<p>Surfactants, typically soluble in the bulk phase, undergo adsorption–desorption processes at the interface, thereby modulating surface concentration and influencing droplet dynamics. While previous studies have largely demonstrated that surfactants tend to reduce droplet velocity, the role of surface chemical reactions has often been overlooked. This study examines the impact of surface chemical reactions on the dynamics of spherical droplets in cylindrical Poiseuille flow. The analysis considers a droplet in an ambient chemical concentration gradient that catalyses surface reactions without directly influencing surfactant transport over the interface. Using the solenoidal decomposition method, we analytically determine the droplet’s migration velocity through regular perturbation expansion in terms of a small surface Péclet number <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="33_2025_2543_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="41" /> </InlineMediaObject> <EquationSource Format="TEX">$(Pe_s)$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <mi>P</mi> <msub> <mi>e</mi> <mi>s</mi> </msub> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>. Results reveal that interfacial reactions influence the streamwise migration velocity at the first-order of <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="33_2025_2543_Article_IEq2.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="30" /> </InlineMediaObject> <EquationSource Format="TEX">$Pe_s$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>P</mi> <msub> <mi>e</mi> <mi>s</mi> </msub> </mrow> </math></EquationSource> </InlineEquation>, whereas cross-stream migration responds to the reaction only at the second-order. A trade-off between the Damköhler number (<i>Da</i>), representing reaction kinetics, and the surfactant-induced Marangoni number <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="33_2025_2543_Article_IEq3.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="49" /> </InlineMediaObject> <EquationSource Format="TEX">$(Ma_\Gamma )$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <mi>M</mi> <msub> <mi>a</mi> <mi mathvariant="normal">Γ</mi> </msub> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> is analysed, identifying optimal combinations <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="33_2025_2543_Article_IEq4.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="80" /> </InlineMediaObject> <EquationSource Format="TEX">$(Da, Ma_\Gamma )$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <mi>D</mi> <mi>a</mi> <mo>,</mo> <mi>M</mi> <msub> <mi>a</mi> <mi mathvariant="normal">Γ</mi> </msub> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> for migration velocity. These findings provide valuable insights into surfactant-laden droplet dynamics, with potential applications in microfluidics and lab-on-a-chip technologies.</p>

Impact of surface chemical reaction on droplet dynamics

期刊论文
发表日期：

2025年7月14日

查看全文

Arindam Basak,
Rajaram Lakkaraju,
G. P. Raja Sekhar

摘要

Surfactants, typically soluble in the bulk phase, undergo adsorption–desorption processes at the interface, thereby modulating surface concentration and influencing droplet dynamics. While previous studies have largely demonstrated that surfactants tend to reduce droplet velocity, the role of surface chemical reactions has often been overlooked. This study examines the impact of surface chemical reactions on the dynamics of spherical droplets in cylindrical Poiseuille flow. The analysis considers a droplet in an ambient chemical concentration gradient that catalyses surface reactions without directly influencing surfactant transport over the interface. Using the solenoidal decomposition method, we analytically determine the droplet’s migration velocity through regular perturbation expansion in terms of a small surface Péclet number $(Pe_s)$ $(P e_{s})$ . Results reveal that interfacial reactions influence the streamwise migration velocity at the first-order of $Pe_s$ $P e_{s}$ , whereas cross-stream migration responds to the reaction only at the second-order. A trade-off between the Damköhler number (Da), representing reaction kinetics, and the surfactant-induced Marangoni number $(Ma_\Gamma )$ $(M a_{Γ})$ is analysed, identifying optimal combinations $(Da, Ma_\Gamma )$ $(D a, M a_{Γ})$ for migration velocity. These findings provide valuable insights into surfactant-laden droplet dynamics, with potential applications in microfluidics and lab-on-a-chip technologies.