Microgel Translocation Through Narrow Capillaries

Abstract

The transport of soft viscoelastic gels through confined geometries underlies critical processes in biomedical, biological, and industrial systems. Here, we examine the translocation of a spherical microgel through a narrow capillary whose diameter is smaller than the equilibrium gel size. Using coarse-grained molecular dynamics simulations in tandem with mean-field theory and mechanical analysis, we uncover a critical threshold diameter $d_c$ below which the microgel cannot enter, regardless of the applied pressure. This geometric limit emerges from the interplay between gel elasticity and its internal network connectivity, captured quantitatively by a graph-theoretic model. We construct a phase diagram in the parameter space of tube diameter $d$, applied force $f_g$, and gel stiffness $Y$ (Young's modulus), which delineates the regimes of successful translocation and mechanical arrest. Under negligible wall friction, gel mobility scales with the applied force; however, beyond a cutoff set by the network topology, progressive densification in the constriction stalls the microgel. Our results reveal the mechanical and topological determinants of soft-gel transport in confinement and provide predictive guidelines for engineering gel-based systems in microfluidics, drug delivery, and tissue-level filtration.

Figures (13)

• Figure 1: Schematic of the corrugated tube geometry used in the simulations. The tube consists of a hollow cylinder of diameter $D>2R_{\mathrm{gel}}$ ( a), where $R_{\mathrm{gel}}$ is the undeformed microgel radius, followed by a conical frustum ( b) connecting to a constricted cylindrical segment of diameter $d<2R_{\mathrm{gel}}<D$ ( c). A mirror-symmetric conical frustum and wide cylinder are attached downstream ( d and e), with the terminal wide cylinders ( a and e) connected via periodic boundary conditions. Solvent flow is from left to right. The lower panel illustrates representative microgel conformations along the tube. An initially undeformed microgel resides in the wide section ( a) and encounters an entropic barrier at the constriction entrance ( b). Upon entry, the gel undergoes biaxial confinement and adopts an elongated cylindrical shape ( c). Downstream of the constriction, the gel expands upon release from confinement ( d) and subsequently forms a discoid shape due to solvent jetting from the narrow capillary ( e). Within the constricted region, network strands predominantly align with the tube axis.
• Figure 2: Translocation of a crosslinked polymer microgel (green beads) through a corrugated channel in a good solvent with explicit solvent particles. The channel consists of two cylindrical segments of diameters $D = 60\sigma$ and $d = 20\sigma$ connected by a tapered segment. A constant force $f_s = 0.05\,k_B T/\sigma$ is applied to each solvent particle along the channel axis (left to right). The color scale from blue to red denotes increasing solvent velocity. Panel (a) shows the unperturbed microgel prior to forcing, while panels (b)--(i) illustrate successive stages of gel translocation through the corrugated channel under solvent-driven flow.
• Figure 3: Schematic illustration of an ideal flexible Bethe branched chain entering a cylindrical tube of diameter $d$. (a) Network strands (green) connected by fixed nodes (magenta) of functionality $f$. (b) Under confinement, strands reorient and align parallel to the tube axis. (c) Blob representation of a dendron chain inside a narrow capillary, where the blob size $\zeta_i$ decreases with generation index while satisfying $\sigma < \zeta_i < d$. (d) Simulation snapshot of an $n=6$ dendron stalled at the tube entrance, consistent with the cutoff condition derived in SI Eq. 15. (e) Schematic of the topological characterization of a numerically synthesized gel network. The peak of the parallel connectivity distribution provides an effective measure of the number of load-bearing subchains in the $n^{\mathrm{th}}$ generation, which is used to estimate the critical translocation diameter shown in (f). (g) Phase diagram showing the maximum generation of an infinite dendron that can enter a tube of diameter $d_c$, as determined from SI Eq. 15. The boundary follows $\ln d_c = n_0 + \alpha n$.
• Figure 4: Mean shortest-path distribution of the gel networks, $P(s)$, and the mean parallel connectivity distribution, $P(c_{||})$, resolved at each generation as a function of path length for different gels (a–d). The monomer density distribution along the tube axis, $\rho(x)$, and the number of load-bearing subchains per axial bin obtained from MD simulations, $P(c_{||})_{\mathrm{MD}}$, are measured while the gel resides inside a narrow capillary with radius slightly above the critical cutoff diameter. A direct correspondence is observed between the intrinsic parallel connectivity $P(c_{||})$ and the axial subchain count from simulations, $P(c_{||})_{\mathrm{MD}}$, demonstrating that network topology dictates the effective strand organization under confinement. This agreement confirms that the gel is able to translocate through the constriction. The elasticity $Y$ and the number of network nodes $\mu$ are systematically varied from (a) to (d) to test the robustness of this correspondence across gels of differing mechanical and topological properties.
• Figure 5: Phase diagram of the successful gel translocation for different radii $d/2$ of the constricted capillaries with force on gel $f_g$ for different Young's moduli, $Y$, of gels. Data are shown on a logarithmic scale to highlight scaling behavior (see SI Fig. 12 for the 3D phase diagram). The solid boundary separates the mobile and mechanically arrested regimes and follows the power-law relation $f_g \propto d^{-7/2 \pm 0.2}$ over the accessible range of parameters.