Transport and eruption of mantle xenoliths creates a lagging problem

Crustal and mantle xenoliths are fragments of foreign rock incorporated into magmas and are widely used to infer the composition, structure, and thermal state of the crust and mantle lithosphere. Mantle xenoliths, in particular, provide key constraints on mantle composition and on magma ascent rates because they often remain chemically out of equilibrium with their host melts during transport. Prior work commonly assumes that to transport xenoliths, magma must ascend faster than xenoliths settle, but this still implies continuous settling of dense mantle cargo relative to low-viscosity, alkaline magmas. The authors hypothesize that such differential motion creates a significant lag time between the eruption of the sampling magma and the subsequent arrival of its entrained xenoliths at the surface. They aim to quantify this lag using settling calculations and to explore implications for xenolith distribution, sampling bias of the mantle lithosphere, and constraints on eruption durations and volumes, with particular emphasis on kimberlites and diamond transport.

The study builds on extensive literature documenting xenolith use in reconstructing crustal and mantle properties and constraining magma ascent rates. Prior approaches include thermal/chemical disequilibrium indicators, laboratory reaction and diffusion experiments (e.g., H in olivine, Ar in phlogopite), and simple settling constraints based on Stokes law. Earlier models proposed that a magma yield strength (Bingham rheology) due to high crystal contents could couple xenoliths to ascending magma. However, field observations frequently show low crystallinity in xenolith-bearing alkaline magmas, and there is no consistent correlation between crystal content and xenolith abundance. The authors revisit these ideas using yield number theory and recent rheology results showing that appreciable yield stresses require particle volume fractions near maximum packing, conditions unlikely during rapid ascent of hot, low-viscosity, xenolith-rich magmas.

The authors compute xenolith terminal settling velocities using Stokes law as a lower bound: V_T = (2 g Δρ r^2) / (9 η), where Δρ is the xenolith–magma density contrast, r is xenolith radius, and η is magma viscosity. They assess the validity range with the particle Reynolds number Re_p = V_T ρ_m d / η and define a critical viscosity η_c satisfying Re_p ~ 1, leading to a corresponding critical settling velocity. Coupling by yield stress is assessed with the Yield number Y = 3 τ_y / (g d (ρ_x − ρ_m)); motion ceases if Y > 0.145. Yield stress τ_y is related to crystal fraction via τ_y = τ*[(1 − (1 − φ/φ_m)^(-2)) − 1], with τ* reflecting particle size/shape. Using cautious τ* values (0.01–1 Pa) and realistic φ, they show small yield strengths and continued settling for xenoliths even <10 cm unless φ approaches ~0.8. The key transport metric is the lag time between magma and xenolith arrival. They express lag as a kinematic relation independent of Stokes assumptions: Δt = X (1/V_m − 1/V_x) with V_x = V_m + V_T (sign convention: V_T negative for settling), showing lag increases with depth, xenolith size, and lower magma ascent rate. They also derive D_m = (V_m V_x / (V_m + V_T)) X_s / V_m as a proxy for the minimum magma column needed to bring xenoliths to the surface. Calculations employ representative alkaline/kimberlite magma properties (ρ_m ~ 2700–3000 kg m−3, η ~ 1–100 Pa s), xenolith densities ~3250 kg m−3, and sizes from 5 to >30 cm, implemented in MATLAB. An example parameter set is summarized (e.g., d = 25 cm; V_m = 4 m s−1; depths 50–160 km), and sensitivity to V_m and V_T is explored.

• Mantle xenoliths are generally decoupled from their host low-viscosity magmas and settle continuously during ascent; realistic yield stresses at observed crystallinities are insufficient to halt settling for common xenolith sizes. • Lag times of hours are expected between eruption onset and xenolith arrival. Example: a 25 cm xenolith sampled at 50 km with V_m ≈ 4 m s−1 and V_T ≈ −2 m s−1 arrives ~3 h after the sampling magma; at 80 km depth, lag is ~5 h. • Lag scales strongly with xenolith size and inversely with magma ascent rate. For X = 80 km and V_m = 4 m s−1: d ≤ 10 cm yields lag <1 h; d ~ 25 cm yields lag ~5 h; d ~ 30 cm yields lag >10 h. Xenoliths larger than ~36.5 cm have settling velocities exceeding 4 m s−1 and are unlikely to reach the surface under those conditions. • As V_m approaches |V_T|, lag times approach infinity; increasing V_m substantially reduces lag (e.g., for V_T = −2 m s−1 at X = 80 km, lag decreases from ~7 h to ~2 h as V_m increases from 4 to 6 m s−1). • The magma that ultimately erupts a xenolith commonly postdates the sampling magma (inheritance), implying a petrological/geochemical decoupling between erupted magma and xenolith cargo and setting a minimum magma volume required for delivery. • Extended residence (lagging) fosters mechanical abrasion, rounding, production of fine chips susceptible to assimilation, and partial thermal/chemical re-equilibration of susceptible lithologies; ablation-driven assimilation further modifies cargo. • Vesiculation during ascent can decrease bulk density and viscosity and promote separated two-phase flow, enhancing decoupling and stratification (gas-rich head, bubble-rich middle, xenolith-rich tail), yielding heterogeneous xenolith distributions across eruptive phases. • Kimberlite application: For V_m ≈ 4 m s−1, a 25 cm xenolith sampled at 160 km has lag ~7 h and total transit ~18 h. Minimum erupted volume at xenolith arrival is ~100 × 10^6 m^3, and cumulative magma passing through the diamond window exceeds 250 × 10^6 m^3 by that time. Short-duration, low-volume eruptions (e.g., Igwisi Hills ~3.5 × 10^6 m^3) lack large, deep xenoliths and diamonds, whereas larger pipes (10^7–10^8 m^3) more commonly are diamondiferous.

The calculations demonstrate that continuous settling of dense mantle xenoliths relative to low-viscosity magmas naturally produces a lag time between the eruption of sampling magma and subsequent xenolith arrival. This addresses the research question by showing that xenolith–magma decoupling is expected under realistic ascent conditions, without invoking large yield stresses, and that lag magnitude depends systematically on xenolith size, sampling depth, and ascent rate. The results explain qualitative field observations of uneven or late xenolith occurrence within deposits and predict stratigraphic heterogeneity and clustering of xenolith assemblages representing discrete sampling events. They imply that geothermobarometric inferences from a single deposit may be biased by which eruptive phase is sampled and that erupted magma composition can be decoupled from xenolith provenance. For kimberlites, the framework links diamond preservation and grade to eruption duration and volume: only sufficiently long-lived, voluminous eruptions can deliver large, deep xenoliths from within the diamond stability field. The model also highlights how vesiculation and evolving magma properties can further increase decoupling and enhance heterogeneity in xenolith distributions.

Mantle xenoliths in low-viscosity magmas are not generally coupled to the melt; instead, they settle throughout ascent, creating significant lag times that can span hours. This lag provides a unifying explanation for heterogeneous and phase-dependent xenolith distributions, petrological decoupling between magma and cargo, and modification of xenoliths during transport. The framework offers quantitative constraints on the minimum eruption duration and magma volume required to erupt xenoliths from given depths, with direct implications for diamondiferous kimberlites: large, long-duration eruptions are needed to deliver deep, large xenoliths and diamonds to the surface. Future work should integrate more detailed, depth-dependent rheology and vesiculation, transient ascent dynamics, particle-shape effects, and quantitative field datasets of xenolith size and stratigraphic distributions to refine lag predictions and sampling biases.

Settling velocities are estimated using Stokes law and spherical particles, while many regimes exceed Re_p ≈ 1; thus, V_T values represent idealized or lower-bound estimates. Magma properties (viscosity, density, crystallinity, vesicularity) are treated as simple averages or constants along the ascent path, whereas natural systems evolve strongly with depth, decompression, and degassing. Yield-stress assessments rely on parameterized relationships and assumed particle fractions near maximum packing that may vary with crystal size/shape distributions. Quantitative field data on xenolith abundance, size distributions, and stratigraphic positions are limited, constraining validation. The model is primarily 1D and does not include complex conduit geometry, turbulent effects, or detailed two-phase flow, which could alter coupling and lag.