Solute Delivery Through a Porous‐Walled Microtube With Sinusoidal Roughness by Electroosmotic Pumping

This study investigates the delivery of a neutral solute through a porous-walled microtube with sinusoidal roughness under mixed electroosmotic flow pumping, using an external direct current electric field. The effects of various operating conditions, geometries, and properties of the wall, solute, and solvent are investigated. The novelty of this work lies in exploring the impact of sinusoidal roughness on the solute mass flux delivery. It is found that a higher relative roughness amplitude (𝛿 = 0.1) and roughness wavenumber (𝜆 = 12) decrease the average cross-sectional velocity by up to 31% by judiciously tuning the parameters for better solute delivery. The effects of roughness parameters (𝛿, 𝜆), tube length ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics><mml:mrow><mml:mi>L</mml:mi> <mml:mo>)</mml:mo></mml:mrow> <mml:annotation>$L)$</mml:annotation></mml:semantics> </mml:math> , mean tube diameter ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics> <mml:mrow><mml:msub><mml:mi>d</mml:mi> <mml:mi>m</mml:mi></mml:msub> <mml:mrow><mml:mo>)</mml:mo> <mml:mo>,</mml:mo></mml:mrow> </mml:mrow> <mml:annotation>${d_m}), $</mml:annotation></mml:semantics> </mml:math> pump flow rate <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics><mml:mrow><mml:mo>(</mml:mo> <mml:msub><mml:mi>Q</mml:mi> <mml:mi>p</mml:mi></mml:msub> <mml:mo>)</mml:mo> <mml:mo>,</mml:mo></mml:mrow> <mml:annotation>$({Q_p}),$</mml:annotation></mml:semantics> </mml:math> electric field strength ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics> <mml:mrow><mml:msub><mml:mi>E</mml:mi> <mml:mi>z</mml:mi></mml:msub> <mml:mrow><mml:mo>)</mml:mo> <mml:mo>,</mml:mo></mml:mrow> </mml:mrow> <mml:annotation>${E_z}), $</mml:annotation></mml:semantics> </mml:math> wall permeability ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics> <mml:mrow><mml:msub><mml:mi>L</mml:mi> <mml:mi>p</mml:mi></mml:msub> <mml:mrow><mml:mo>)</mml:mo></mml:mrow> </mml:mrow> <mml:annotation>${L_p})$</mml:annotation></mml:semantics> </mml:math> , trans-wall pressure drop ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics><mml:mrow><mml:mi>Δ</mml:mi> <mml:msub><mml:mi>P</mml:mi> <mml:mi>w</mml:mi></mml:msub> </mml:mrow> <mml:annotation>$\Delta {P_w}$</mml:annotation></mml:semantics> </mml:math> ), real retention ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics> <mml:mrow><mml:msub><mml:mi>R</mml:mi> <mml:mi>r</mml:mi></mml:msub> <mml:mrow><mml:mo>)</mml:mo></mml:mrow> </mml:mrow> <mml:annotation>${R_r})$</mml:annotation></mml:semantics> </mml:math> , solute diffusivity <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics><mml:mrow><mml:mo>(</mml:mo> <mml:mi>D</mml:mi> <mml:mo>)</mml:mo></mml:mrow> <mml:annotation>$( D )$</mml:annotation></mml:semantics> </mml:math> , and osmotic pressure coefficient <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics><mml:mrow><mml:mo>(</mml:mo> <mml:msub><mml:mi>α</mml:mi> <mml:mrow><mml:mn>1</mml:mn> <mml:mspace></mml:mspace></mml:mrow> </mml:msub> <mml:mo>)</mml:mo></mml:mrow> <mml:annotation>$({\alpha _{1\;}})$</mml:annotation></mml:semantics> </mml:math> on the solute permeation mass flux are quantified. Among these parameters, the effect of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics><mml:mrow><mml:mi>Δ</mml:mi> <mml:msub><mml:mi>P</mml:mi> <mml:mi>w</mml:mi></mml:msub> </mml:mrow> <mml:annotation>$\Delta {P_w}$</mml:annotation></mml:semantics> </mml:math> is the most dominant in increasing the solute permeation flux of the rough-walled microtube, compared to the smooth wall. For example, by changing <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics><mml:mrow><mml:mi>Δ</mml:mi> <mml:msub><mml:mi>P</mml:mi> <mml:mi>w</mml:mi></mml:msub> </mml:mrow> <mml:annotation>$\Delta {P_w}$</mml:annotation></mml:semantics> </mml:math> from 5 to 20 kPa, the enhancement is about 16% in assisting flow and 19% in opposing flow. It is anticipated that the results of this study will provide valuable design perspectives for customized drug delivery systems using microfluidic channels, as well as enhance the understanding of nutrient transport in biological systems.