Breakup of liquids by high velocity flow and size distribution of chondrules

As a new approach to understanding the chondrule formation process, we carried out aerodynamic experiments in which a liquid layer was attached to solid cores, and the breakup of this layer occurred by means of the interaction with a high-velocity gas flow. The size distribution of the dispersed droplets was investigated and compared with the size distributions of chondrules. Both distributions had an exponential form. Using the experimental results, the hydrodynamic pressure to produce the chondrule size distributions was estimated to be ∼ 10⁴ Pa.     

Shock-wave heating model for chondrule formation: Hydrodynamic simulation of molten droplets exposed to gas flows

Millimeter-sized, spherical silicate grains abundant in chondritic meteorites, which are called as chondrules, are considered to be a strong evidence of the melting event of the dust particles in the protoplanetary disk. One of the most plausible scenarios is that the chondrule precursor dust particles are heated and melt in the high-velocity gas flow (shock-wave heating model). We developed the non-linear, time-dependent, and three-dimensional hydrodynamic simulation code for analyzing the dynamics of molten droplets exposed to the gas flow. We confirmed that our simulation results showed a good agreement in a linear regime with the linear solution analytically derived by Sekyia et al. [Sekyia, M., Uesugi, M., Nakamoto, T., 2003. Prog. Theor. Phys. 109, 717-728]. We found that the non-linear terms in the hydrodynamical equations neglected by Sekiya et al. [Sekiya, M., Uesugi, M., Nakamoto, T., 2003. Prog. Theor. Phys. 109, 717-728] can cause the cavitation by producing negative pressure in the droplets. We discussed that the fragmentation through the cavitation is a new mechanism to determine the upper limit of chondrule sizes. We also succeeded to reproduce the fragmentation of droplets when the gas ram pressure is stronger than the effect of the surface tension. Finally, we compared the deformation of droplets in the shock-wave heating with the measured data of chondrules and suggested the importance of other effects to deform droplets, for example, the rotation of droplets. We believe that our new code is a very powerful tool to investigate the hydrodynamics of molten droplets in the framework of the shock-wave heating model and has many potentials to be applied to various problems.     

Maximal size of chondrules in shock wave heating model: Stripping of liquid surface in a hypersonic rarefied gas flow

Abstract— We examined partially molten dust particles that have a solid core and a surrounding liquid mantle, and estimated the maximal size of chondrules in a framework of the shock wave heating model for chondrule formation. First, we examined the dynamics of the liquid mantle by analytically solving the hydrodynamics equations for a core‐mantle structure via a linear approximation. We obtained the deformation, internal flow, pressure distribution in the liquid mantle, and the force acting on the solid core. Using these results, we estimated conditions in which liquid mantle is stripped off from the solid core. We found that when the particle radius is larger than about 1–2 mm, the stripping is expected to take place before the entire dust particle melts. So chondrules larger than about 1–2 mm are not likely to be formed by the shock wave heating mechanism. Also, we found that the stripping of the liquid mantle is more likely to occur than the fission of totally molten particles. Therefore, the maximal size of chondrules may be determined by the stripping of the liquid mantle from the partially molten dust particles in the shock waves. This maximal size is consistent with the sizes of natural chondrules.     

Macrochondrules in chondrites—Formation by melting of mega‐sized dust aggregates and/or by rapid collisions at high temperatures?

Abstract– Seventy‐four macrochondrules with sizes >3 mm were studied. Considering the extraordinary size of the chondrules (occasionally achieving a mass of 1000 times (and more) the mass of a normal‐sized chondrule), the conditions in the formation process must have been somewhat different compared with the conditions for the formation of the common chondrules. Macrochondrules are typically rich in olivine and texturally similar to specific chondrule types (barred, radial, porphyritic, and cryptocrystalline) of normal‐sized chondrules. However, our studies show that most of the macrochondrules are fine‐grained or have elongated crystals (mostly BO, RP, and C), which lead to the assumption that they were once totally molten and cooled quite rapidly. Porphyritic chondrules belong to the least abundant types of macrochondrules. This distribution of chondrule types is highly unusual and just a reverse of the distribution of chondrule types among the typical‐sized chondrules in most chondrite groups except for the CH and CB chondrites. New chondrule subtypes (like radial‐olivine [RO] or multi‐radial [MR] chondrules) are defined to better describe the textures of certain large chondrules. Macrochondrules may have formed due to melting of huge precursor dust aggregates or due to rapid collisions of superheated melt droplets, which led to the growth of large molten spherules in regions with high dust densities and high electrostatic attraction.     

Motion of iron sulfide inclusions inside a shock‐melted chondrule

Abstract— We calculated the trajectories of molten spheres of iron sulfide inclusions inside a melted chondrule during the nebular shock wave heating. Our calculations included the effects of high‐velocity internal flow in the melted chondrule and apparent gravitational force caused by the drag force of nebular gas flow. The calculated results show that large iron sulfide inclusions, which have radii 0.23 times larger than those of the parent chondrules, must reach the surface of the melted chondrule within a short period of time (<<1 s). This effect will provide us with very important information about chondrule formation by nebular shock wave heating.     

A Shock-Wave Heating Model for Chondrule Formation: Effects of Evaporation and Gas Flows on Silicate Particles

A shock-wave heating model is one of the possible models for chondrule formation. We examine, within the framework of a shock-wave heating model, the effects of evaporation on the heating of chondrule precursor particles and the stability of their molten state in the postshock flow. We numerically simulate the heating process in the flow taking into account evaporation. We find that the melting criterion and the minimum radius criterion do not change significantly. However, if the latent heat cooling due to the evaporation dominates the radiative cooling from the precursor particle, the peak temperature of the precursor particle is suppressed by a few hundred Kelvins. We also find that the total gas pressure (ram plus static) acting on the precursor particle exceeds the vapor pressure of the molten precursor particle. Therefore, it is possible to form chondrules in the shock-wave heating model if the precursor temperature increases up to the melting point.     

Magnetite-sulfide chondrules and nodules in CK carbonaceous chondrites: Implications for the timing of CK oxidation

Abstract— CK carbonaceous chondrites contain rare (～0.1 vol%) magnetite-sulfide chondrules. These objects range from ～240 to 500 μm in apparent diameter and have ellipsoidal to spheroidal morphologies, granular textures and concentric layering. They are very similar in size, shape, texture, mineralogy and mineral composition to the magnetite-sulfide nodules which occur inside mafic silicate chondrules in CK chondrites. It seems likely that the magnetite-sulfide chondrules constitute the subset of magnetite-sulfide nodules that escaped as immiscible droplets from their molten silicate chondrule hosts during chondrule formation. The intactness of the magnetite-sulfide chondrules and nodules implies that oxidation of CK metal occurred before agglomeration; otherwise, the factor of two increase in molar volume associated with the conversion of metallic Fe-Ni into magnetite would have disrupted the objects and destroyed their concentrically layered textures. Hence, the pervasive silicate darkening of CK chondrites documented previously was caused by the shock mobilization of magnetite and sulfide, not metallic Fe-Ni and sulfide as in shock-darkened ordinary chondrites.     

The origin of chondrules and chondrites: Debris from low‐velocity impacts between molten planetesimals?

Abstract– We investigate the hypothesis that many chondrules are frozen droplets of spray from impact plumes launched when thin‐shelled, largely molten planetesimals collided at low speed during accretion. This scenario, here dubbed “splashing,” stems from evidence that such planetesimals, intensely heated by ²⁶Al, were abundant in the protoplanetary disk when chondrules were being formed approximately 2 Myr after calcium‐aluminum‐rich inclusions (CAIs), and that chondrites, far from sampling the earliest planetesimals, are made from material that accreted later, when ²⁶Al could no longer induce melting. We show how “splashing” is reconcilable with many features of chondrules, including their ages, chemistry, peak temperatures, abundances, sizes, cooling rates, indented shapes, “relict” grains, igneous rims, and metal blebs, and is also reconcilable with features that challenge the conventional view that chondrules are flash‐melted dust‐clumps, particularly the high concentrations of Na and FeO in chondrules, but also including chondrule diversity, large phenocrysts, macrochondrules, scarcity of dust‐clumps, and heating. We speculate that type I (FeO‐poor) chondrules come from planetesimals that accreted early in the reduced, partially condensed, hot inner nebula, and that type II (FeO‐rich) chondrules come from planetesimals that accreted in a later, or more distal, cool nebular setting where incorporation of water‐ice with high Δ¹⁷O aided oxidation during heating. We propose that multiple collisions and repeated re‐accretion of chondrules and other debris within restricted annular zones gave each chondrite group its distinctive properties, and led to so‐called “complementarity” and metal depletion in chondrites. We suggest that differentiated meteorites are numerically rare compared with chondrites because their initially plentiful molten parent bodies were mostly destroyed during chondrule formation.     

Origin of three-dimensional shapes of chondrules: I. Hydrodynamics simulations of rotating droplet exposed to high-velocity rarefied gas flow

The origin of three-dimensional shapes of chondrules is an important information to identify their formation mechanism in the early solar nebula. The measurement of their shapes by using X-ray computed topography suggested that they are usually close to perfect spheres, however, some of them have rugby-ball-like (prolate) shapes [Tsuchiyama, A., Shigeyoshi, R., Kawabata, T., Nakano, T., Uesugi, K., Shirono, S., 2003. Lunar Planet. Sci. 34, 1271-1272]. We considered that the prolate shapes reflect the deformations of chondrule precursor dust particles when they are heated and melted in the high velocity gas flow. In order to reveal the origin of chondrule shapes, we carried out the three-dimensional hydrodynamics simulations of a rotating molten chondrule exposed to the gas flow in the framework of the shock-wave heating model for chondrule formation. We adopted the gas ram pressure acting on the chondrule surface of in a typical shock wave. Considering that the chondrule precursor dust particle has an irregular shape before melting, the ram pressure causes a net torque to rotate the particle. The estimated angular velocity is for the precursor radius of r₀=1 mm, though it has a different value depending on the irregularity of the shape. In addition, the rotation axis is likely to be perpendicular to the direction of the gas flow. Our calculations showed that the rotating molten chondrule elongates along the rotation axis, in contrast, shrinks perpendicularly to it. It is a prolate shape. The reason why the molten chondrule is deformed to a prolate shape was clearly discussed. Our study gives a complementary constraint for chondrule formation mechanisms, comparing with conventional chemical analyses and dynamic crystallization experiments that have mainly constrained the thermal evolutions of chondrules.     

Shapes of chondrules determined from the petrofabric of the CR2 chondrite NWA 801

The approximately spherical shapes of chondrules has long been attributed to surface tension acting on ~1 mm melt droplets that formed and cooled in the microgravity field of the solar nebula. However, chondrule shapes commonly depart significantly from spherical. In this study, 109 chondrules in a sample of CR2 chondrite NWA 801 were imaged by X-ray computed tomography and best-fitted to ellipsoids. The analysis confirms that many chondrules are indeed not spherical, and also that the chondrules’ collective shape fabric records a definite 13% compaction in the host meteorite. Dehydration of phyllosilicates within chondrules may account for that strain. However, retro-deforming all chondrules shows that a large majority were already far from spherical prior to accretion. Possible models for these initial shapes include prior deformation of individual chondrules in earlier hosts, and, as suggested by previous authors, rotation of chondrules as they were solidifying, and/or “streaming” of molten chondrules by their differential velocities with their gaseous hosts after melting. More in situ 3-D work such as this study on a variety of unequilibrated chondrites, combined with detailed structural petrography, should help further constrain these models and refine our understanding of chondrite formation.     

Size-frequency distributions of chondrules in CO3 chondrites

Abstract— The size-frequency distributions of chondrules in 11 CO3 chondrites were determined by petrographic analysis of thin sections. CO chondrites have the smallest chondrules of any major chondrite group. In order of decreasing chondrule size, chondrite groups can be arranged as CV ≥ LL > L > H ≥ CM ≥ EH > CO. Chondrule size varies significantly among different CO chondrites; there is a tendency for chondrules to increase in average size with increasing metamorphic grade of the whole-rock. Different chondrule types in CO chondrites have distinct size-frequency distributions: in order of decreasing chondrule size, BO > PO > PP > POP > RP = C. The large size of BO chondrules is problematic; however, PO chondrules are among the largest because ～20% of them contain very coarse relict olivine grains that constitute 40–90 vol.% of the individual chondrules. PP chondrules may be larger than POP chondrules because some of them contain coarse relict pyroxene grains; a compound object consisting of a POP chondrule attached to a large relict pyroxene grain occurs in Lancé. The mean proportions of chondrule types in CO chondrites are estimated to be 69% POP, 18% PP, 8% PO, 2% BO, 2% RP, 1% C and <0.1% GOP. CO chondrites thus contain a smaller proportion of nonporphyritic chondrules than ordinary or EH chondrites, but a larger proportion than CV chondrites. Relative proportions of chondrule types vary with size interval: PO chondrules decrease fairly regularly in abundance with decreasing chondrule size, and RP chondrules appear to be most abundant in the smallest size intervals.     

SIZE-FREQUENCY-DISTRIBUTIONS OF EH3 CHONDRULES

The size-frequency-distributions of different chondrule types in the Qingzhen, Kota-Kota and Allan Hills A77156 EH3 chondrites were determined by petrographic analysis of thin sections and, in the case of Qingzhen, by examination of large separated chondrules. EH chondrules are considerably smaller than L and LL chondrules and are probably slightly smaller than H, CM and CO chondrules. In the EH3 chondrites, radial pyroxene (RP) chondrules are somewhat (85% confidence level) larger than cryptocrystalline (C) chondrules, nonporphyritic chondrules have a broader size-frequency-distribution than porphyritic chondrules, and porphyritic olivine-pyroxene (POP) chondrules are considerably (98% confidence level) larger than porphyritic pyroxene (PP) chondrules. The larger size of RP chondrules relative to C chondrules in EH3 chondrites may be due to a tendency of the chondrule-forming mechanism not to have heated large precursor aggregates above the liquidus. Consequent retention of numerous relict grains would have caused these objects to develop RP rather than C textures upon cooling. The large proportion (≥50%) of nonporphyritic EH3 chondrules among the smaller chondrule size-fractions may have been caused by preferential disruption of large nonporphyritic chondrule droplets. The large proportion (≥50%) of nonporphyritic EH3 chondrules among the larger chondrule size-fractions is problematic. The larger size of POP relative to PP chondrules is due to reaction of fine-grained olivine with free silica to form pyroxene during mild thermal metamorphism of the whole-rocks.     

Compound chondrule formation in the shock-wave heating model: Three-dimensional hydrodynamics simulation of the disruption of a partially-molten dust particle

We carried out three-dimensional hydrodynamics simulations of the disruption of a partially-molten dust particle exposed to high-speed gas flow to examine the compound chondrule formation due to mutual collisions between the fragments (fragment-collision model; [Miura, H., Yasuda, S., Nakamoto, T., 2008a. Icarus194, 811-821]).In the shock-wave heating model, which is one of the most plausible models for chondrule formation, the gas friction heats and melts the surface of the cm-sized dust particle (parent particle) and then the strong gas ram pressure causes the disruption of the molten surface layer. The hydrodynamics simulation shows details of the disruptive motion of the molten surface, production of many fragments and their trajectories parting from the parent particle, and mutual collisions among them. In our simulation, we identified 32 isolated fragments extracted from the parent particle. The size distribution of the fragments was similar to that obtained from the aerodynamic experiment in which a liquid layer was attached to a solid core and it was exposed to a gas flow. We detected 12 collisions between the fragments, which may result in the compound chondrule formation. We also analyzed the paths of all the fragments in detail and found the importance of the shadow effect in which a fragment extracted later blocks the gas flow toward a fragment extracted earlier. We examined the collision velocity and impact parameter of each collision and found that 11 collisions should result in coalescence. It means that the ratio of coalescent bodies to single bodies formed in this disruption of a parent particle is R_coa=11/(32-11)=0.52. We concluded that compound chondrule formation can occur just after the disruption of a cm-sized molten dust particle in shock-wave heating.     

Chondrule and metal grain size sorting from jet flows

Abstract— We examine the size sorting of chondrules and metal grains within the context of the jet flow model for chondrule/CAI formation. In this model, chondrules, CAIs, AOAs, metal grains, and related components of meteorites are assumed to have formed in the outflow region of the innermost regions of the solar nebula and then were ejected, via the agency of a bipolar jet flow, to outer regions of the nebula. We wish to see if size sorting of chondrules and metal grains is a natural consequence of this model. To assist in this task, we used a multiprocessor system to undertake Monte Carlo simulations of the early solar nebula. The paths of a statistically significant number of chondrules and metal grains were analyzed as they were ejected from the outflow and travelled over or into the solar nebula. For statistical reasons, only distances ≤3 AU from the Sun were examined. Our results suggest that size sorting can occur provided that the solar nebula jet flow had a relatively constant flow rate as function of time. A constant flow rate outflow produces size sorting, but it also produces a sharp size distribution of particles across the nebula and a metal‐rich Fe/Si ratio. When the other extreme of a fully random flow rate was examined, it was found that size sorting was removed, and the initial material injected into the flow was simply spread over most of the the solar nebula. These results indicate that the outflow can act as a size and density classifier. By simply varying the flow rate, the outflow can produce different types of proto‐meteorites from the same chondrule and metal grain feed stock. As a consequence of these investigations, we observed that the number of particles that impact into the nebula drops off moderately rapidly as a function of distance r from the Sun. We also derive a corrected form of the Epstein stopping time.     

Chondrule formation by repeated evaporative melting and condensation in collisional debris clouds around planetesimals

Abstract– A synthesis of previous work leads to a model of chondrule formation that involves periodic melting of dispersed dust in debris clouds that were generated by collisions between chondritic planetesimals. I suggest that chondrules formed by the passage of nebular shock waves through these dust clumps, which temporarily surrounded disrupted planetesimals. Type I chondrules formed by more intense evaporative heating of fewer particles in tenuous clumps, or at the edges of dense clumps, and type II chondrules formed by less intense evaporative heating of more particles deeper within dense clumps. Chondrules reaccreted by self‐gravity into the planetesimals, mixing with less heated dust and rock. This process of disruption, melting, and reaccretion could have repeated many times. In this way, chondrite components of various origins and thermal histories could remain preserved in planetesimals as a distinctive mix of materials for extended periods of time, while still allowing for a repetitive melting process that converted some of the planetesimal debris into chondrules. I also suggest that during chondrule formation, the inner solar nebula gas was evolving by the gradual incorporation and heating of icy bodies depleted in ¹⁶O, causing a general increase in gaseous Δ¹⁷O with time in most places, especially close to the “snow line.” In this model, early formed type I chondrules in C chondrites with lower Δ¹⁷O values were produced inside the snow line, and later formed type I and type II chondrules in C and O chondrites with higher Δ¹⁷O values were created nearer the snow line after it had moved closer to the young Sun.     

Cooling rates of type I chondrules from Renazzo: Implications for chondrule formation

Cooling rates are one of the few fundamental constraints on models of chondrule formation. In this study, we used Cu and Ga diffusion profiles in metal grains to determine the cooling rates of type I chondrules in the Renazzo CR2 chondrite. To improve previous estimations of cooling rates obtained using this method, we used CT scanning and serial polishing of our sections to analyze equatorial sections of large metal grains. Through the cores of these metal grains situated at the surface of chondrules, the cooling rates calculated range from 21 to 86 K h⁻¹ for a peak temperature T_p ~ 1623–1673 K. A metal grain embedded in the core of a chondrule exhibits a cooling rate of 1.2 K h⁻¹ at a T_p ~ 1573 K. We also measured Cu-Ga diffusion profiles from nonequatorial sections of metal grains and calculated a lower range of cooling rates of 15–69 K h⁻¹ for T_p ~ 1473–1603 K compared to our results from equatorial sections. The high cooling rates inferred from the lightning model (several thousand K h⁻¹) are clearly at odds with the values obtained in this work. The X-wind model predicts cooling rates (~6–10 K h⁻¹) lower than most of our results. The cooling rates calculated here are in close agreement with those inferred from shock wave models, in particular for temperatures at which olivine crystallizes (from ~10 to several hundreds K h⁻¹ between 1900 and 1500 K). However, the chemical compositions of metal grains in Renazzo are consistent with the splashing model, in which a spray of metal droplets originated from a partially molten planetesimal. Volatile siderophile element depletion is explained by evaporation before metal was engulfed within silicate droplets. Liquid metal isolated from the liquid silicate crystallized during cooling, reacted with the ambient gas, and then re-accreted within partially molten chondrules.     

The importance of experiments: Constraints on chondrule formation models

Abstract— We review a number of constraints that have been placed on the formation of chondrules and show how these can be used to test chondrule formation models. Four models in particular are examined: the “X‐wind” model (sudden exposure to sunlight <0.1 AU from the proto‐Sun, with subsequent launching in a magnetocentrifugal outflow); solar nebula lightning; nebular shocks driven by eccentric planetesimals; and nebular shocks driven by diskwide gravitational instabilities. We show that constraints on the thermal histories of chondrules during their melting and crystallization are the most powerful constraints and provide the least ambiguous tests of the chondrule formation models. Such constraints strongly favor melting of chondrules in nebular shocks. Shocks driven by gravitational instabilities are somewhat favored over planetesimal bow shocks.     

Size‐frequency distributions of chondrules and chondrule fragments in LL3 chondrites: Implications for parent‐body fragmentation of chondrules

Abstract— We measured the sizes and textural types of 719 intact chondrules and 1322 chondrule fragments in thin sections of Semarkona (LL3.0), Bishunpur (LL3.1), Krymka (LL3.1), Piancaldoli (LL3.4) and Lewis Cliff 88175 (LL3.8). The mean apparent diameter of chondrules in these LL3 chondrites is 0.80 φ units or 570 μm, much smaller than the previous rough estimate of ～900 μm. Chondrule fragments in the five LL3 chondrites have a mean apparent cross‐section of 1.60 φ units or 330 μm. The smallest fragments are isolated olivine and pyroxene grains; these are probably phenocrysts liberated from disrupted porphyritic chondrules. All five LL3 chondrites have fragment/ chondrule number ratios exceeding unity, suggesting that substantial numbers of the chondrules in these rocks were shattered. Most fragmentation probably occurred on the parent asteroid. Porphyritic chondrules (porphyritic olivine + porphyritic pyroxene + porphyritic olivine‐pyroxene) are more readily broken than droplet chondrules (barred olivine + radial pyroxene + cryptocrystalline). The porphyritic fragment/chondrule number ratio (2.0) appreciably exceeds that of droplet‐textured objects (0.9). Intact droplet chondrules have a larger mean size than intact porphyritic chondrules, implying that large porphyritic chondrules are fragmented preferentially. This is consistent with the relatively low percentage of porphyritic chondrules within the set of the largest chondrules (57%) compared to that within the set of the smallest chondrules (81%). Differences in mean size among chondrule textural types may be due mainly to parent‐body chondrule‐fragmentation events and not to chondrule‐formation processes in the solar nebula.     

Barred olivine chondrules in ordinary chondrites: Constraints on chondrule formation

In general, barred olivine (BO) chondrules formed from completely melted precursors. Among BO chondrules in unequilibrated ordinary chondrites, there are significant positive correlations among chondrule diameter, bar thickness, and rim thickness. In the nebula, smaller BO precursor droplets cooled faster than larger droplets (due to their higher surface area/volume ratios) and grew thinner bars and rims. There is a bimodal distribution in the olivine FeO content in BO chondrules, with a hiatus between 11 and 19 wt% FeO. The ratio of (FeO rich)/(FeO poor) BO chondrules decreases from 12.0 in H to 1.6 in L to 1.3 in LL. This is the opposite of the case for porphyritic chondrules: the mean (FeO rich)/(FeO poor) modal ratio increases from 0.8 in H to 1.8 in L to 2.8 in LL. During H chondrite agglomeration, most precursor dustballs were small with low bulk FeO/(FeO + MgO) ratios and moderately high melting temperatures. The energy available for chondrule melting from flash heating was relatively low, capable of completely melting many ferroan dusty precursors (to form FeO-rich BO chondrules), but incapable of completely melting many magnesian dusty precursors (to form FeO-poor BO chondrules). When L and LL chondrites agglomerated somewhat later, significant proportions of precursor dustballs were relatively large and had moderately high bulk FeO/(FeO + MgO) ratios. The energy available from flash heating was higher, capable of completely melting higher proportions of magnesian dusty precursors to form FeO-poor BO chondrules. These differences may have resulted from an increase in the amplitude of lightning discharges in the nebula caused by enhanced charge separation.     

Chondrule collisions in shock waves

Abstract— Detailed numerical models have shown that solar nebula shock waves would be able to thermally process chondrules in a way that is consistent with experimental constraints. However, it has recently been argued that the high relative velocities that would be generated between chondrules of different sizes immediately behind the shock front would lead to energetic collisions that would destroy the chondrules as they were processed rather than preserving them for incorporation into meteorite parent bodies. Here the outcome of these collisions is quantitatively explored using a simple analytic expression for the viscous dissipation of collisional energy in a liquid layer. It is shown that molten chondrules can survive collisions at velocities as high as a few hundred meters per second. It is also shown that the thermal evolution of chondrules in a given shock wave varies with chondrule size, which may allow chondrules of different textures to form in a given shock wave. While experiments are needed to further constrain the parameters used in this work, these calculations show that the expected outcomes from collisions behind shock waves are consistent with what is observed in meteorites.