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Geometry-Weighted Decay, Screening, and Sector Placement in Catalytic Wedge-Pore Diffusio-Osmotic Circulation

Mohammad Yousuff Hussaini1, Maria Hussaini Baloch1
1Department of Mathematics, Florida State University, Tallahassee, USA

Abstract

Pores with catalytic wedge walls experience diffusio-osmotic slip due to wall reactions producing tangent gradients of solute concentration in the corner region. The goal of the work is to determine the dependence of several characteristics on opening angle, catalytic-sector radius, and wall reaction sign: maximum angular gain, slip screening length, residue of the first modal circulation due to signed forcing, and dominance of near versus far catalytic sectors. Calculations are carried out in terms of a low-Peclet number concentration field equation and a Stokes streamfunction boundary-value problem. Relevant quantities include wedge eigenvalues, finite sector moments, angular gain functions, signed modal weights, radial interaction factor, and derivatives at interval endpoints. For the given settings, the calculations indicate a dominating influence of the wedge opening angle on angular circulation, as widening the uniformly actuated wedge from π/4 to 3π/4 enhances the one-wall gain of streamfunction from 0.119 to 0.409 and the corresponding two-wall gain from 0.076 to 0.249. On the contrary, localization is associated with an opposite behavior. Thus, the flux-balanced right-angle wedge features a slip field decaying as (b*/ρ)3, which vanishes to 5% of the reference value at the distance 2.71b*. As concerns modal weight differences caused by sector positioning, even with the same physical lengths of coatings, the dominance of far sectors relative to near sectors amounts to factors 6.52 and 11.66 in two respective reflective wedges. Finally, neither equal nor opposite catalytic forces can compensate the first modal effect; rather, residual circulation ratios reach 0.734 and 0.842 in the above two cases, while complete compensation occurs at the relative force reductions of 0.153 and 0.086. The analysis of endpoint derivatives additionally indicates advantages in radial shifts of intervals over their elongation near the wedge vertex. Numerically, these observations directly respond to the formulated problem: circulation strength depends primarily on the opening angle, localization relies on decay exponent and flux balance, and leakage/cancellation is dictated by the first modal signed moment of the considered sectors.

Keywords: diffusio-osmosis, wedge flow, catalytic microfluidics, active pores, response matrix, low-Reynolds-number flow
Citation
Mohammad Yousuff Hussaini, Maria Hussaini Baloch. Geometry-Weighted Decay, Screening, and Sector Placement in Catalytic Wedge-Pore Diffusio-Osmotic Circulation[J], TK Techforum Journal (ThyssenKrupp Techforum), Volume 2026 (2). 54-74.

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