical to the hydrodynamic slip length for the scenario considered here and allows straightforward determination of the average Nusselt number for any cavity fraction and relative rib/cavity module width.

scholarly journals Perturbation analysis of subphase gas and meniscus curvature effects for longitudinal flows over superhydrophobic surfaces

2017 ◽  
Vol 822 ◽  
pp. 307-326 ◽  
Author(s):  
Darren G. Crowdy
Keyword(s):  
Slip Length ◽  
Working Fluid ◽  
Integral Expression ◽  
First Order ◽  
Curvature Effects ◽  
Effective Slip Length ◽  
Hydrodynamic Slip ◽  
Effective Slip ◽  
First Order Correction ◽  
Math Phys

Integral expressions for the first-order correction to the effective slip length for longitudinal flows over a unidirectional superhydrophobic surface with rectangular grooves are determined under the assumptions that the meniscus curvature is small and the viscosity contrast between the groove-trapped subphase gas and the working fluid is significant. Both pressure-driven channel flows and semi-infinite shear flows are considered. Reciprocity ideas, based on use of Green’s second identity, provide the integral expressions with integrands dependent on known flat-meniscus solutions found by Philip (Z. Angew. Math. Phys., vol. 23, 1972, pp. 353–372). The results extend earlier work by Sbragaglia & Prosperetti (Phys. Fluids, vol. 19, 2007, 043603) on how weak meniscus curvature affects hydrodynamic slip. In particular, we derive a new integral expression for the first-order slip length correction due to weak meniscus curvature.

Hydrodynamic slip length as a surface property

2016 ◽  
Vol 93 (2) ◽  
Author(s):  
Bladimir Ramos-Alvarado ◽  
Satish Kumar ◽  
G. P. Peterson
Keyword(s):  
Surface Property ◽  
Slip Length ◽  
Hydrodynamic Slip
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