COMPARATIVE DIMENSIONLESS ANALYSIS OF STATIC AND FLOW REGIMES OF THERMALLY ACTIVATED SOL-GEL SILICA DEPOSITION IN PHOTOPOLYMER MICROCHANNELS

Abstract

To date, there has been no systematic dimensionless analysis unifying static and flow regimes in a single formulation. The aim of this work is to compare the regimes based on the analysis of dimensionless similarity criteria, to construct a regime map in the (Da_z, Pe_T) coordinates, and to determine the optimal sol flow-rate window. The method is an analytical dimensionless analysis of the conjugate heat and mass transfer problem and polycondensation of tetraethoxysilane (TEOS) in an axisymmetric microchannel of radius R = 250 μm and length L = 30 mm at wall temperature T_wall = 60 °C. It was found that in the static regime the Rayleigh number Ra ≈ 61 ≪ Rac = 1708 — natural convection is geometrically suppressed; the characteristic length of monomer diffusive depletion is L_dep ≈ 1.0 mm, concentrating more than 90% of the deposit mass in the first 5–7 mm of the channel. In the flow regime, the governing parameters are the axial Damköhler number Da_z and the thermal Péclet number Pe_T. The optimal flow-rate window Q ∈ [0.1; 2] μL/min ensures simultaneous fulfillment of Da_z < 1 and Pe_T < 1, i.e. uniform deposition along the channel and complete thermal activation of the reaction. The transition from static to flow regime fundamentally changes the limiting mechanism — from diffusive depletion to convective reagent renewal.